@Preamble{
"\def \noopsort#1{}"
# "\def \l{\char32l}"
# "\def \v#1{{\accent20 #1}} \let\^^_=\v"
# "\def \hbk{hardback}"
# "\def \pbk{paperback}"
# "\ifx \undefined \mathrm \let \mathrm = \relax \fi"
# "\ifx \undefined \textup \let \textup = \relax \fi"
# "\ifx \undefined \upshape \let \upshape = \relax \fi"
}
@String{j-ACM = "J. Assoc. Comput. Mach."}
@String{j-ACM-SIGSOFT = "ACM Sigsoft"}
@String{j-ACTA-MATH = "Acta Mathematica"}
@String{j-ACTA-NUMERICA = "Acta Numerica"}
@String{j-AHC = "Annals of the History of Computing"}
@String{j-ALGORITHMICA = "Algorithmica"}
@String{j-AM-J-MATH = "American Journal of Mathematics"}
@String{j-AMER-STAT = "The American Statistician"}
@String{j-AMM = "Amer. Math. Monthly"}
@String{j-ANAL-CHEM = "Analytical Chemistry"}
@String{j-ANN-MATH-STAT = "Annals of mathematical statistics"}
@String{j-ANN-NUM-MATH = "Annals of Numerical Mathematics"}
@String{j-ANN-PROBAB = "Annals of Probability"}
@String{j-ANN-STAT = "Ann. Statist."}
@String{j-APP-MATH-COMP = "Appl. Math. Comput."}
@String{j-APP-MATH-LETT = "Applied Mathematics Letters"}
@String{j-APP-NUM-MATH = "Appl. Numer. Math."}
@String{j-APPL-MATH-LETT = "Applied Mathematics Letters"}
@String{j-APPROX = "J. Approximation Theory"}
@String{j-ART-INTELL = "Artificial Intelligence"}
@String{j-ASA = "J. Amer. Statist. Assoc."}
@String{j-ASTRON-J = "Astronomical Journal"}
@String{j-Adv-Comp-Math = "Adv. in Comput. Math."}
@String{j-BAMS = "Bull. Amer. Math. Soc."}
@String{j-BIOGRAPH-MEMOIRS-FELLOWS-ROY-SOC = "Biographical Memoirs of Fellows
of the Royal Society"}
@String{j-BIT = "BIT"}
@String{j-BRITISH-J-CANCER = "British Journal of Cancer"}
@String{j-BULL-AUSTRAL-MATH-SOC = "Bulletin of the Australian Mathematical
Society"}
@String{j-BULL-GEODESIQUE = "Bulletin G\'eod\'esique (Toulouse)"}
@String{j-BULL-LOND-MATH-SOC = "Bulletin of the London Mathematical
Society"}
@String{j-BYTE = "BYTE Magazine"}
@String{j-C-R-ACAD-SCI = "Comptes Rendus de l'Acad{\'e}mie des
Sciences"}
@String{j-CACM = "Comm. ACM"}
@String{j-CAN-MATH-BULL = "Canadian mathematical bulletin = Bulletin
canadien de math{\'e}matiques"}
@String{j-CELEST-MECH-DYN-ASTR = "Celestial Mechanics and Dynamical
Astronomy"}
@String{j-CMJ = "College Mathematics Journal"}
@String{j-COMP-J = "Comput. J."}
@String{j-COMP-LANG-MAG = "Computer Language Magazine"}
@String{j-COMP-MATH-APPL = "Computers Math. Applic."}
@String{j-COMP-PHYS-COMM = "Computer Physics Communications"}
@String{j-COMP-SURV = "ACM Computing Surveys"}
@String{j-COMPUT-GRAPH-STAT = "Journal of Computational and Graphical
Statistics"}
@String{j-COMPUTER = "Computer"}
@String{j-COMPUTING = "Computing"}
@String{j-COMPUTING = "Computing: Archiv f{\"u}r informatik und
numerik"}
@String{j-CSE = "Computing in Science and Engineering"}
@String{j-DDJ = "Dr. Dobb's Journal of Software Tools"}
@String{j-DEMONSTRATIO-MATHEMATICA = "Demonstratio Mathematica"}
@String{j-DISCRETE-COMPUT-GEOM = "Discrete and Computational Geometry"}
@String{j-DUKE-MATH-J = "Duke Mathematical Journal"}
@String{j-EL = "Electronics Letters"}
@String{j-ELA = "The Electronic Journal of Linear Algebra"}
@String{j-ETNA = "Electron. Trans. Numer. Anal."}
@String{j-EUROMATH-BULL = "Euromath Bulletin"}
@String{j-FOCM = "Found. Comput. Math."}
@String{j-HIST-MATH = "Historia Mathematica"}
@String{j-IBM-JRD = "IBM Journal of Research and Development"}
@String{j-IBM-SYS-J = "IBM Systems Journal"}
@String{j-IEEE-AC = "IEEE Trans. Automat. Control"}
@String{j-IEEE-AHC = "IEEE Annals of the History of Computing"}
@String{j-IEEE-ASSP = "IEEE Trans. Acoust., Speech, Signal
Processing"}
@String{j-IEEE-C = "IEEE Trans. Comput."}
@String{j-IEEE-MG = "IEEE Trans. Magnetics"}
@String{j-IEEE-MICRO = "IEEE Micro"}
@String{j-IEEE-PC = "IEEE Trans. Prof. Commun."}
@String{j-IEEE-SE = "IEEE Trans. Software Engrg."}
@String{j-IEEE-SP = "IEEE Trans. Signal Processing"}
@String{j-IEEE-TRANS-AEROSP-ELECTRON-SYST = "IEEE Transactions on Aerospace
and Electronic Systems"}
@String{j-IJC = "Internat. J. Control"}
@String{j-IJNME = "Internat. J. Numer. Methods Eng."}
@String{j-IJSA = "Internat. J. Supercomputer Appl."}
@String{j-IMA-BULL = "IMA Bulletin"}
@String{j-IMAJNA = "IMA J. Numer. Anal."}
@String{j-INFPL = "Inform. Process. Lett."}
@String{j-INT-J-HIGH-SPEED-COMPUTING = "International Journal of High Speed
Computing"}
@String{j-INTEL-TECH-J = "Intel Technology Journal"}
@String{j-J-ECON-LIT = "Journal of economic literature"}
@String{j-J-INF-PROCESS = "Journal of Information Processing"}
@String{j-J-INFO-PROC-CYBERNETICS-EIK = "Journal of Information Processing and
Cybernetics: EIK"}
@String{j-J-MATH-ANAL-APPL = "Journal of Mathematical Analysis and
Applications"}
@String{j-J-RES-NATL-BUR-STAND-B = "Journal of Research of the National Bureau
of Standards. Section B, Mathematics
and Mathematical Physics"}
@String{j-J-SUPERCOMPUTING = "The Journal of Supercomputing"}
@String{j-JAMS = "J. Amer. Math. Soc."}
@String{j-JCAM = "J. Comput. Appl. Math."}
@String{j-JCOMP-PHYS = "J. Comput. Phys."}
@String{j-JIMA = "J. Inst. Maths. Applics."}
@String{j-JMAA = "J. Math. Anal. and Appl."}
@String{j-JNLAA = "Journal of Numerical Linear Algebra with
Applications"}
@String{j-JOTA = "J. Optimization Theory and Applications"}
@String{j-JSV = "Journal of Sound and Vibration"}
@String{j-JUCS = "Journal of Universal Computer Science"}
@String{j-LAA = "Linear Algebra Appl."}
@String{j-LMA = "Linear and Multilinear Algebra"}
@String{j-MATH-COMP = "Math. Comp."}
@String{j-MATH-CONTROL-SIGNALS-SYST = "Mathematics of control, signals, and
systems: MCSS"}
@String{j-MATH-GAZ = "Mathematical Gazette"}
@String{j-MATH-PROG = "Math. Programming"}
@String{j-MATH-PROG-STUDY = "Mathematical Programming Study"}
@String{j-MATH-REV = "Mathematical Reviews"}
@String{j-MATH-SCAND = "Mathematica Scandinavica"}
@String{j-MATH-STOS = "Math. Stos."}
@String{j-MATH-TABLES-OTHER-AIDS-COMPUT = "Mathematical Tables and Other Aids
to Computation"}
@String{j-MATH-TODAY = "Mathematics Today"}
@String{j-MATHEMATICA-J = "Mathematica Journal"}
@String{j-MATHWORKS-NEWSLETTER = "The MathWorks Newsletter"}
@String{j-MTAC = "M.T.A.C."}
@String{j-NA-DIGEST = "NA Digest"}
@String{j-NAMS = "Notices Amer. Math. Soc."}
@String{j-NEW-SCIENTIST = "New Scientist"}
@String{j-NFAO = "Numerical Functional Analysis and
Optimization"}
@String{j-NLAA = "Numerical Linear Algebra with Applications"}
@String{j-NUM-ALG = "Numerical Algorithms"}
@String{j-NUM-LIN-ALG-APPL = "Numerical Linear Algebra with Applications"}
@String{j-NUM-MATH = "Numer. Math."}
@String{j-NY-TIMES = "New York Times"}
@String{j-Nature = "Nature"}
@String{j-PAC-J-MATH = "Pacific Journal of Mathematics"}
@String{j-PAR-COMP = "Parallel Comput."}
@String{j-PHIL-MAGAZINE = "Philosophical Magazine"}
@String{j-PROC-AMER-PHIL-SOC = "Proceedings of the {American Philosophical
Society} held at {Philadelphia} for
promoting useful knowledge"}
@String{j-PROC-AMS = "Proc. Amer. Math. Soc."}
@String{j-PROC-CAMBRIDGE-PHIL-SOC = "Proceedings of the Cambridge
Philosophical Society. Mathematical and
physical sciences"}
@String{j-PROC-CONTROL-AUTOMATION = "Process Control and Automation"}
@String{j-PROC-IEEE = "Proceedings of the IEEE"}
@String{j-PROC-LONDON-MATH-SOC-3 = "Proceedings of the London Mathematical
Society. Third Series"}
@String{j-PROC-R-SOC-EDINB = "Proceedings of the Royal Society of
Edinburgh"}
@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI = "Proceedings of the Royal
Society of London. Series A, Mathematical
and physical sciences"}
@String{j-PSYCHO = "Psychometrika"}
@String{j-QJMAM = "Quart. J. Mech. Appl. Math."}
@String{j-QUART-J-MATH = "Quarterly Journal of Mathematics"}
@String{j-REE = "The Radio and Electronic Engineer"}
@String{j-SCI-AMER = "Scientific American"}
@String{j-SCI-PROG = "Scientific Programming"}
@String{j-SCIENCE = "Science"}
@String{j-SCL = "Systems and Control Letters"}
@String{j-SIAD = "SIAM J. Alg. Discrete Methods"}
@String{j-SIAM = "J. Soc. Indust. Appl. Math."}
@String{j-SIAM-J-DISCR-MATH = "SIAM Journal on Discrete Mathematics"}
@String{j-SIAM-NEWS = "SIAM News"}
@String{j-SIAMA = "SIAM J. Appl. Math."}
@String{j-SICOMP = "SIAM J. Comput."}
@String{j-SICOPT = "SIAM J. Control Optim."}
@String{j-SIDM = "SIAM J. Disc. Math."}
@String{j-SIGNUM = "ACM SIGNUM Newsletter"}
@String{j-SIGPLAN = "ACM SIG{\-}PLAN Notices"}
@String{j-SIMA = "SIAM J. Math. Anal."}
@String{j-SIMAX = "SIAM J. Matrix Anal. Appl."}
@String{j-SINUM = "SIAM J. Numer. Anal."}
@String{j-SIOPT = "SIAM J. Optim."}
@String{j-SIREV = "SIAM Rev."}
@String{j-SISC = "SIAM J. Sci. Comput."}
@String{j-SISSC = "SIAM J. Sci. Statist. Comput."}
@String{j-SOVIET-PHYS-DOKL = "Soviet Physics---Doklady"}
@String{j-SPE = "Soft{\-}ware\emdash Prac{\-}tice and
Experience"}
@String{j-STUDIES-APPL-MATH = "Studies in Applied Mathematics"}
@String{j-TOMS = "ACM Trans. Math. Software"}
@String{j-TOPLAS = "ACM Transactions on Programming Languages
and Systems"}
@String{j-TPLS = "ACM Trans. Program. Lang. Syst."}
@String{j-TRANS-AMER-INST-ELEC-ENG = "Transactions of the American Institute
of Electrical Engineers"}
@String{j-USSR-COMP-MATH-MATH-PHYS = "U.S.S.R. Computational Mathematics and
Mathematical Physics"}
@String{j-WALL-ST-J = "Wall Street Journal"}
@String{j-ZAMM = "Z. Angew. Math. Mech."}
@String{j-ZAMP = "Z. Angew. Math. Phys."}
@String{t-NAREP = "Numerical Analysis Report"}
@String{inst-ATT = "AT\&T Bell Laboratories"}
@String{inst-ATT:adr = "Murray Hill, NJ, USA"}
@String{inst-Bell = "Bell Laboratories"}
@String{inst-Belladr = "Murray Hill, NJ, USA"}
@String{inst-Berkeley = "University of California"}
@String{inst-Berkeley-CS = "Department of Computer Science, University
of California"}
@String{inst-Berkeley-Math = "Department of Mathematics, University of
California"}
@String{inst-Berkeley:adr = "Berkeley, CA, USA"}
@String{inst-CERFACS = "CERFACS"}
@String{inst-CERFACS:adr = "Toulouse, France"}
@String{inst-CS-Lucent = "Computing Sciences Research Center, Bell
Laboratories"}
@String{inst-CS-Lucent:adr = "Murray Hill, NJ"}
@String{inst-CS-U-KY = "Department of Mathematics, University of
Kentucky"}
@String{inst-CS-U-KY:adr = "Lexington, KY, USA"}
@String{inst-CS-U-MARYLAND = "Department of Computer Science, University
of Maryland"}
@String{inst-CS-U-MARYLAND:adr = "College Park, MD, USA"}
@String{inst-CS-U-STANFORD = "Department of Computer Science, Stanford
University"}
@String{inst-CS-U-Tenn = "Department of Computer Science, University
of Tennessee"}
@String{inst-CS-U-Tenn:adr = "Knoxville, TN, USA"}
@String{inst-CS-U-Umea = "Institute of Information Processing,
University of Ume{\aa}"}
@String{inst-CS-U-Umea:adr = "Ume{\aa}, Sweden"}
@String{inst-Cornell = "Cornell University"}
@String{inst-Cornell:adr = "Ithaca, NY, USA"}
@String{inst-DAMTP = "Department of Applied Mathematics and
Theoretical Physics, University of
Cambridge"}
@String{inst-DAMTP:adr = "Cambridge, UK"}
@String{inst-ENSEEIHT = "Dept. Informatique et Maths Appls.,
ENSEEIHT-IRIT"}
@String{inst-ENSEEIHT:adr = "31071 Toulouse Cedex, France"}
@String{inst-HARWELL = "{AERE} {Harwell} Laboratory"}
@String{inst-HARWELL:adr = "Chilton, Oxon, England"}
@String{inst-IAN = "Istituto di Analisi Numerica del CNR"}
@String{inst-IAN:adr = "Pavia, Italy"}
@String{inst-IMA = "Institute for Mathematics and Its
Applications, University of Minnesota"}
@String{inst-IMA-UK = "The Institute of Mathematics and Its
Applications"}
@String{inst-IMA-UK:adr = "Southend-On-Sea, Essex, UK"}
@String{inst-IMA:adr = "Minneapolis, MN, USA"}
@String{inst-M-Utrecht = "Department of Mathematics, Utrecht
University"}
@String{inst-M-Utrecht:adr = "Utrecht, Netherlands"}
@String{inst-MCCM = "Manchester Centre for Computational
Mathematics"}
@String{inst-MCCM:adr = "Manchester, England"}
@String{inst-MCS-Argonne = "Mathematics and Computer Science Division,
Argonne National Laboratory"}
@String{inst-MCS-Argonne:adr = "Argonne, IL, USA"}
@String{inst-Math-U-Strath = "Department of Mathematics, University of
Strathclyde"}
@String{inst-Math-U-Strath:adr = "Glasgow, Scotland"}
@String{inst-Math-UCLA = "Department of Mathematics, University of
California"}
@String{inst-Math-UCLA:adr = "Los Angeles, USA"}
@String{inst-Math-UCSD = "Department of Mathematics, University of
California"}
@String{inst-Math-UCSD:adr = "San Diego, USA"}
@String{inst-NAG = "NAG Ltd."}
@String{inst-NAG:adr = "Oxford, UK"}
@String{inst-NASA-Ames = "NASA Ames Research Center"}
@String{inst-NASA-Ames:adr = "Moffett Field, CA, USA"}
@String{inst-NPL = "National Physical Laboratory"}
@String{inst-NPL:adr = "Teddington, UK"}
@String{inst-OR-U-STANFORD = "Department of Operations Research, Stanford
University"}
@String{inst-ORNL = "Oak Ridge National Laboratory"}
@String{inst-ORNL:adr = "Oak Ridge, TN, USA"}
@String{inst-OUCL = "Numerical Analysis Group, Oxford University
Computing Laboratory"}
@String{inst-OUCL:adr = "Oxford, UK"}
@String{inst-RAL = "Atlas Centre, Rutherford Appleton
Laboratory"}
@String{inst-RAL:adr = "Didcot, Oxon, UK"}
@String{inst-RICE-CAM = "Department of Computational and Applied
Mathematics"}
@String{inst-RICE-CAM:adr = "Rice University, Houston, TX, USA"}
@String{inst-TU-Chemnitz = "Fak. f. Mathematik, Technische
Universit{\"a}t Chemnitz-Zwickau"}
@String{inst-TU-Chemnitz:adr = "Chemnitz, FRG"}
@String{inst-U-Bremen-ZT = "Zentrum f{\"u}r Technomathematik,
Universit{\"a}t Bremen"}
@String{inst-U-Bremen-ZT:adr = "Bremen, Germany"}
@String{inst-U-Dundee = "Department of Mathematics and Computer
Science, University of Dundee"}
@String{inst-U-Dundee:adr = "Dundee, Scotland"}
@String{inst-U-Manchester = "University of Manchester"}
@String{inst-U-Manchester:adr = "Manchester, England"}
@String{inst-U-STANFORD:adr = "Stanford, CA, USA"}
@String{pub-ACADEMIC = "Academic Press"}
@String{pub-ACADEMIC:adr = "New York, NY, USA"}
@String{pub-ACM = "ACM Press"}
@String{pub-ACM:adr = "New York"}
@String{pub-ADAM-HILGER = "Adam Hilger Ltd."}
@String{pub-ADAM-HILGER:adr = "Bristol, UK"}
@String{pub-AMS = "American Mathematical Society"}
@String{pub-AMS:adr = "Providence, RI, USA"}
@String{pub-AP = "Academic Press"}
@String{pub-AP:adr-B = "Boston, MA, USA"}
@String{pub-AP:adr-L = "London"}
@String{pub-AP:adr-NY = "New York"}
@String{pub-AP:adr-S = "San Diego, CA, USA"}
@String{pub-AW = "Ad{\-d}i{\-s}on-Wes{\-l}ey"}
@String{pub-AW:adr = "Reading, MA, USA"}
@String{pub-AWLongman = "Addison Wesley Longman"}
@String{pub-AWLongman:adr = "Harlow, Essex, UK"}
@String{pub-BH = "Birkh{\"{a}}user"}
@String{pub-BH:adr = "Boston, MA, USA"}
@String{pub-BH:adr-Basel = "Basel, Switzerland"}
@String{pub-Blaisdell = "Blaisdell"}
@String{pub-Blaisdell:adr-MA = "Waltham, MA, USA"}
@String{pub-Blaisdell:adr-NY = "New York"}
@String{pub-BrooksCole = "Brooks/Cole"}
@String{pub-BrooksCole:adr = "Pacific Grove, CA, USA"}
@String{pub-CH = "Chapman and Hall"}
@String{pub-CH:adr-L = "London"}
@String{pub-CH:adr-NY = "New York"}
@String{pub-CHCRC = "Chapman and Hall/CRC"}
@String{pub-CLARENDON = "Clarendon Press"}
@String{pub-CLARENDON:adr = "Oxford, UK"}
@String{pub-CRC = "CRC Press"}
@String{pub-CRC:adr = "Boca Raton, FL, USA"}
@String{pub-CUP = "Cambridge University Press"}
@String{pub-CUP:adr = "Cambridge, UK"}
@String{pub-DCH = "D. C. Heath"}
@String{pub-DCH:adr = "Lexington, MA, USA"}
@String{pub-DEKKER = "Marcel Dekker, Inc."}
@String{pub-DEKKER:adr = "New York, NY, USA"}
@String{pub-Dover = "Dover"}
@String{pub-Dover:adr = "New York"}
@String{pub-EH = "Ellis Horwood"}
@String{pub-EH:adr = "New York"}
@String{pub-ELS = "Elsevier"}
@String{pub-ELS:adr = "Amsterdam, The Netherlands"}
@String{pub-ELSNH = "Elsevier/North-Hol{\-}land"}
@String{pub-ELSNH:adr = "Amsterdam, The Netherlands"}
@String{pub-Freeman = "W. H. Freeman"}
@String{pub-Freeman:adr = "New York"}
@String{pub-Gruyter = "Walter de Gruyter"}
@String{pub-Gruyter:adr = "Berlin"}
@String{pub-HMSO = "Her Majesty's Stationary Office"}
@String{pub-HMSO:adr = "London"}
@String{pub-HRW = "Holt, Rinehart and Winston"}
@String{pub-HRW:adr = "New York"}
@String{pub-Harvard = "Harvard University Press"}
@String{pub-Harvard:adr = "Cambridge, MA, USA"}
@String{pub-IEC = "International Electrotechnical Commission"}
@String{pub-IEC:adr = "Geneva, Switzerland"}
@String{pub-JH = "Johns Hopkins University Press"}
@String{pub-JH:adr = "Baltimore, MD, USA"}
@String{pub-JOHNS-HOPKINS = "The Johns Hopkins University Press"}
@String{pub-JOHNS-HOPKINS:adr = "Baltimore, MD, USA"}
@String{pub-Kluwer = "Kluwer Academic Publishers"}
@String{pub-Kluwer:adr = "Dordrecht, The Netherlands"}
@String{pub-Kluwer:adr-NY = "New York"}
@String{pub-Longman-ST = "Longman Scientific and Technical"}
@String{pub-Longman-ST:adr = "Essex, UK"}
@String{pub-MAA = "Mathematical Association of America"}
@String{pub-MAA:adr = "Washington, D.C."}
@String{pub-MD = "Marcel Dekker"}
@String{pub-MD:adr = "New York"}
@String{pub-MH = "Mc{\-}Graw-Hill"}
@String{pub-MH:adr = "New York"}
@String{pub-MIT = "MIT Press"}
@String{pub-MIT:adr = "Cambridge, MA, USA"}
@String{pub-NH = "North-Hol{\-}land"}
@String{pub-NH:adr = "Amsterdam, The Netherlands"}
@String{pub-OUP = "Oxford University Press"}
@String{pub-OUP:adr-NY = "New York"}
@String{pub-PH = "Pren{\-}tice-Hall"}
@String{pub-PUP = "Princeton University Press"}
@String{pub-PUP:adr = "Princeton, NJ, USA"}
@String{pub-Penguin = "Penguin"}
@String{pub-Penguin:adr-H = "Harmondsworth, UK"}
@String{pub-Penguin:adr-L = "London"}
@String{pub-Penguin:adr-NY = "New York"}
@String{pub-Peters = "A K Peters"}
@String{pub-Peters:adr = "Wellesley, Massachusetts"}
@String{pub-Plenum = "Plenum Press"}
@String{pub-Plenum:adr = "New York"}
@String{pub-PH2:adr = "Upper Saddle River, NJ, USA"}
@String{pub-PH:adr = "Englewood Cliffs, NJ, USA"}
@String{pub-PHI = "Pren{\-}tice-Hall International"}
@String{pub-PHI:adr = "Englewood Cliffs, NJ, USA"}
@String{pub-SIAM = "Society for Industrial and Applied
Mathematics"}
@String{pub-SIAM:adr = "Philadelphia, PA, USA"}
@String{pub-Springer = "Spring{\-}er-Ver{\-}lag"}
@String{pub-Springer:adr-B = "Berlin"}
@String{pub-Springer:adr-NY = "New York"}
@String{pub-SV = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr = "Berlin, Germany~/ Heidelberg,
Germany~/ London, UK~/ etc."}
@String{pub-WS = "World Scientific"}
@String{pub-WS:adr = "Singapore"}
@String{pub-Wellesley = "Wellesley-Cambridge Press"}
@String{pub-Wellesley:adr = "Wellesley, MA, USA"}
@String{pub-Wiley = "Wiley"}
@String{pub-Wiley:adr = "New York"}
@String{pub-Wiley:adr-C = "Chichester, UK"}
@String{pub-reidel = "D. Reidel"}
@String{pub-reidel:adr = "Dordrecht, Holland"}
@Article{Aasen:1971:RSM,
author = "Jan Ole Aasen",
title = "On the Reduction of a Symmetric Matrix to Tridiagonal
Form",
journal = j-BIT,
volume = "11",
pages = "233--242",
year = "1971",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Alpert:1993:WLB,
author = "B. Alpert and G. Beylkin and R. Coifman and V.
Rokhlin",
title = "Wavelet-Like Bases for the Fast Solution of
Second-Kind Integral Equations",
journal = j-SISC,
volume = "14",
number = "1",
pages = "159--184",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Anderson:1992:GQF,
author = "E. Anderson and Z. Bai and J. Dongarra",
title = "Generalized {QR} Factorization and Its Applications",
journal = j-LAA,
volume = "162--164",
pages = "243--271",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Abdelmalek:1971:REA,
author = "Nabih N. Abdelmalek",
title = "Round Off Error Analysis for {Gram--Schmidt} Method
and Solution of Linear Least Squares Problems",
journal = j-BIT,
volume = "11",
pages = "345--368",
year = "1971",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Ahac:1988:SFM,
author = "Alan A. Ahac and John J. Buoni and D. D. Olesky",
title = "Stable {$LU$} Factorization of {$H$}-Matrices",
journal = j-LAA,
volume = "99",
pages = "97--110",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{acm87,
key = "ACM Press",
title = "{ACM Turing} Award Lectures: {The} First Twenty Years,
1966--1985",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xviii + 483",
year = "1987",
ISBN = "0-201-54885-2",
ISBN-13 = "978-0-201-54885-3",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Acton:1970:NMW,
author = "Forman S. Acton",
title = "Numerical Methods That Work",
publisher = "Harper and Row",
address = "New York",
pages = "xviii + 541",
year = "1970",
ISBN = "0-88385-450-3",
ISBN-13 = "978-0-88385-450-1",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted by Mathematical Association of America,
Washington, D.C., with new preface and additional
problems, 1990",
}
@Book{Acton:1996:RCM,
author = "Forman S. Acton",
title = "Real Computing Made Real: {Preventing} Errors in
Scientific and Engineering Calculations",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "xv + 259",
year = "1996",
ISBN = "0-691-03663-2",
ISBN-13 = "978-0-691-03663-2",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Adams:1967:SCP,
author = "Duane A. Adams",
title = "A Stopping Criterion for Polynomial Root Finding",
journal = j-CACM,
volume = "10",
number = "10",
pages = "655--658",
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Arioli:1989:SSL,
author = "M. Arioli and J. W. Demmel and I. S. Duff",
title = "Solving Sparse Linear Systems with Sparse Backward
Error",
journal = j-SIMAX,
volume = "10",
number = "2",
pages = "165--190",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Arioli:1989:ASA,
author = "M. Arioli and I. S. Duff and P. P. M. de Rijk",
title = "On the Augmented System Approach to Sparse
Least-Squares Problems",
journal = j-NUM-MATH,
volume = "55",
pages = "667--684",
year = "1989",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Arioli:1992:SCI,
author = "Mario Arioli and Iain S. Duff and Daniel Ruiz",
title = "Stopping Criteria for Iterative Solvers",
journal = j-SIMAX,
volume = "13",
number = "1",
pages = "138--144",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Almacany:1984:DCA,
author = "M. Almacany and C. B. Dunham and J. Williams",
title = "Discrete {Chebyshev} Approximation by Interpolating
Rationals",
journal = j-IMAJNA,
volume = "4",
pages = "467--477",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Aggarwal:1979:REM,
author = "Vijay B. Aggarwal and James W. Burgmeier",
title = "A Round-Off Error Model With Applications to
Arithmetic Expressions",
journal = j-SICOMP,
volume = "8",
number = "1",
pages = "60--72",
year = "1979",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Ashcraft:1998:ASI,
author = "Cleve Ashcraft and Roger G. Grimes and John G. Lewis",
title = "Accurate Symmetric Indefinite Linear Equation
Solvers",
journal = j-SIMAX,
volume = "20",
number = "2",
pages = "513--561",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Alonso:1997:BEA,
author = "P. Alonso and M. Gasca and J. M. Pe{\~n}a",
title = "Backward Error Analysis of {Neville} Elimination",
journal = j-APP-NUM-MATH,
volume = "23",
pages = "193--204",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Ahlberg:1963:CPS,
author = "J. H. Ahlberg and E. N. Nilson",
title = "Convergence Properties of the Spline Fit",
journal = j-SIAM,
volume = "11",
number = "1",
pages = "95--104",
year = "1963",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InCollection{Ewing:1991:PHP,
editor = "John H. Ewing and F. W. Gehring",
key = "Albers, Donald J.",
booktitle = "{Paul Halmos}: {Celebrating} 50 Years of Mathematics",
title = "{Paul Halmos} By Parts (Interviews by {Donald J.
Albers})",
publisher = pub-Springer,
address = pub-Springer:adr-B,
pages = "3--32",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Alefeld:1983:IIC,
author = "G{\"o}ltz Alefeld and J{\"u}rgen Herzberger",
title = "Introduction to Interval Computations",
publisher = pub-AP,
address = pub-AP:adr-NY,
pages = "xviii + 333",
year = "1983",
ISBN = "0-12-049820-0",
ISBN-13 = "978-0-12-049820-8",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Althoen:1987:GJR,
author = "Steven C. Althoen and Renate Mclaughlin",
title = "{Gauss--Jordan} Reduction: {A} Brief History",
journal = j-AMM,
volume = "94",
number = "2",
pages = "130--142",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Alt:1981:CBC,
author = "H. Alt and J. van Leeuwen",
title = "The Complexity of Basic Complex Operations",
journal = j-COMPUTING,
volume = "27",
pages = "205--215",
year = "1981",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Amodio:1994:BEA,
author = "Pierluigi Amodio and Francesca Mazzia",
title = "Backward Error Analysis of Cyclic Reduction for the
Solution of Tridiagonal Systems",
journal = j-MATH-COMP,
volume = "62",
number = "206",
pages = "601--617",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Anderson:1971:SAT,
author = "T. W. Anderson",
title = "The Statistical Analysis of Time Series",
publisher = pub-Wiley,
address = pub-Wiley:adr,
pages = "xiv + 704",
year = "1971",
ISBN = "0-471-02900-9",
ISBN-13 = "978-0-471-02900-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Anderson:1991:RTS,
author = "Edward Anderson",
title = "Robust Triangular Solves for Use in Condition
Estimation",
type = "Technical Report",
number = "CS-91-142",
institution = inst-CS-U-Tenn,
address = inst-CS-U-Tenn:adr,
pages = "35",
month = aug,
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "LAPACK Working Note 36",
}
@Article{Anderson:1999:DAF,
author = "I. J. Anderson",
title = "A Distillation Algorithm for Floating-Point
Summation",
journal = j-SISC,
volume = "20",
number = "5",
pages = "1797--1806",
year = "1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Ando:1987:TPM,
author = "T. Ando",
title = "Totally Positive Matrices",
journal = j-LAA,
volume = "90",
pages = "165--219",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Andrew:1990:ESV,
author = "Alan L. Andrew",
title = "Eigenvalues and Singular Values of Certain Random
Matrices",
journal = j-JCAM,
volume = "30",
pages = "165--171",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Anonymous:1922:CC,
author = "Anonymous",
title = "Le {Commandant Cholesky}",
journal = j-BULL-GEODESIQUE,
pages = "159--161",
year = "1922",
CODEN = "BGDQAG",
ISSN = "0007-4632",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Translation by Richard W. Cottle (``Major
{Cholesky}'') appears in
\cite[Appendix]{Maindonald:1984:SC} and in NA Digest,
Volume 90, Issue 7, 1990",
fjournal = "Bulletin G\'eod\'esique (Toulouse)",
journal-URL = "http://link.springer.com/journal/190",
}
@Article{Anda:1994:FPR,
author = "Andrew A. Anda and Haesun Park",
title = "Fast Plane Rotations with Dynamic Scaling",
journal = j-SIMAX,
volume = "15",
number = "1",
pages = "162--174",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Anderson:1987:GRO,
author = "T. W. Anderson and I. Olkin and L. G. Underhill",
title = "Generation of Random Orthogonal Matrices",
journal = j-SISSC,
volume = "8",
number = "4",
pages = "625--629",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Computer:1988:ANM,
author = "Apple Computer",
title = "Apple Numerics Manual",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Computer:1994:IMP,
author = "Apple Computer",
title = "Inside {Macintosh}: {PowerPC} Numerics",
publisher = pub-AW,
address = pub-AW:adr,
year = "1994",
ISBN = "0-201-40728-0",
ISBN-13 = "978-0-201-40728-0",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InCollection{Alvarado:1993:HPS,
author = "Fernando L. Alvarado and Alex Pothen and Robert S.
Schreiber",
editor = "J. Alan George and John R. Gilbert and Joseph W. H.
Liu",
booktitle = "Graph Theory and Sparse Matrix Computations",
title = "Highly Parallel Sparse Triangular Solution",
volume = "56",
publisher = pub-Springer # ", " # pub-Springer:adr-NY,
pages = "141--158",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "IMA Volumes in Mathematics and Its Applications",
}
@TechReport{Arioli:2000:SCC,
author = "Mario Arioli",
title = "A Stopping Criterion for the Conjugate Gradient
Algorithm in a Finite Element Method Framework",
type = "Technical Report",
number = "1179",
institution = "Istituto di Analisi Numerica - C.N.R.",
address = "Pavia, Italy",
pages = "12",
year = "2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Arnold:1984:GEA,
author = "William F. Arnold and Alan J. Laub",
title = "Generalized Eigenproblem Algorithms and Software for
Algebraic {Riccati} Equations",
journal = j-PROC-IEEE,
volume = "72",
number = "12",
pages = "1746--1754",
year = "1984",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}
@Article{Arioli:1985:EAA,
author = "M. Arioli and A. Laratta",
title = "Error Analysis of an Algorithm for Solving an
Underdetermined Linear System",
journal = j-NUM-MATH,
volume = "46",
pages = "255--268",
year = "1985",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Arioli:1986:EAA,
author = "M. Arioli and A. Laratta",
title = "Error Analysis of Algorithms for Computing the
Projection of a Point onto a Linear Manifold",
journal = j-LAA,
volume = "82",
pages = "1--26",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Arioli:1992:SCC,
author = "Mario Arioli and Francesco Romani",
title = "Stability, Convergence, and Conditioning of Stationary
Iterative Methods of the Form {$x^{(i+1)} = P x^{(i)} +
q$} for the Solution of Linear Systems",
journal = j-IMAJNA,
volume = "12",
pages = "21--30",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Ashenhurst:1965:EEC,
author = "R. L. Ashenhurst and N. Metropolis",
title = "Error Estimation in Computer Calculation",
journal = j-AMM,
volume = "72",
number = "2",
pages = "47--58",
year = "1965",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
part = "II",
}
@Article{Asplund:1959:IMW,
author = "Edgar Asplund",
title = "Inverses of Matrices {$\{a_{ij}\}$} Which Satisfy
{$a_{ij}=0$} For {$j>i+p$}",
journal = j-MATH-SCAND,
volume = "7",
pages = "57--60",
year = "1959",
CODEN = "MTSCAN",
ISSN = "0025-5521 (print), 1903-1807 (electronic)",
ISSN-L = "0025-5521",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Mathematica Scandinavica",
}
@Misc{Atanasoff:1940:CMS,
author = "John V. Atanasoff",
title = "Computing Machine for the Solution of Large Systems of
Linear Algebraic Equations",
howpublished = "Unpublished manuscript, Iowa State College, Ames, IA,
USA",
month = aug,
year = "1940",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted in \cite[pp.~315--335]{Randell:1975:ODC}",
}
@Book{Axelsson:1994:ISM,
author = "Owe Axelsson",
title = "Iterative Solution Methods",
publisher = pub-CUP,
pages = "xiii + 654",
year = "1994",
ISBN = "0-521-44524-8",
ISBN-13 = "978-0-521-44524-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Barlow:1985:RED,
author = "Jesse L. Barlow and E. H. Bareiss",
title = "On Roundoff Error Distributions in Floating Point and
Logarithmic Arithmetic",
journal = j-COMPUTING,
volume = "34",
pages = "325--347",
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Barlow:1985:PEA,
author = "Jesse L. Barlow and E. H. Bareiss",
title = "Probabilistic Error Analysis of {Gaussian} Elimination
in Floating Point and Logarithmic Arithmetic",
journal = j-COMPUTING,
volume = "34",
pages = "349--364",
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@InProceedings{Babuska:1969:NSM,
author = "Ivo Babu{\v{s}}ka",
booktitle = "Proc. IFIP Congress",
title = "Numerical Stability in Mathematical Analysis",
publisher = pub-NH # ", " # pub-NH:adr,
pages = "11--23",
year = "1969",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Information Processing 68",
}
@Article{Bai:1993:SDB,
author = "Zhaojun Bai and James W. Demmel",
title = "On Swapping Diagonal Blocks in Real {Schur} Form",
journal = j-LAA,
volume = "186",
pages = "73--95",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bai:1993:CGS,
author = "Zhaojun Bai and James W. Demmel",
title = "Computing the Generalized Singular Value
Decomposition",
journal = j-SISC,
volume = "14",
number = "6",
pages = "1464--1486",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Bailey:1988:SNA,
author = "D. H. Bailey and H. R. P. Ferguson",
booktitle = "Proceedings of Supercomputing '88",
title = "A {Strassen--Newton} Algorithm for High-Speed
Parallelizable Matrix Inversion",
publisher = "IEEE Computer Society Press, New York",
pages = "419--424",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Barwell:1976:CAS,
author = "Victor Barwell and Alan George",
title = "A Comparison of Algorithms for Solving Symmetric
Indefinite Systems of Linear Equations",
journal = j-TOMS,
volume = "2",
number = "3",
pages = "242--251",
year = "1976",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Bartels:1992:SSV,
author = "Sven G. Bartels and Desmond J. Higham",
title = "The Structured Sensitivity of {Vandermonde}-like
Systems",
journal = j-NUM-MATH,
volume = "62",
pages = "17--33",
year = "1992",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Bailey:1988:EHS,
author = "David H. Bailey",
title = "Extra High Speed Matrix Multiplication on the
{Cray}-2",
journal = j-SISSC,
volume = "9",
number = "3",
pages = "603--607",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bailey:1988:CDD,
author = "David H. Bailey",
title = "The Computation of {$\pi$} to 29,360,000 Decimal
Digits Using {Borweins'} Quartically Convergent
Algorithm",
journal = j-MATH-COMP,
volume = "50",
number = "181",
pages = "283--296",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bailey:1993:AMT,
author = "David H. Bailey",
title = "Algorithm 719: {Multiprecision} Translation and
Execution of {FORTRAN} Programs",
journal = j-TOMS,
volume = "19",
number = "3",
pages = "288--319",
year = "1993",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Bailey:1995:FBM,
author = "David H. Bailey",
title = "A {Fortran} 90-Based Multiprecision System",
journal = j-TOMS,
volume = "21",
number = "4",
pages = "379--387",
year = "1995",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Barlow:1987:SGR,
author = "Jesse L. Barlow and Ilse C. F. Ipsen",
title = "Scaled {Givens} Rotations for the Solution of Linear
Least Squares Problems on Systolic Arrays",
journal = j-SISSC,
volume = "8",
number = "5",
pages = "716--733",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Baksalary:1979:ME,
author = "J. K. Baksalary and R. Kala",
title = "The Matrix Equation {$AX-YB=C$}",
journal = j-LAA,
volume = "25",
pages = "41--43",
year = "1979",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Baksalary:1980:ME,
author = "J. K. Baksalary and R. Kala",
title = "The Matrix Equation {$AXB + CYD = E$}",
journal = j-LAA,
volume = "30",
pages = "141--147",
year = "1980",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Ballester:1967:CDA,
author = "C. Ballester and V. Pereyra",
title = "On the Construction of Discrete Approximations to
Linear Differential Expressions",
journal = j-MATH-COMP,
volume = "21",
pages = "297--302",
year = "1967",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Bard:1974:NPE,
author = "Yonathan Bard",
title = "Nonlinear Parameter Estimation",
publisher = pub-AP,
address = pub-AP:adr-NY,
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InCollection{Bauer:1971:IPD,
author = "F. L. Bauer and C. Reinsch",
editor = "J. H. Wilkinson and C. Reinsch",
booktitle = "Linear Algebra",
title = "Inversion of Positive Definite Matrices by the
{Gauss--Jordan} Method",
volume = "II",
publisher = pub-Springer,
address = pub-Springer:adr-B,
pages = "45--49",
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Contribution I/3",
series = "Handbook for Automatic Computation",
mycrossref = "Wilkinson:1971:LA",
}
@PhdThesis{Barlow:1981:PEA,
author = "Jesse L. Barlow",
title = "Probabilistic Error Analysis of Floating Point and
{CRD} Arithmetics",
school = "Northwestern University",
address = "Evanston, IL, USA",
month = jun,
year = "1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Barlow:1981:DAR,
author = "Jesse L. Barlow",
booktitle = "Proc. 5th IEEE Symposium on Computer Arithmetic, Ann
Arbor, Michigan",
title = "On the Distribution of Accumulated Roundoff Error in
Floating Point Arithmetic",
pages = "100--105",
year = "1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{barl86,
author = "Jesse L. Barlow",
title = "A Note on Monitoring the Stability of Triangular
Decomposition of Sparse Matrices",
journal = j-SISSC,
volume = "7",
number = "1",
pages = "166--168",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Barlow:1988:EAI,
author = "Jesse L. Barlow",
title = "Error Analysis and Implementation Aspects of Deferred
Correction for Equality Constrained Least Squares
Problems",
journal = j-SINUM,
volume = "25",
number = "6",
pages = "1340--1358",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Barlow:1991:EAP,
author = "Jesse L. Barlow",
title = "Error Analysis of a Pairwise Summation Algorithm to
Compute the Sample Variance",
journal = j-NUM-MATH,
volume = "58",
pages = "583--590",
year = "1991",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Bank:1977:MAE,
author = "Randolph E. Bank and Donald J. Rose",
title = "Marching Algorithms for Elliptic Boundary Value
Problems. {I}: The Constant Coefficient Case",
journal = j-SINUM,
volume = "14",
number = "5",
pages = "792--829",
year = "1977",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Barrett:1989:FMA,
author = "Geoff Barrett",
title = "Formal Methods Applied to a Floating-Point Number
System",
journal = j-IEEE-SE,
volume = "15",
number = "5",
pages = "611--621",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Barrlund:1991:PBD,
author = "Anders Barrlund",
title = "Perturbation Bounds for the {$LDL^H$} and {$LU$}
Decompositions",
journal = j-BIT,
volume = "31",
pages = "358--363",
year = "1991",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Barrlund:1994:PBG,
author = "Anders Barrlund",
title = "Perturbation Bounds for the Generalized {$QR$}
Factorization",
journal = j-LAA,
volume = "207",
pages = "251--271",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@MastersThesis{Bartels:1991:TTM,
author = "Sven G. Bartels",
title = "Two Topics in Matrix Analysis: {Structured}
Sensitivity for {Vandermonde}-Like Systems and a
Subgradient Method for Matrix Norm Estimation",
type = "{M.Sc.} {Thesis}",
school = inst-U-Dundee,
address = inst-U-Dundee:adr,
month = sep,
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Barnett:1968:SAL,
author = "S. Barnett and C. Storey",
title = "Some Applications of the {Lyapunov} Matrix Equation",
journal = j-JIMA,
volume = "4",
pages = "33--42",
year = "1968",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bartels:1972:ASM,
author = "R. H. Bartels and G. W. Stewart",
title = "Algorithm 432: {Solution} of the Matrix Equation
{$AX+XB=C$}",
journal = j-CACM,
volume = "15",
number = "9",
pages = "820--826",
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Barron:1960:SSL,
author = "D. W. Barron and H. P. F. Swinnerton--Dyer",
title = "Solution of Simultaneous Linear Equations Using a
Magnetic-Tape Store",
journal = j-COMP-J,
volume = "3",
number = "1",
pages = "28--33",
year = "1960",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Bauer:1963:OSMa,
author = "F. L. Bauer",
title = "Optimally Scaled Matrices",
journal = j-NUM-MATH,
volume = "5",
pages = "73--87",
year = "1963",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@InProceedings{Bauer:1963:OSMb,
author = "F. L. Bauer",
editor = "Cicely M. Popplewell",
booktitle = "Proc. IFIP Congress 1962",
title = "Optimal Scaling of Matrices and the Importance of the
Minimal Condition",
publisher = pub-NH # ", " # pub-NH:adr,
pages = "198--201",
year = "1963",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Information Processing 62",
}
@Article{Bauer:1966:GLL,
author = "F. L. Bauer",
title = "Genauigkeitsfragen bei der {L{\"o}sung} linearer
{Gleichungssysteme}",
journal = j-ZAMM,
volume = "46",
number = "7",
pages = "409--421",
year = "1966",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bauer:1969:ROS,
author = "F. L. Bauer",
title = "Remarks on Optimally Scaled Matrices",
journal = j-NUM-MATH,
volume = "13",
pages = "1--3",
year = "1969",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Bauer:1974:CGR,
author = "F. L. Bauer",
title = "Computational Graphs and Rounding Errors",
journal = j-SINUM,
volume = "11",
number = "1",
pages = "87--96",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Barlow:1992:RDM,
author = "Jesse L. Barlow and Udaya B. Vemulapati",
title = "Rank Detection Methods for Sparse Matrices",
journal = j-SIMAX,
volume = "13",
number = "4",
pages = "1279--1297",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Barlow:1992:NDC,
author = "Jesse L. Barlow and Udaya B. Vemulapati",
title = "A Note on Deferred Correction for Equality Constrained
Least Squares Problems",
journal = j-SINUM,
volume = "29",
number = "1",
pages = "249--256",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Barlow:1998:GGE,
author = "Jesse L. Barlow and Hongyuan Zha",
title = "Growth in {Gaussian} Elimination, Orthogonal Matrices,
and the {$2$}-Norm",
journal = j-SIMAX,
volume = "19",
number = "3",
pages = "807--815",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Borwein:1989:RME,
author = "J. M. Borwein and P. B. Borwein and D. H. Bailey",
title = "Ramanujan, Modular Equations, and Approximations to
{Pi} or How to Compute One Billion Digits of {Pi}",
journal = j-AMM,
volume = "96",
number = "3",
pages = "201--219",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InCollection{Bliss:1992:API,
author = "B. Bliss and M.-C. Brunet and E. Gallopoulos",
editor = "E. N. Houstis and J. R. Rice and R. Vichnevetsky",
booktitle = "Expert Systems for Scientific Computing",
title = "Automatic Program Instrumentation with Applications in
Performance and Error Analysis",
publisher = pub-NH # ", " # pub-NH:adr,
pages = "235--260",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Blackford:1997:PEN,
author = "L. S. Blackford and A. Cleary and A. Petitet and R. C.
Whaley and J. Demmel and I. Dhillon and H. Ren and K.
Stanley and J. Dongarra and S. Hammarling",
title = "Practical Experience in the Numerical Dangers of
Heterogeneous Computing",
journal = j-TOMS,
volume = "23",
number = "2",
pages = "133--147",
year = "1997",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Book{Burgisser:1997:ACT,
author = "Peter B{\"u}rgisser and Michael Clausen and M. Amin
Shokrollahi",
title = "Algebraic Complexity Theory",
publisher = pub-Springer,
address = pub-Springer:adr-B,
pages = "xxiii + 618",
year = "1997",
ISBN = "0-540-60582-7",
ISBN-13 = "978-0-540-60582-8",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Blackford:2002:USB,
author = "L. Susan Blackford and James Demmel and Jack Dongarra
and Iain Duff and Sven Hammarling and Greg Henry and
Michael Heroux and Linda Kaufman and Andrew Lumsdaine
and Antoine Petitet and Roldan Pozo and Karin Remington
and R. Clint Whaley",
title = "An updated set of {Basic Linear Algebra Subprograms
(BLAS)}",
journal = j-TOMS,
volume = "28",
number = "2",
pages = "135--151",
month = jun,
year = "2002",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/567806.567807",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Nov 9 11:16:50 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
abstract = "This paper expands the specification of a set of
kernel routines for linear algebra, historically called
the Basic Linear Algebra Subprograms and commonly known
as the BLAS.\par
Numerical linear algebra, particularly the solution of
linear systems of equations, linear least squares
problems, eigenvalue problems and singular value
problems, is fundamental to most calculations in
scientific computing, and is often the computationally
intense part of such calculations. Designers of
computer programs involving linear algebraic operations
have frequently chosen to implement certain low level
operations, such as the dot product or the matrix
vector product, as separate subprograms. This may be
observed both in many published codes and in codes
written for specific applications at many computer
installations.\par
A major aim of the standards defined in this paper is
to enable linear algebra libraries (both public domain
and commercial) to interoperate efficiently, reliably
and easily.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@TechReport{Bai:1997:TMC,
author = "Zhaojun Bai and David Day and James Demmel and Jack
Dongarra",
title = "A Test Matrix Collection for Non-{Hermitian}
Eigenvalue Problems (Release 1.0)",
type = "Technical Report",
number = "CS-97-355",
institution = inst-CS-U-Tenn,
address = inst-CS-U-Tenn:adr,
pages = "45",
month = mar,
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "LAPACK Working Note 123",
}
@Article{Bai:1997:SDN,
author = "Zhaojun Bai and James W. Demmel and Jack J. Dongarra
and Antoine Petitet and Howard Robinson and K.
Stanley",
title = "The Spectral Decomposition of Nonsymmetric Matrices on
Distributed Memory Parallel Computers",
journal = j-SISC,
volume = "18",
number = "5",
pages = "1446--1461",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bai:1997:IFP,
author = "Zhaojun Bai and James W. Demmel and Ming Gu",
title = "Inverse Free Parallel Spectral Divide and Conquer
Algorithms for Nonsymmetric Eigenproblems",
journal = j-NUM-MATH,
volume = "76",
pages = "279--308",
year = "1997",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@TechReport{Browne:1994:NSR,
author = "Shirley V. Browne and Jack J. Dongarra and Stan C.
Green and Keith Moore and Thomas H. Rowan and Reed C.
Wade",
title = "Netlib Services and Resources",
type = "Report",
number = "ORNL/TM-12680",
institution = inst-ORNL,
address = inst-ORNL:adr,
pages = "42",
month = apr,
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bai:1993:CCN,
author = "Zhaojun Bai and James W. Demmel and Alan McKenney",
title = "On Computing Condition Numbers for the Nonsymmetric
Eigenproblem",
journal = j-TOMS,
volume = "19",
number = "2",
pages = "202--223",
year = "1993",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Bunch:1989:SSA,
author = "James R. Bunch and James W. Demmel and Charles F. {Van
Loan}",
title = "The Strong Stability of Algorithms for Solving
Symmetric Linear Systems",
journal = j-SIMAX,
volume = "10",
number = "4",
pages = "494--499",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Beckermann:2000:CNR,
author = "Bernhard Beckermann",
title = "The Condition Number of Real {Vandermonde}, {Krylov}
and Positive Definite {Hankel} Matrices",
journal = j-NUM-MATH,
volume = "85",
pages = "553--577",
year = "2000",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Bell:1931:RCH,
author = "E. T. Bell",
title = "Review of ``{Contributions to the History of
Determinants}, 1900-1920'', by {Sir Thomas Muir}",
journal = j-AMM,
volume = "38",
pages = "161--164",
year = "1931",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Bellman:1970:IMA,
author = "Richard Bellman",
title = "Introduction to Matrix Analysis",
publisher = pub-MH,
address = pub-MH:adr,
edition = "Second",
pages = "xxiii + 403",
year = "1970",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted by Society for Industrial and Applied
Mathematics, Philadelphia, PA, USA, 1997. ISBN
0-89871-399-4",
}
@Book{Bell:1971:CSR,
author = "C. Gordon Bell and Allen Newell",
title = "Computer Structures: {Readings} and Examples",
publisher = pub-MH,
address = pub-MH:adr,
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Benford:1938:LAN,
author = "Frank Benford",
title = "The Law of Anomalous Numbers",
journal = j-PROC-AMER-PHIL-SOC,
volume = "78",
number = "4",
pages = "551--572",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003-049X (print), 2326-9243 (electronic)",
ISSN-L = "0003-049X",
bibdate = "Thu Feb 15 16:28:28 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
note = "See comments about Benford's biased rounding practices
\cite{Diaconis:1979:RP}.",
URL = "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G",
ZMnumber = "JFM 64.0555.03; Zbl 0018.26502",
abstract = "It has been observed that the first pages of a table
of common logarithms show more wear than do the last
pages, indicating that more used numbers begin with the
digit 1 than with the digit 9. A compilation of some
20,000 first digits taken from widely divergent sources
shows that there is a logarithmic distribution of first
digits when the numbers are composed of four or more
digits. An analysis of the numbers from different
sources shows that the numbers taken from unrelated
subjects, such as a group of newspaper items, show a
much better agreement with a logarithmic distribution
than do numbers from mathematical tabulations or other
formal data. There is here the peculiar fact that
numbers that individually are without relationship are,
when considered in large groups, in good agreement with
a distribution law---hence the name ``Anomalous
Numbers.''\par
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
digits the geometric relation still holds but the
simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a multi-digit number, and it
is shown that the same law applies to
reciprocals.\par
There are many instances showing that the geometric
series, or the logarithmic law, has long been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairs.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = ack-nhfb,
author-dates = "1883--December 4, 1948",
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journal-URL = "http://www.jstor.org/journal/procamerphilsoci",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573--585 (1938)]. That is why Benford's
paper caught the attention of physicists in the early
1940's and was much discussed. This led to the notes in
Nature by Goudsmit and Furry [3] and Furry and Hurwitz
[4] containing an effort to explain Benford's law. We
considered it at that time merely a welcome diversion
and did not expect that over thirty papers would be
devoted to this subject in subsequent years.'' The 2006
bibliography \cite{Hurlimann:2006:BLB} cites 325
publications about Benford's Law.",
xxURL = "http://en.wikipedia.org/wiki/Frank_Benford",
}
@Article{Benoit:1924:NMR,
author = "Commandant Benoit",
title = "Note sur une m\'ethode de r\'esolution des \'equations
normales provenant de l'application de la m\'ethode des
moindres carr\'es \`a un syst\`eme d'\'equations
lin\'eaires en nombre inf\'erieur \`a celui des
inconnues. {Application} de la m\'ethode \`a la
r\'esolution d'un syst\`eme d\'efini d'\'equations
lin\'eaires \upshape{\char40}{Proc\'ed\'e du Commandant
Cholesky}\upshape{\char41}",
journal = "Bulletin G\'eod\'esique
\upshape{(}Toulouse\upshape{)}",
volume = "2",
pages = "67--77",
year = "1924",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Cited in \cite[Cottle's
translation]{Anonymous:1922:CC}",
}
@Book{Berman:1994:NMM,
author = "Abraham Berman and Robert J. Plemmons",
title = "Nonnegative Matrices in the Mathematical Sciences",
volume = "9",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xx + 340",
year = "1994",
DOI = "https://doi.org/10.1137/1.9781611971262",
ISBN = "0-89871-321-8",
ISBN-13 = "978-0-89871-321-3",
LCCN = "QA188 .B47 1994",
MRclass = "15A48 (15-02 60J10 90C33)",
MRnumber = "1298430 (95e:15013)",
bibdate = "Fri Nov 21 06:49:56 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
note = "Revised reprint of \cite{Berman:1979:NMM}.",
series = "Classics in Applied Mathematics",
URL = "http://www.loc.gov/catdir/enhancements/fy0708/94037449-d.html;
http://www.loc.gov/catdir/enhancements/fy0708/94037449-t.html",
abstract = "Here is a valuable text and research tool for
scientists and engineers who use or work with theory
and computation associated with practical problems
relating to Markov chains and queuing networks,
economic analysis, or mathematical programming.
Originally published in 1979, this new edition adds
material that updates the subject relative to
developments from 1979 to 1993. Theory and applications
of nonnegative matrices are blended here, and extensive
references are included in each area. You will be led
from the theory of positive operators via the
Perron-Frobenius theory of nonnegative matrices and the
theory of inverse positivity, to the widely used topic
of $M$-matrices. On the way, semigroups of nonnegative
matrices and symmetric nonnegative matrices are
discussed. Later, applications of nonnegativity and
$M$-matrices are given; for numerical analysis the
example is convergence theory of iterative methods, for
probability and statistics the examples are finite
Markov chains and queuing network models, for
mathematical economics the example is input-output
models, and for mathematical programming the example is
the linear complementarity problem. Nonnegativity
constraints arise very naturally throughout the
physical world. Engineers, applied mathematicians, and
scientists who encounter nonnegativity or
generalizations of nonegativity in their work will
benefit from topics covered here, connecting them to
relevant theory. Researchers in one area, such as
queuing theory, may find useful the techniques
involving nonnegative matrices used by researchers in
another area, say, mathematical programming. Exercises
and biographical notes are included with each
chapter.",
acknowledgement = ack-njh # " and " # ack-nhfb # " and " # ack-rah,
tableofcontents = "1: Matrices Which Leave a Cone Invariant \\
2: Nonnegative Matrices \\
3: Semigroups of Nonnegative Matrices \\
4: Symmetric Nonnegative Matrices \\
5: Generalized Inverse-Positivity \\
6: $M$-Matrices \\
7: Iterative Methods for Linear Systems \\
8: Finite Markov Chains \\
9: Input-Output Analysis in Economics \\
10: The Linear Complementarity Problem \\
11: Supplement 1979--1993 \\
References \\
Index",
}
@Article{Benschop:1971:MSE,
author = "N. F. Benschop and H. C. Ratz",
title = "A Mean Square Estimate of the Generated Roundoff Error
in Constant Matrix Iterative Processes",
journal = j-ACM,
volume = "18",
number = "1",
pages = "48--62",
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Berenbaum:1991:DSM,
author = "M. C. Berenbaum",
title = "Direct Search Methods in the Optimisation of Cancer
Chemotherapy",
journal = j-BRITISH-J-CANCER,
volume = "61",
pages = "101--109",
year = "1991",
CODEN = "BJCAAI",
ISSN = "0007-0920 (print), 1532-1827 (electronic)",
ISSN-L = "0007-0920",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "British Journal of Cancer",
}
@Article{Beam:1993:ASB,
author = "Richard M. Beam and Robert F. Warming",
title = "The Asymptotic Spectra of Banded {Toeplitz} and
Quasi-{Toeplitz} Matrices",
journal = j-SISC,
volume = "14",
number = "4",
pages = "971--1006",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Boley:1994:FPF,
author = "Daniel Boley and Gene H. Golub and Samy Makar and
Nirmal Saxena and Edward J. McCluskey",
title = "Floating Point Fault Tolerance with Backward Error
Assertions",
journal = j-IEEE-C,
volume = "44",
number = "2",
pages = "302--311",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Buzbee:1970:DMS,
author = "B. L. Buzbee and G. H. Golub and C. W. Nielson",
title = "On Direct Methods for Solving {Poisson's} Equations",
journal = j-SINUM,
volume = "7",
number = "4",
pages = "627--656",
year = "1970",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Bhatia:1997:MA,
author = "Rajendra Bhatia",
title = "Matrix Analysis",
volume = "169",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xii + 347",
year = "1997",
DOI = "https://doi.org/10.1007/978-1-4612-0653-8",
ISBN = "0-387-94846-5 (print), 1-4612-0653-7 (e-book)",
ISBN-13 = "978-0-387-94846-1 (print), 978-1-4612-0653-8
(e-book)",
LCCN = "QA188 .B485 1996",
MRclass = "15-02 (47-02)",
MRnumber = "1477662 (98i:15003)",
MRreviewer = "R. J. Bumcrot",
bibdate = "Fri Nov 21 06:49:56 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/numana1990.bib",
series = "Graduate Texts in Mathematics",
URL = "http://catdir.loc.gov/catdir/enhancements/fy0818/96032217-d.html;
http://www.gbv.de/dms/goettingen/213798093.pdf",
abstract = "The aim of this book is to present a substantial part
of matrix analysis that is functional analytic in
spirit. Much of this will be of interest to graduate
students and research workers in operator theory,
operator algebras, mathematical physics, and numerical
analysis. The book can be used as a basic text for
graduate courses on advanced linear algebra and matrix
analysis. It can also be used as supplementary text for
courses in operator theory and numerical analysis.
Among topics covered are the theory of majorization,
variational principles of eigenvalues, operator
monotone and convex functions, perturbation of matrix
functions, and matrix inequalities. Much of this is
presented for the first time in a unified way in a
textbook. The reader will learn several powerful
methods and techniques of wide applicability, and see
connections with other areas of mathematics. A large
selection of matrix inequalities will make this book a
valuable reference for students and researchers who are
working in numerical analysis, mathematical physics and
operator theory.",
acknowledgement = ack-nhfb # " and " # ack-rah,
tableofcontents = "Preface / v \\
I A Review of Linear Algebra / 1 \\
1.1 Vector Spaces and Inner Product Spaces / 1 \\
1.2 Linear Operators and Matrices / 3 \\
1.3 Direct Sums / 9 \\
1.4 Tensor Products / 12 \\
1.5 Symmetry Classes / 16 \\
1.6 Problems / 20 \\
1.7 Notes and References / 26 \\
II Majorisation and Doubly Stochastic Matrices / 28 \\
11.1 Basic Notions / 28 \\
11.2 Birkhoff's Theorem / 36 \\
11.3 Convex and Monotone Functions / 40 \\
11.4 Binary Algebraic Operations and Majorisation / 48
\\
11.5 Problems / 50 \\
11.6 Notes and References / 54 \\
III Variational Principles for Eigenvalues / 57 \\
III.1 The Minimax Principle for Eigenvalues / 57 \\
111.2 Weyl's Inequalities / 62 \\
111.3 Wielandt's Minimax Principle / 65 \\
111.4 Lidskii's Theorems / 68 \\
III.5 Eigenvalues of Real Parts and Singular Values /
73 \\
111.6 Problems / 75 \\
111.7 Notes and References / 78 \\
IV Symmetric Norms / 84 \\
IV.1 Norms on $C^n$ / 84 \\
IV.2 Unitarily Invariant Norms on Operators on $C^n$ /
91 \\
IV.3 Lidskii's Theorem (Third Proof) / 98 \\
IV.4 Weakly Unitarily Invariant Norms / 101 \\
IV.5 Problems / 107 \\
IV.6 Notes and References / 109 \\
V Operator Monotone and Operator Convex Functions / 112
\\
V.1 Definitions and Simple Examples / 112 \\
V.2 Some Characterisations / 117 \\
V.3 Smoothness Properties / 123 \\
V.4 Loewner's Theorems / 131 \\
V.5 Problems / 147 \\
V.6 Notes and References / 149 \\
VI Spectral Variation of Normal Matrices / 152 \\
VI.1 Continuity of Roots of Polynomials / 153 \\
VI.2 Hermitian and Skew-Hermitian Matrices / 155 \\
VI.3 Estimates in the Operator Norm / 159 \\
VI.4 Estimates in the Frobenius Norm / 165 \\
VI.5 Geometry and Spectral Variation: the Operator Norm
/ 168 \\
VI.6 Geometry and Spectral Variation: wui Norms / 173
\\
VI.7 Some Inequalities for the Determinant / 181 \\
VI.8 Problems / 184 \\
VI.9 Notes and References / 190 \\
VII Perturbation of Spectral Subspaces of Normal
Matrices / 194 \\
VII.1 Pairs of Subspaces / 195 \\
VII.2 The Equation $A X -X B = Y$ / 203 \\
VII.3 Perturbation of Eigenspaces / 211 \\
VII.4 A Perturbation Bound for Eigenvalues / 212 \\
VII.5 Perturbation of the Polar Factors / 213 \\
VII.6 Appendix: Evaluating the (Fourier) constants /
216 \\
VII.7 Problems / 221 \\
VII.8 Notes and References / 223 \\
VIII Spectral Variation of Nonnormal Matrices / 226 \\
VIII.1 General Spectral Variation Bounds / 227 \\
VIII.4 Matrices with Real Eigenvalues / 238 \\
VIII.5 Eigenvalues with Symmetries / 240 \\
VIII.6 Problems / 244 \\
VIII.7 Notes and References / 249 \\
IX A Selection of Matrix Inequalities / 253 \\
IX.1 Some Basic Lemmas / 253 \\
IX.2 Products of Positive Matrices / 255 \\
IX.3 Inequalities for the Exponential Function / 258
\\
IX.4 Arithmetic-Geometric Mean Inequalities / 262 \\
IX.5 Schwarz Inequalities / 266 \\
IX.6 The Lieb Concavity Theorem / 271 \\
IX.7 Operator Approximation / 275 \\
IX.8 Problems / 279 \\
IX.9 Notes and References / 285 \\
X Perturbation of Matrix Functions / 289 \\
X.1 Operator Monotone Functions / 289 \\
X.2 The Absolute Value / 296 \\
X.3 Local Perturbation Bounds / 301 \\
X.4 Appendix: Differential Calculus / 310 \\
X.5 Problems / 317 \\
X.6 Notes and References / 320 \\
References / 325 \\
Index / 339",
xxpages = "xi + 347",
}
@TechReport{Balle:1993:STM,
author = "Susanne M. Balle and Per Christian Hansen and Nicholas
J. Higham",
title = "A {Strassen}-Type Matrix Inversion Algorithm for the
{Connection Machine}",
number = "CNC/1993/028",
institution = "Centre for Novel Computing, " # inst-U-Manchester,
address = inst-U-Manchester:adr,
type = "Technical Report",
pages = "29",
month = oct,
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bhatia:1994:VUP,
author = "Rajendra Bhatia and Kalyan Mukherjea",
title = "Variation of the Unitary Part of a Matrix",
journal = j-SIMAX,
volume = "15",
number = "3",
pages = "1007--1014",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bhatia:1997:HWS,
author = "Rajendra Bhatia and Peter Rosenthal",
title = "How and Why To Solve the Operator Equation {$AX - XB =
Y$}",
journal = j-BULL-LOND-MATH-SOC,
volume = "29",
pages = "1--21",
year = "1997",
CODEN = "LMSBBT",
ISSN = "0024-6093 (print), 1469-2120 (electronic)",
ISSN-L = "0024-6093",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Bulletin of the London Mathematical Society",
journal-URL = "http://blms.oxfordjournals.org/content/by/year",
}
@Article{Brent:1980:AIB,
author = "Richard P. Brent and Judith A. Hooper and J. Michael
Yohe",
title = "An {AUGMENT} Interface for {Brent's} Multiple
Precision Arithmetic Package",
journal = j-TOMS,
volume = "6",
number = "2",
pages = "146--149",
year = "1980",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Birkhoff:1979:IDT,
author = "Garrett Birkhoff and Surender Gulati",
title = "Isotropic Distributions of Test Matrices",
journal = "J. Appl. Math. Phys. \textup{(}ZAMP\textup{)}",
volume = "30",
pages = "148--158",
year = "1979",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bini:1980:SFA,
author = "Dario Bini and Grazia Lotti",
title = "Stability of Fast Algorithms for Matrix
Multiplication",
journal = j-NUM-MATH,
volume = "36",
pages = "63--72",
year = "1980",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{Birkhoff:1977:SMA,
author = "Garrett Birkhoff and Saunders Mac Lane",
title = "A Survey of Modern Algebra",
publisher = "Macmillan",
address = "New York",
edition = "Fourth",
pages = "xi + 500",
year = "1977",
ISBN = "0-02-310070-2",
ISBN-13 = "978-0-02-310070-3",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Bini:1994:PMC,
author = "Dario Bini and Victor Y. Pan",
title = "Polynomial and Matrix Computations. Volume 1:
{Fundamental} Algorithms",
publisher = pub-BH,
address = pub-BH:adr,
pages = "xvi + 415",
year = "1994",
ISBN = "0-8176-3786-9",
ISBN-13 = "978-0-8176-3786-6",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Birkhoff:1975:THN,
author = "Garrett Birkhoff",
title = "Two {Hadamard} Numbers for Matrices",
journal = j-CACM,
volume = "18",
number = "1",
pages = "25--29",
year = "1975",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Bischof:1990:ICEa,
author = "Christian H. Bischof",
title = "Incremental Condition Estimation",
journal = j-SIMAX,
volume = "11",
number = "2",
pages = "312--322",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bischof:1987:WRP,
author = "Christian H. Bischof and Charles F. {Van Loan}",
title = "The {WY} Representation for Products of {Householder}
Matrices",
journal = j-SISSC,
volume = "8",
number = "1",
pages = "s2--s13",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bjorck:1973:ACV,
author = "{\AA}ke Bj{\"o}rck and Tommy Elfving",
title = "Algorithms for Confluent {Vandermonde} Systems",
journal = j-NUM-MATH,
volume = "21",
pages = "130--137",
year = "1973",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Bjorck:1967:IRLa,
author = "{\AA}ke Bj{\"o}rck and Gene H. Golub",
title = "Iterative Refinement of Linear Least Squares Solutions
by {Householder} Transformation",
journal = j-BIT,
volume = "7",
pages = "322--337",
year = "1967",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Bjorck:1967:IRLb,
author = "{\AA}ke Bj{\"o}rck",
title = "Iterative Refinement of Linear Least Squares Solutions
{I}",
journal = j-BIT,
volume = "7",
pages = "257--278",
year = "1967",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Bjorck:1967:SLL,
author = "{\AA}ke Bj{\"o}rck",
title = "Solving Linear Least Squares Problems by
{Gram--Schmidt} Orthogonalization",
journal = j-BIT,
volume = "7",
pages = "1--21",
year = "1967",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Bjorck:1968:IRL,
author = "{\AA}ke Bj{\"o}rck",
title = "Iterative Refinement of Linear Least Squares Solutions
{II}",
journal = j-BIT,
volume = "8",
pages = "8--30",
year = "1968",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Bjorck:1978:CIR,
author = "{\AA}ke Bj{\"o}rck",
title = "Comment on the Iterative Refinement of Least-Squares
Solutions",
journal = j-ASA,
volume = "73",
number = "361",
pages = "161--166",
year = "1978",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bjorck:1987:SAM,
author = "{\AA}ke Bj{\"o}rck",
title = "Stability Analysis of the Method of Seminormal
Equations for Linear Least Squares Problems",
journal = j-LAA,
volume = "88/89",
pages = "31--48",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Bjorck:1990:LSM,
author = "{\AA}ke Bj{\"o}rck",
editor = "P. G. Ciarlet and J. L. Lions",
booktitle = "Handbook of Numerical Analysis",
title = "Least Squares Methods",
volume = "I: Finite Difference Methods---Solution of Equations
in {$R^n$}",
publisher = pub-ELSNH,
address = pub-ELSNH:adr,
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Bjorck:1990:IRR,
author = "{\AA}ke Bj{\"o}rck",
editor = "M. G. Cox and S. J. Hammarling",
booktitle = "Reliable Numerical Computation",
title = "Iterative Refinement and Reliable Computing",
publisher = pub-OUP,
pages = "249--266",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
mycrossref = "Cox:1990:RNC",
}
@Article{Bjorck:1991:CWP,
author = "{\AA}ke Bj{\"o}rck",
title = "Component-Wise Perturbation Analysis and Error Bounds
for Linear Least Squares Solutions",
journal = j-BIT,
volume = "31",
pages = "238--244",
year = "1991",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@InProceedings{Bjorck:1992:PSA,
author = "{\AA}ke Bj{\"o}rck",
editor = "D. F. Griffiths and G. A. Watson",
booktitle = "Numerical Analysis \textup{1991}, Proceedings of the
\textup{14}th Dundee Conference",
title = "Pivoting and Stability in the Augmented System
Method",
volume = "260",
publisher = pub-Longman-ST # ", " # pub-Longman-ST:adr,
pages = "1--16",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Pitman Research Notes in Mathematics",
}
@Article{Bjorck:1994:NGS,
author = "{\AA}ke Bj{\"o}rck",
title = "Numerics of {Gram--Schmidt} Orthogonalization",
journal = j-LAA,
volume = "197/198",
pages = "297--316",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Bjorck:1996:NML,
author = "{\AA}ke Bj{\"o}rck",
title = "Numerical Methods for Least Squares Problems",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xvii + 408",
year = "1996",
ISBN = "0-89871-360-9",
ISBN-13 = "978-0-89871-360-2",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bjorck:1992:LRO,
author = "{\AA}ke Bj{\"o}rck and C. C. Paige",
title = "Loss and Recapture of Orthogonality in the Modified
{Gram--Schmidt} Algorithm",
journal = j-SIMAX,
volume = "13",
number = "1",
pages = "176--190",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bjorck:1994:SAL,
author = "{\AA}ke Bj{\"o}rck and C. C. Paige",
title = "Solution of Augmented Linear Systems Using Orthogonal
Factorizations",
journal = j-BIT,
volume = "34",
pages = "1--24",
year = "1994",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Bjorck:1970:SVS,
author = "{\AA}ke Bj{\"o}rck and Victor Pereyra",
title = "Solution of {Vandermonde} Systems of Equations",
journal = j-MATH-COMP,
volume = "24",
number = "112",
pages = "893--903",
year = "1970",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Unpublished{Boros:1994:FAS,
author = "T. Boros and T. Kailath and V. Olshevsky",
title = "Fast Algorithms for Solving {Vandermonde} and
{Chebyshev--Vandermonde} Systems",
pages = "22",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Manuscript",
}
@Article{Bunch:1976:DSM,
author = "James R. Bunch and Linda Kaufman and Beresford N.
Parlett",
title = "Decomposition of a Symmetric Matrix",
journal = j-NUM-MATH,
volume = "27",
pages = "95--109",
year = "1976",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@InProceedings{Bailey:1993:MPM,
author = "David H. Bailey and Robert Krasny and Richard Pelz",
editor = "Richard F. Sincovec and David E. Keyes and Michael R.
Leuze and Linda R. Petzold and Daniel A. Reed",
booktitle = "Proceedings of the Sixth SIAM Conference on Parallel
Processing for Scientific Computing, {Volume I}",
title = "Multiple Precision, Multiple Processor Vortex Sheet
Roll-Up Computation",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "52--56",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Blanch:1964:NEC,
author = "G. Blanch",
title = "Numerical Evaluation of Continued Fractions",
journal = j-SIREV,
volume = "6",
number = "4",
pages = "383--421",
year = "1964",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{BLAST,
key = "Basic Linear Algebra Subprograms Technical (BLAST)
Forum",
title = "{Basic Linear Algebra Subprograms Technical (BLAST)
Forum Standard}",
journal = "Int. J. High Performance Applications and
Supercomputing",
volume = "",
number = "",
year = "2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "To appear",
}
@InProceedings{Bloch:1948:MC,
author = "Richard M. Bloch",
title = "Mark {I} Calculator",
crossref = "harv48",
pages = "23--30",
year = "1948",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bischof:1990:ICEb,
author = "Christian H. Bischof and John G. Lewis and Daniel J.
Pierce",
title = "Incremental Condition Estimation for Sparse Matrices",
journal = j-SIMAX,
volume = "11",
number = "4",
pages = "644--659",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bailey:1991:USA,
author = "David H. Bailey and King Lee and Horst D. Simon",
title = "Using {Strassen's} Algorithm to Accelerate the
Solution of Linear Systems",
journal = j-J-SUPERCOMPUTING,
volume = "4",
pages = "357--371",
year = "1991",
CODEN = "JOSUED",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@Article{Blue:1978:PFP,
author = "James L. Blue",
title = "A Portable {Fortran} Program to Find the {Euclidean}
Norm of a Vector",
journal = j-TOMS,
volume = "4",
number = "1",
pages = "15--23",
year = "1978",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Bowdler:1966:SRC,
author = "H. J. Bowdler and R. S. Martin and G. Peters and J. H.
Wilkinson",
title = "Solution of Real and Complex Systems of Linear
Equations",
journal = j-NUM-MATH,
volume = "8",
pages = "217--234",
year = "1966",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Also in \cite[pp.~93--110]{Wilkinson:1971:LA},
Contribution I/7",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Bjorstad:1992:EMM,
author = "P. Bj{\o}rstad and F. Manne and T. S{\o}revik and M.
Vajter\v{s}ic",
title = "Efficient Matrix Multiplication on {SIMD} Computers",
journal = j-SIMAX,
volume = "13",
number = "1",
pages = "386--401",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Bargmann:1946:SLS,
author = "V. Bargmann and D. Montgomery and J. von Neumann",
title = "Solution of Linear Systems of High Order",
type = "Report prepared for {Navy Bureau of Ordnance}",
year = "1946",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted in \cite[pp.~421--477]{Taub:1963:JNC}",
}
@Article{Barlow:1988:IME,
author = "J. L. Barlow and N. K. Nichols and R. J. Plemmons",
title = "Iterative Methods for Equality-Constrained Least
Squares Problems",
journal = j-SISSC,
volume = "9",
number = "5",
pages = "892--906",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bodewig:1949:RRE,
author = "E. Bodewig",
title = "Review of ``{Rounding-Off Errors in Matrix
Processes}'' by {A. M. Turing}",
journal = j-MATH-REV,
volume = "10",
pages = "405",
year = "1949",
CODEN = "MAREAR",
ISSN = "0025-5629",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Mathematical Reviews",
}
@Article{Bondeli:1994:CRS,
author = "S. Bondeli and W. Gander",
title = "Cyclic Reduction for Special Tridiagonal Systems",
journal = j-SIMAX,
volume = "15",
number = "1",
pages = "321--330",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bohlender:1977:FPC,
author = "Gerd Bohlender",
title = "Floating-point Computation of Functions with Maximum
Accuracy",
journal = j-IEEE-C,
volume = "C-26",
number = "7",
pages = "621--632",
year = "1977",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bohte:1975:BRE,
author = "Z. Bohte",
title = "Bounds for Rounding Errors in the {Gaussian}
Elimination For Band Systems",
journal = j-JIMA,
volume = "16",
pages = "133--142",
year = "1975",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bollen:1984:NSD,
author = "Jo A. M. Bollen",
title = "Numerical Stability of Descent Methods for Solving
Linear Equations",
journal = j-NUM-MATH,
volume = "43",
pages = "361--377",
year = "1984",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@InCollection{Bowden:1953:OTM,
author = "B. V. Bowden",
editor = "B. V. Bowden",
booktitle = "Faster than Thought: {A} Symposium on Digital
Computing Machines",
title = "The Organization of a Typical Machine",
publisher = "Pitman",
address = "London",
pages = "67--77",
year = "1953",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Boyd:1974:PMN,
author = "David W. Boyd",
title = "The Power Method for {$\ell^p$} Norms",
journal = j-LAA,
volume = "9",
pages = "95--101",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Boyer:1989:HM,
author = "Carl B. Boyer",
title = "A History of Mathematics",
publisher = pub-Wiley,
address = pub-Wiley:adr,
edition = "Second",
pages = "xviii + 762",
year = "1989",
ISBN = "0-471-50357-6",
ISBN-13 = "978-0-471-50357-6",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Revised by Uta C. Merzbach",
}
@Article{Boyle:1994:AFS,
author = "Jeff Boyle",
title = "An Application of {Fourier} Series to the Most
Significant Digit Problem",
journal = j-AMM,
volume = "101",
number = "11",
pages = "879--886",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Boisvert:1997:MMW,
author = "Ronald F. Boisvert and Roldan Pozo and Karin Remington
and Richard F. Barrett and Jack J. Dongarra",
editor = "Ronald F. Boisvert",
booktitle = "Quality of Numerical Software: {Assessment} and
Enhancement",
title = "{Matrix Market}: {A Web} Resource for Test Matrix
Collections",
publisher = pub-CH # ", " # pub-CH:adr-L,
pages = "125--136",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Beaton:1976:ARS,
author = "Albert E. Beaton and Donald B. Rubin and John L.
Barone",
title = "The Acceptability of Regression Solutions: {Another}
Look at Computational Accuracy",
journal = j-ASA,
volume = "71",
number = "353",
pages = "158--168",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Brent:1970:EAA,
author = "R. P. Brent",
title = "Error Analysis of Algorithms for Matrix Multiplication
and Triangular Decomposition Using {Winograd's}
Identity",
journal = j-NUM-MATH,
volume = "16",
pages = "145--156",
year = "1970",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@TechReport{Brent:1970:AMM,
author = "R. P. Brent",
title = "Algorithms for Matrix Multiplication",
type = "Technical Report",
number = "CS 157",
institution = inst-CS-U-STANFORD,
address = inst-U-STANFORD:adr,
pages = "ii + 52",
month = mar,
year = "1970",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Brent:1973:PAV,
author = "Richard P. Brent",
title = "On the Precision Attainable with Various
Floating-Point Number Systems",
journal = j-IEEE-C,
volume = "C-22",
number = "6",
pages = "601--607",
year = "1973",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Brent:19xx:FMP,
author = "Richard P. Brent",
title = "A {Fortran} Multiple-Precision Arithmetic Package",
journal = j-TOMS,
volume = "4",
number = "1",
pages = "57--70",
year = "{\noopsort{a}}1978",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Brent:19xx:AMF,
author = "Richard P. Brent",
title = "{ALGORITHM 524} {MP}, {A} {Fortran} Multiple-Precision
Arithmetic Package",
journal = j-TOMS,
volume = "4",
number = "1",
pages = "71--81",
year = "{\noopsort{b}}1978",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@InCollection{Brezinski:1996:ALC,
author = "Claude Brezinski",
booktitle = "{A} Numerical Analysis Conference in Honour of {Jean
Meinguet}",
title = "{Andr\'e Louis Cholesky}",
pages = "45--50",
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Published as a supplement to the Bulletin of the
Belgian Mathematical Society. Also available as
Publication ANO-347, Laboratoire d'Analyse Num\'erique
et d'Optimisation, Universit\'e des Sciences et
Technologies de Lille, Nov. 1995,
\path|http://ano.univ-lille1.fr|",
}
@Book{Briggs:1995:DOM,
author = "William L. Briggs and Van Emden Henson",
title = "The {DFT}: {An} Owner's Manual for the Discrete
{Fourier} Transform",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xv + 434",
year = "1995",
ISBN = "0-89871-342-0",
ISBN-13 = "978-0-89871-342-8",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Britton:1992:CWM,
editor = "J. L. Britton",
title = "Collected Works of {A. M. Turing}: {Pure}
Mathematics",
publisher = pub-NH,
address = pub-NH:adr,
pages = "xxii + 287",
year = "1992",
ISBN = "0-444-88059-3",
ISBN-13 = "978-0-444-88059-8",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bleher:1987:SFE,
author = "J. H. Bleher and S. M. Rump and U. Kulisch and M.
Metzger and Ch. Ullrich and W. Walter",
title = "A Study of a {FORTRAN} Extension for
Engineering/Scientific Computation with Access to
{ACRITH}",
journal = j-COMPUTING,
volume = "39",
pages = "93--110",
year = "1987",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Brown:1981:SRM,
author = "W. S. Brown",
title = "A Simple but Realistic Model of Floating-Point
Arithmetic",
journal = j-TOMS,
volume = "7",
number = "4",
pages = "445--480",
year = "1981",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@InProceedings{Bleher:1985:AHA,
author = "J. H. Bleher and A. E. Roeder and S. M. Rump",
editor = "Kai Hwang",
booktitle = "Proceedings of the 7th Symposium on Computer
Arithmetic",
title = "{ACRITH}: {High}-Accuracy Arithmetic. {An} Advanced
Tool for Numerical Computation",
publisher = "IEEE Computer Society Press, Silver Spring, MD, USA",
pages = "318--321",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@PhdThesis{Brunet:1989:CFL,
author = "Marie-Christine Brunet",
title = "Contribution {\`a} la Fiabilit{\'e} de Logiciels
Num{\'e}riques et {\`a} {L}'analyse de Leur
Comportement: Une Approche Statistique",
school = "Universit\'e de Paris IX Dauphine, U.E.R.
Math\'ematiques de la D\'ecision",
pages = "viii + 214",
month = jan,
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bailey:1989:FPA,
author = "David H. Bailey and Horst D. Simon and John T. Barton
and Martin J. Fouts",
title = "Floating Point Arithmetic in Future Supercomputers",
journal = j-IJSA,
volume = "3",
number = "3",
pages = "86--90",
year = "1989",
CODEN = "IJSAE9",
ISSN = "0890-2720",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "International Journal of Supercomputer Applications",
journal-URL = "http://hpc.sagepub.com/content/by/year",
}
@Article{Bauer:1961:AMN,
author = "F. L. Bauer and J. Stoer and C. Witzgall",
title = "Absolute and Monotonic Norms",
journal = j-NUM-MATH,
volume = "3",
pages = "257--264",
year = "1961",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Buchholz:1959:FFC,
author = "W. Buchholz",
title = "Fingers or Fists? ({The} Choice of Decimal or Binary
Representation)",
journal = j-CACM,
volume = "2",
number = "12",
pages = "3--11",
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Buchholz:1981:OWE,
author = "W. Buchholz",
title = "Origin of the Word {\emph{Byte}}",
journal = j-AHC,
volume = "3",
number = "1",
pages = "72",
year = "1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bukhberger:1973:MIT,
author = "B. Bukhberger and G. A. Emel'yanenko",
title = "Methods of Inverting Tridiagonal Matrices",
journal = j-USSR-COMP-MATH-MATH-PHYS,
volume = "13",
pages = "10--20",
year = "1973",
CODEN = "CMMPA9",
ISSN = "0041-5553, 0502-9902",
ISSN-L = "0041-5553",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "U.S.S.R. Computational Mathematics and Mathematical Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00415553",
}
@Article{Businger:1965:LLS,
author = "P. Businger and G. H. Golub",
title = "Linear Least Squares Solutions by {Householder}
Transformations",
journal = j-NUM-MATH,
volume = "7",
pages = "269--276",
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Also in \cite[pp.~111--118]{Wilkinson:1971:LA},
Contribution I/8",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Bunch:1977:SSM,
author = "James R. Bunch and Linda Kaufman",
title = "Some Stable Methods for Calculating Inertia and
Solving Symmetric Linear Systems",
journal = j-MATH-COMP,
volume = "31",
number = "137",
pages = "163--179",
year = "1977",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bunch:1971:ESM,
author = "James R. Bunch",
title = "Equilibration of Symmetric Matrices in the Max-Norm",
journal = j-ACM,
volume = "18",
number = "4",
pages = "566--572",
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bunch:1971:ADP,
author = "James R. Bunch",
title = "Analysis of the Diagonal Pivoting Method",
journal = j-SINUM,
volume = "8",
number = "4",
pages = "656--680",
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bunch:1974:PPS,
author = "James R. Bunch",
title = "Partial Pivoting Strategies for Symmetric Matrices",
journal = j-SINUM,
volume = "11",
number = "3",
pages = "521--528",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bunch:1982:NSD,
author = "James R. Bunch",
title = "A Note on the Stable Decomposition of Skew-Symmetric
Matrices",
journal = j-MATH-COMP,
volume = "38",
number = "158",
pages = "475--479",
year = "1982",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bunch:1987:WSS,
author = "James R. Bunch",
title = "The Weak and Strong Stability of Algorithms in
Numerical Linear Algebra",
journal = j-LAA,
volume = "88/89",
pages = "49--66",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Bunch:1971:DMS,
author = "James R. Bunch and Beresford N. Parlett",
title = "Direct Methods for Solving Symmetric Indefinite
Systems of Linear Equations",
journal = j-SINUM,
volume = "8",
number = "4",
pages = "639--655",
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Burdakov:1997:GAO,
author = "Oleg Burdakov",
title = "A Greedy Algorithm for the Optimal Basis Problem",
journal = j-BIT,
volume = "37",
number = "3",
pages = "591--599",
year = "1997",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Businger:1968:MWC,
author = "P. A. Businger",
title = "Matrices Which Can Be Optimally Scaled",
journal = j-NUM-MATH,
volume = "12",
pages = "346--348",
year = "1968",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Businger:1971:MNS,
author = "P. A. Businger",
title = "Monitoring the numerical stability of {Gaussian}
elimination",
journal = j-NUM-MATH,
volume = "16",
pages = "360--361",
year = "1971",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{Butcher:1987:NAO,
author = "J. C. Butcher",
title = "The Numerical Analysis of Ordinary Differential
Equations: {Runge--Kutta} and General Linear Methods",
publisher = pub-Wiley,
address = pub-Wiley:adr-C,
pages = "xv + 512",
year = "1987",
ISBN = "0-471-91046-5",
ISBN-13 = "978-0-471-91046-6",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Buchanan:1992:NMA,
author = "James L. Buchanan and Peter R. Turner",
title = "Numerical Methods and Analysis",
publisher = pub-MH,
address = pub-MH:adr,
pages = "xv + 751",
year = "1992",
ISBN = "0-07-008717-2, 0-07-112922-7 (international \pbk\
edition)",
ISBN-13 = "978-0-07-008717-0, 978-0-07-112922-0 (international
\pbk\ edition)",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Byers:1984:LSC,
author = "Ralph Byers",
title = "A {LINPACK}-Style Condition Estimator for the Equation
{$AX-XB^T=C$}",
journal = j-IEEE-AC,
volume = "AC-29",
number = "10",
pages = "926--928",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Byers:1985:NCA,
author = "Ralph Byers",
editor = "B. N. Datta",
booktitle = "Linear Algebra and Its Role in Systems Theory",
title = "Numerical Condition of the Algebraic {Riccati}
Equation",
volume = "47",
publisher = pub-AMS # ", " # pub-AMS:adr,
pages = "35--49",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Contemporary Math.",
}
@Article{Byers:1987:SAR,
author = "Ralph Byers",
title = "Solving the Algebraic {Riccati} Equation with the
Matrix Sign Function",
journal = j-LAA,
volume = "85",
pages = "267--279",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Byers:1988:BMM,
author = "Ralph Byers",
title = "A Bisection Method for Measuring the Distance of a
Stable Matrix to the Unstable Matrices",
journal = j-SISSC,
volume = "9",
number = "5",
pages = "875--881",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Byers:1987:SVL,
author = "Ralph Byers and Stephen Nash",
title = "On the Singular ``Vectors'' of the {Lyapunov}
Operator",
journal = j-SIAD,
volume = "8",
number = "1",
pages = "59--66",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Carpenter:1986:MTA,
editor = "B. E. Carpenter and R. W. Doran",
title = "{A. M. Turing's} {ACE} Report of 1946 and Other
Papers",
volume = "10",
publisher = pub-MIT,
address = pub-MIT:adr,
pages = "vii + 141",
year = "1986",
ISBN = "0-262-03114-0",
ISBN-13 = "978-0-262-03114-1",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Charles Babbage Institute Reprint Series for the
History of Computing",
}
@Article{Caffney:1963:ATM,
author = "John Caffney",
title = "Another Test Matrix for Determinants and Inverses",
journal = j-CACM,
volume = "6",
number = "6",
pages = "310",
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Book{Campbell:1979:GIL,
author = "S. L. Campbell and C. D. {Meyer, Jr.}",
title = "Generalized Inverses of Linear Transformations",
publisher = "Pitman",
address = "London",
pages = "xi + 272",
year = "1979",
ISBN = "0-486-66693-X",
ISBN-13 = "978-0-486-66693-8",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted by Dover, New York, 1991",
}
@Article{Campbell-Kelly:1981:PPA,
author = "Martin Campbell-Kelly",
title = "Programming the {Pilot ACE}: {Early} Programming
Activity at the {National Physical Laboratory}",
journal = j-AHC,
volume = "3",
number = "2",
pages = "133--162",
year = "1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Campbell-Kelly:1984:RAT,
author = "Martin Campbell-Kelly",
title = "Review of {``Alan Turing: The Enigma'', by Andrew
Hodges}",
journal = j-AHC,
volume = "6",
number = "2",
pages = "176--178",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Caprani:1971:ILR,
author = "Ole Caprani",
title = "Implementation of a Low Round-Off Summation Method",
journal = j-BIT,
volume = "11",
pages = "271--275",
year = "1971",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Calvetti:1992:CVS,
author = "D. Calvetti and L. Reichel",
title = "A {Chebychev-Vandermonde} Solver",
journal = j-LAA,
volume = "172",
pages = "219--229",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Calvetti:1993:FIV,
author = "D. Calvetti and L. Reichel",
title = "Fast Inversion of {Vandermonde}-Like Matrices
Involving Orthogonal Polynomials",
journal = j-BIT,
volume = "33",
pages = "473--484",
year = "1993",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Carr:1959:EAF,
author = "John W. {Carr III}",
title = "Error Analysis in Floating Point Arithmetic",
journal = j-CACM,
volume = "2",
number = "5",
pages = "10--15",
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Carter:1991:MFP,
author = "Russell Carter",
title = "{Y-MP} Floating Point and {Cholesky} Factorization",
journal = j-INT-J-HIGH-SPEED-COMPUTING,
volume = "3",
number = "3/4",
pages = "215--222",
year = "1991",
CODEN = "IHSCEZ",
ISSN = "0129-0533",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "International Journal of High Speed Computing",
journal-URL = "http://www.worldscientific.com/worldscinet/ijhsc",
}
@Article{Cao:1986:NIH,
author = "Wei-Lu Cao and William J. Stewart",
title = "A Note on Inverses of {Hessenberg}-Like Matrices",
journal = j-LAA,
volume = "76",
pages = "233--240",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Cauchy:1841:EAP,
author = "A. Cauchy",
title = "Exercices d'Analyse et de Phys. Math.",
volume = "2",
address = "Paris",
year = "1841",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Cited in \cite{Savage:1954:TIF}",
}
@Article{Cody:1984:PRW,
author = "W. J. Cody and J. T. Coonen and D. M. Gay and K.
Hanson and D. Hough and W. Kahan and R. Karpinski and
J. Palmer and F. N. Ris and D. Stevenson",
title = "A Proposed Radix- and Word-Length-Independent Standard
for Floating-Point Arithmetic",
journal = j-IEEE-MICRO,
volume = "4",
number = "4",
pages = "86--100",
year = "1984",
CODEN = "IEMIDZ",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@InProceedings{Cline:1982:GLC,
author = "Alan K. Cline and Andrew R. Conn and Charles F. {Van
Loan}",
editor = "J. P. Hennart",
booktitle = "Numerical Analysis, Mexico 1981",
title = "Generalizing the {LINPACK} Condition Estimator",
volume = "909",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
pages = "73--83",
year = "1982",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Lecture Notes in Mathematics",
}
@Article{Chan:1983:ACS,
author = "Tony F. Chan and Gene H. Golub and Randall J.
LeVeque",
title = "Algorithms for Computing the Sample Variance:
{Analysis} and Recommendations",
journal = j-AMER-STAT,
volume = "37",
number = "3",
pages = "242--247",
year = "1983",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Concus:1985:BPC,
author = "P. Concus and G. H. Golub and G. Meurant",
title = "Block Preconditioning for the Conjugate Gradient
Method",
journal = j-SISSC,
volume = "6",
number = "1",
pages = "220--252",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Conn:1992:LFP,
author = "Andrew R. Conn and Nicholas I. M. Gould and Philippe
L. Toint",
title = "{LANCELOT}: {A Fortran} Package for Large-Scale
Nonlinear Optimization (Release {A})",
publisher = pub-Springer,
address = pub-Springer:adr-B,
pages = "xviii + 330",
year = "1992",
ISBN = "0-387-55470-X",
ISBN-13 = "978-0-387-55470-9",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Chatelin:1993:EM,
author = "Fran{\c{c}}oise Chatelin",
title = "Eigenvalues of Matrices",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xviii + 382",
year = "1993",
ISBN = "0-471-93538-7",
ISBN-13 = "978-0-471-93538-4",
LCCN = "QA188 .C44 1993",
MRclass = "65-01 (15A18 65F15 65F50)",
MRnumber = "1232655 (94d:65002)",
bibdate = "Fri Nov 21 06:49:56 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/numana1990.bib;
z3950.loc.gov:7090/Voyager",
note = "With exercises by Mario Ahu{\'e}s and the author,
Translated from the French and with additional material
by Walter Ledermann",
series = "Pure and applied mathematics",
URL = "http://www.loc.gov/catdir/enhancements/fy0707/93003430-d.html;
http://www.loc.gov/catdir/toc/onix04/93003430.html",
acknowledgement = ack-nhfb # " and " # ack-rah,
subject = "Matrices; Eigenvalues",
tableofcontents = "Preface / xi \\
Preface to the English Edition / xv \\
Notation / xvii \\
1: Supplements from Linear Algebra / 1 \\
1.1 Notation and definitions / 1 \\
1.2 The canonical angles between two subspaces / 5 \\
1.3 Projections / 8 \\
1.4 The gap between two subspaces / 10 \\
1.5 Convergence of a sequence of subspaces / 14 \\
1.6 Reduction of Square matrices / 18 \\
1.7 Spectral decomposition / 27 \\
1.8 Rank and linear independence / 31 \\
1.9 Hermitian and normal matrices / 32 \\
1.10 Non-negative matrices / 33 \\
1.11 Sections and Rayleigh quotients / 34 \\
1.12 Sylvester's equation / 35 \\
1.13 Regular pencils of matrices / 42 \\
1.14 Bibliographical comments / 43 \\
Exercises / 43 \\
2: Elements of Spectral Theory / 61 \\
2.1 Revision of some properties of functions of a
complex variable / 61 \\
2.2 Singularities of the resolvent / 63 \\
2.3 The reduced resolvent and the partial inverse / 73
\\
2.4 The block-reduced resolvent / 76 \\
2.5 Linear perturbations of the matrix A / 79 \\
2.6 Analyticity of the resolvent / 82 \\
2.7 Analyticity of the spectral projection / 84 \\
2.8 The Rellich--Kato expansions / 85 \\
2.9 The Rayleigh--Schr{\"o}dinger expansions / 86 \\
2.10 Non-linear equation and Newton's method / 89 \\
2.11 Modified methods / 92 \\
2.12 The local approximate inverse and the method of
residual correction / 95 \\
2.13 Bibliographical comments / 98 \\
Exercises / 98 \\
3: Why Compute Eigenvalues? / 111 \\
3.1 Differential equations and difference equations /
111 \\
3.2 Markov chains / 114 \\
3.3 Theory of economics / 117 \\
3.4 Factorial analysis of data / 119 \\
3.5 The dynamics of structures / 120 \\
3.6 Chemistry / 122 \\
3.7 Fredholm's integral equation / 124 \\
3.8 Bibliographical comments / 126 \\
Exercises / 126 \\
4: Error Analysis / 149 \\
4.1 Revision of the conditioning of a System / 149 \\
4.2 Stability of a spectral problem / 150 \\
4.3 A priori analysis of errors / 165 \\
4.4 A posteriori analysis of errors / 170 \\
4.5 A is almost diagonal / 177 \\
4.6 A is Hermitian / 180 \\
4.7 Bibliographical comments / 190 \\
Exercises / 191 \\
5: Foundations of Methods for Computing Eigenvalues /
205 \\
5.1 Convergence of a Krylov sequence of subspaces / 205
\\
5.2 The method of subspace iteration / 208 \\
5.3 The power method / 213 \\
5.4 The method of inverse iteration / 217 \\
5.5 The $Q R$ algorithm / 221 \\
5.6 Hermitian matrices / 226 \\
5.7 The $Q Z$ algorithm / 226 \\
5.8 Newton's method and the Rayleigh quotient iteration
/ 227 \\
5.9 Modified Newton's method and simultaneous inverse
iterations / 228 \\
5.10 Bibliographical comments / 235 \\
Exercises / 235 \\
6: Numerical Methods for Large Matrices / 251 \\
6.1 The principle of the methods / 251 \\
6.2 The method of subspace iteration revisited / 253
\\
6.3 The Lanczos method / 257 \\
6.4 The block Lanczos method / 266 \\
6.5 The generalized problem $K x = I M x$ / 270 \\
6.6 Arnoldi's method / 272 \\
6.7 Oblique projections / 279 \\
6.8 Bibliographical comments / 280 \\
Exercises / 281 \\
7: Chebyshev's Iterative Methods / 293 \\
7.1 Elements of the theory of uniform approximation for
a compact set in C / 293 \\
7.2 Chebyshev polynomials of a real variable / 299 \\
7.3 Chebyshev polynomials of a complex variable / 300
\\
7.4 The Chebyshev acceleration for the power method /
304 \\
7.5 The Chebyshev iteration method / 305 \\
7.6 Simultaneous Chebyshev iterations (with projection)
/ 308 \\
7.7 Determination of the optimal parameters / 311 \\
7.8 Least Squares polynomials on a polygon / 312 \\
7.9 The hybrid methods of Saad / 314 \\
7.10 Bibliographical comments / 316 \\
Exercises / 316 \\
Appendices / 323 \\
A Solution to Exercises / 323 \\
B References for Exercises / 367 \\
C References / 371 \\
Index / 378",
}
@InProceedings{Brunet:1986:CTS,
author = "Marie-Christine Brunet and Fran{\c{c}}oise Chatelin",
editor = "R. Vichnevetsky and J. Vignes",
booktitle = "Numerical Mathematics and Applications",
title = "{CESTAC}, a Tool for a Stochastic Round-off Error
Analysis in Scientific Computing",
publisher = "Elsevier Science Publishers B.V. (North-Holland)",
address = pub-NH:adr,
pages = "11--20",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Chatelin:1990:PRE,
author = "Fran{\c{c}}oise Chatelin and Marie-Christine Brunet",
editor = "M. G. Cox and S. J. Hammarling",
booktitle = "Reliable Numerical Computation",
title = "A Probabilistic Round-off Error Propagation Model.
{Application} to the Eigenvalue Problem",
publisher = pub-OUP,
pages = "139--160",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@PhdThesis{Cheng:1998:SIM,
author = "Sheung Hun Cheng",
title = "Symmetric Indefinite Matrices: Linear System Solvers
and Modified Inertia Problems",
school = inst-U-Manchester,
address = inst-U-Manchester:adr,
pages = "150",
month = jan,
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Chan:1988:EWC,
author = "Tony F. Chan and David E. Foulser",
title = "Effectively Well-Conditioned Linear Systems",
journal = j-SISSC,
volume = "9",
number = "6",
pages = "963--969",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Chatelin:1992:ECT,
author = "Fran{\c{c}}oise Chatelin and Val{\'e}rie Frayss{\'e}",
editor = "R. Beauwens and P. de Groen",
booktitle = "Iterative Methods in Linear Algebra",
title = "Elements of a Condition Theory for the Computational
Analysis of Algorithms",
publisher = "Elsevier Science Publishers B.V. (North-Holland)",
address = pub-NH:adr,
pages = "15--25",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Chaitin-Chatelin:1996:LFP,
author = "Fran{\c{c}}oise Chaitin-Chatelin and Val{\'e}rie
Frayss{\'e}",
title = "Lectures on Finite Precision Computations",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xv + 235",
year = "1996",
ISBN = "0-89871-358-7",
ISBN-13 = "978-0-89871-358-9",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Chartres:1967:CEB,
author = "Bruce A. Chartres and James C. Geuder",
title = "Computable Error Bounds for Direct Solution of Linear
Equations",
journal = j-ACM,
volume = "14",
number = "1",
pages = "63--71",
year = "1967",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Chu:1985:NEE,
author = "Eleanor Chu and Alan George",
title = "A Note on Estimating the Error in {Gaussian}
Elimination Without Pivoting",
journal = j-SIGNUM,
volume = "20",
number = "2",
pages = "2--7",
year = "1985",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
}
@Article{Cohen:1983:CCP,
author = "Marty S. Cohen and T. E. Hull and V. Carl Hamacher",
title = "{CADAC}: {A} Controlled-Precision Decimal Arithmetic
Unit",
journal = j-IEEE-C,
volume = "C-32",
number = "4",
pages = "370--377",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Chan:1992:SAR,
author = "T. F. Chan and P. C. Hansen",
title = "Some Applications of the Rank Revealing {QR}
Factorization",
journal = j-SISSC,
volume = "13",
number = "3",
pages = "727--741",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Christiansen:1994:ECN,
author = "S{\o}ren Christiansen and Per Christian Hansen",
title = "The Effective Condition Number Applied to Error
Analysis of Certain Boundary Collocation Methods",
journal = j-JCAM,
volume = "54",
pages = "15--36",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Cheng:2001:PIB,
author = "Sheung Hun Cheng and Nicholas J. Higham",
editor = "Rizos Sakellariou and John Keane and John Gurd and Len
Freeman",
booktitle = "Euro-Par \textup{2001}, Parallel Processing",
title = "Parallel Implementation of a Block Algorithm for
Matrix 1-Norm Estimation",
volume = "2150",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
pages = "568--577",
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Lecture Notes in Computer Science",
}
@TechReport{Cheng:2001:ILB,
author = "Sheung Hun Cheng and Nicholas J. Higham",
title = "Implementation for {LAPACK} of a Block Algorithm for
Matrix 1-Norm Estimation",
type = t-NAREP,
number = "No. 393",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "19",
month = aug,
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "LAPACK Working Note 152",
}
@Article{Cheng:1998:MCA,
author = "Sheung Hun Cheng and Nicholas J. Higham",
title = "A Modified {Cholesky} Algorithm Based on a Symmetric
Indefinite Factorization",
journal = j-SIMAX,
volume = "19",
number = "4",
pages = "1097--1110",
month = oct,
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Chandrasekaran:1994:BEE,
author = "Shivkumar Chandrasekaran and Ilse C. F. Ipsen",
title = "Backward Errors for Eigenvalue and Singular Value
Decompositions",
journal = j-NUM-MATH,
volume = "68",
pages = "215--223",
year = "1994",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Chandrasekaran:1995:SSC,
author = "Shivkumar Chandrasekaran and Ilse C. F. Ipsen",
title = "On the Sensitivity of Solution Components in Linear
Systems of Equations",
journal = j-SIMAX,
volume = "16",
number = "1",
pages = "93--112",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Cheng:2001:ALM,
author = "Sheung Hun Cheng and Nicholas J. Higham and Charles S.
Kenney and Alan J. Laub",
title = "Approximating the Logarithm of a Matrix to Specified
Accuracy",
journal = j-SIMAX,
volume = "22",
number = "4",
pages = "1112--1125",
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Chan:1979:CSD,
author = "Tony F. Chan and John Gregg Lewis",
title = "Computing Standard Deivations: {Accuracy}",
journal = j-CACM,
volume = "22",
number = "9",
pages = "526--531",
year = "1979",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Chan:1983:DEE,
author = "N. N. Chan and Kim-Hung Li",
title = "Diagonal Elements and Eigenvalues of a Real Symmetric
Matrix",
journal = j-J-MATH-ANAL-APPL,
volume = "91",
pages = "562--566",
year = "1983",
CODEN = "JMANAK",
ISSN = "0022-247x (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
}
@Article{Chan:1983:AFS,
author = "N. N. Chan and Kim-Hung Li",
title = "{Algorithm 115}: {A} {FORTRAN} Subroutine for Finding
a Real Symmetric Matrix with Prescribed Diagonal
Elements and Eigenvalues",
journal = j-COMP-J,
volume = "26",
number = "2",
pages = "184--186",
year = "1983",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Chan:1996:CGM,
author = "Raymond H. Chan and Michael K. Ng",
title = "Conjugate Gradient Methods for {Toeplitz} Systems",
journal = j-SIREV,
volume = "38",
number = "3",
pages = "427--482",
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Cho:1968:TDC,
author = "Choong Yun Cho",
title = "On the Triangular Decomposition of {Cauchy} Matrices",
journal = j-MATH-COMP,
volume = "2",
number = "104",
pages = "819--825",
year = "1968",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Choi:1983:TTH,
author = "Man-Duen Choi",
title = "Tricks or Treats with the {Hilbert} Matrix",
journal = j-AMM,
volume = "90",
pages = "301--312",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Chang:2001:CPA,
author = "{Xiao-Wen} Chang and Christopher C. Paige",
title = "Componentwise Perturbation Analyses for the {QR}
Factorization",
journal = j-NUM-MATH,
volume = "88",
pages = "319--345",
year = "2001",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Chang:1998:SLF,
author = "{Xiao-Wen} Chang and Christopher C. Paige",
title = "On the Sensitivity of the {LU} Factorization",
journal = j-BIT,
volume = "38",
number = "3",
pages = "486--501",
year = "1998",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Chu:2000:FRA,
author = "Moody T. Chu",
title = "A Fast Recursive Algorithm for Constructing Matrices
with Prescribed Eigenvalues and Singular Values",
journal = j-SINUM,
volume = "37",
number = "3",
pages = "1004--1020",
year = "2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Chu:1987:SME,
author = "{King-wah} Eric Chu",
title = "The Solution of the Matrix Equations {$AXB - CXD = E$}
and {$(YA - DZ, YC - BZ) = (E,F)$}",
journal = j-LAA,
volume = "93",
pages = "93--105",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Chu:1999:CMP,
author = "Moody T. Chu",
title = "On Constructing Matrices with Prescribed Singular
Values and Diagonal Elements",
journal = j-LAA,
volume = "288",
pages = "11--22",
year = "1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{OCinneide:1993:EPT,
author = "Colm Art O'Cinneide",
title = "Entrywise Perturbation Theory and Error Analysis for
{Markov} Chains",
journal = j-NUM-MATH,
volume = "65",
pages = "109--120",
year = "1993",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Coomes:1995:RCS,
author = "Brian A. Coomes and H{\"u}seyin Ko{\c{c}}ak and
Kenneth J. Palmer",
title = "Rigorous Computational Shadowing of Orbits of Ordinary
Differential Equations",
journal = j-NUM-MATH,
volume = "69",
number = "4",
pages = "401--421",
year = "1995",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Clenshaw:1955:NSC,
author = "C. W. Clenshaw",
title = "A Note on the Summation of {Chebyshev} Series",
journal = j-MTAC,
volume = "9",
number = "51",
pages = "118--120",
year = "1955",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Cline:1973:EMS,
author = "A. K. Cline",
title = "An Elimination Method for the Solution of Linear Least
Squares Problems",
journal = j-SINUM,
volume = "10",
number = "2",
pages = "283--289",
year = "1973",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Clinger:1990:HRF,
author = "William D. Clinger",
title = "How to Read Floating Point Numbers Accurately",
journal = j-SIGPLAN,
volume = "25",
number = "6",
pages = "92--101",
year = "1990",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Clenshaw:1984:BFP,
author = "C. W. Clenshaw and F. W. J. Olver",
title = "Beyond Floating Point",
journal = j-ACM,
volume = "31",
number = "2",
pages = "319--328",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Codenotti:2001:RAF,
author = "B. Codenotti and M. Leoncini and F. P. Preparata",
title = "The Role of Arithmetic in Fast Parallel Matrix
Inversion",
journal = j-ALGORITHMICA,
volume = "30",
number = "4",
pages = "685--707",
year = "2001",
CODEN = "ALGOEJ",
ISSN = "0178-4617 (print), 1432-0541 (electronic)",
ISSN-L = "0178-4617",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Algorithmica",
journal-URL = "http://link.springer.com/journal/453",
}
@Article{Cline:1976:SUL,
author = "R. E. Cline and R. J. Plemmons",
title = "{$l_2$}-Solutions to Underdetermined Linear Systems",
journal = j-SIREV,
volume = "18",
number = "1",
pages = "92--106",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Cline:1983:SCE,
author = "A. K. Cline and R. K. Rew",
title = "A Set of Counter-Examples to Three Condition Number
Estimators",
journal = j-SISSC,
volume = "4",
number = "4",
pages = "602--611",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Cline:1979:ECN,
author = "A. K. Cline and C. B. Moler and G. W. Stewart and J.
H. Wilkinson",
title = "An Estimate for the Condition Number of a Matrix",
journal = j-SINUM,
volume = "16",
number = "2",
pages = "368--375",
year = "1979",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Cody:1993:AFS,
author = "W. J. Cody and Jerome T. Coonen",
title = "{ALGORITHM 722}: {Functions} to Support the {IEEE}
Standard for Binary Floating-Point Arithmetic",
journal = j-TOMS,
volume = "19",
number = "4",
pages = "443--451",
year = "1993",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Book{Conte:1980:ENA,
author = "Samuel D. Conte and Carl de Boor",
title = "Elementary Numerical Analysis: {An} Algorithmic
Approach",
publisher = pub-MH,
address = "Tokyo",
edition = "Third",
pages = "xii + 432",
year = "1980",
ISBN = "0-07-066228-2",
ISBN-13 = "978-0-07-066228-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Cody:1973:SDN,
author = "William J. {Cody, Jr.}",
title = "Static and Dynamic Numerical Characteristics of
Floating-Point Arithmetic",
journal = j-IEEE-C,
volume = "C-22",
number = "6",
pages = "598--601",
year = "1973",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Cody:1982:ITF,
author = "W. J. Cody",
editor = "Paul C. Messina and Almerico Murli",
booktitle = "Problems and Methodologies in Mathematical Software
Production",
title = "Implementation and Testing of Function Software",
volume = "142",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
pages = "24--47",
year = "1982",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Lecture Notes in Computer Science",
}
@Article{Cody:1988:AMS,
author = "W. J. Cody",
title = "{ALGORITHM 665 MACHAR}: {A} Subroutine to Dynamically
Determine Machine Parameters",
journal = j-TOMS,
volume = "14",
number = "4",
pages = "303--311",
year = "1988",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@InProceedings{Cody:1988:FPS,
author = "W. J. Cody",
editor = "Ramon E. Moore",
booktitle = "Reliability in Computing: {The} Role of Interval
Methods in Scientific Computing",
title = "Floating-Point Standards---{Theory} and Practice",
publisher = pub-AP # ", " # pub-AP:adr-B,
pages = "99--107",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Cody:1993:ACP,
author = "W. J. Cody",
title = "Algorithm 714. {CELEFUNT}: {A} Portable Test Package
for Complex Elementary Functions",
journal = j-TOMS,
volume = "19",
number = "1",
pages = "121",
year = "1993",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Cohen:1974:NPS,
author = "A. M. Cohen",
title = "A Note on Pivot Size in {Gaussian} Elimination",
journal = j-LAA,
volume = "8",
pages = "361--368",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Cohen:1975:IPM,
author = "A. M. Cohen",
title = "The Inverse of a {Pascal} Matrix",
journal = j-MATH-GAZ,
volume = "59",
number = "408",
pages = "111--112",
year = "1975",
CODEN = "MAGAAS",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Mathematical Gazette",
journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}
@InProceedings{Cox:1998:SHQ,
author = "Anthony J. Cox and Nicholas J. Higham",
editor = "D. F. Griffiths and D. J. Higham and G. A. Watson",
booktitle = "Numerical Analysis \textup{1997}, Proceedings of the
\textup{17}th Dundee Biennial Conference",
title = "Stability of {Householder QR} Factorization for
Weighted Least Squares Problems",
volume = "380",
publisher = pub-AWLongman # ", " # pub-AWLongman:adr,
pages = "57--73",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Pitman Research Notes in Mathematics",
}
@Article{Cox:1999:ASN,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Accuracy and Stability of the Null Space Method for
Solving the Equality Constrained Least Squares
Problem",
journal = j-BIT,
volume = "39",
number = "1",
pages = "34--50",
year = "1999",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Cox:1999:BEB,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Backward Error Bounds for Constrained Least Squares
Problems",
journal = j-BIT,
volume = "39",
number = "2",
pages = "210--227",
year = "1999",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Cox:1999:RWB,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Row-Wise Backward Stable Elimination Methods for the
Equality Constrained Least Squares Problem",
journal = j-SIMAX,
volume = "21",
number = "1",
pages = "313--326",
year = "1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Cornea-Hasegan:1999:IFP,
author = "Marius Cornea-Hasegan and Bob Norin",
title = "{IA-64} Floating-Point Operations and the {IEEE}
Standard for Binary Floating-Point Arithmetic",
journal = j-INTEL-TECH-J,
volume = "Q4",
year = "1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "\path|http://developer.intel.com/technology/itj/|",
}
@InProceedings{cool90,
author = "James W. Cooley",
editor = "Stephen G. Nash",
booktitle = "A History of Scientific Computing",
title = "How the {FFT} Gained Acceptance",
publisher = pub-AW # ", " # pub-AW:adr,
pages = "133--140",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Cooley:1994:LFD,
author = "James W. Cooley",
editor = "J. David Brown and Moody T. Chu and Donald C. Ellison
and Robert J. Plemmons",
booktitle = "Proceedings of the {Cornelius Lanczos} International
Centenary Conference",
title = "{Lanczos} and the {FFT}: {A} Discovery Before Its
Time",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "3--9",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Coonen:1981:UDN,
author = "Jerome T. Coonen",
title = "Underflow and the Denormalized Numbers",
journal = j-COMPUTER,
volume = "14",
pages = "75--87",
year = "1981",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computer",
journal-URL = "http://www.computer.org/portal/web/csdl/magazines/computer",
}
@Article{Cope:1979:BSL,
author = "J. E. Cope and B. W. Rust",
title = "Bounds on Solutions of Linear Systems with Inaccurate
Data",
journal = j-SINUM,
volume = "16",
number = "6",
pages = "950--963",
year = "1979",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Clenshaw:1989:LIA,
author = "C. W. Clenshaw and F. W. J. Olver and P. R. Turner",
editor = "Peter R. Turner",
booktitle = "Numerical Analysis and Parallel Processing, Lancaster
1987",
title = "Level-Index Arithmetic: {An} Introductory Survey",
volume = "1397",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
pages = "95--168",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Lecture Notes in Mathematics",
}
@Article{Cottle:1974:MSC,
author = "Richard W. Cottle",
title = "Manifestations of the {Schur} Complement",
journal = j-LAA,
volume = "8",
pages = "189--211",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Cooley:1965:AMC,
author = "James W. Cooley and John W. Tukey",
title = "An Algorithm for the Machine Calculation of Complex
{Fourier} Series",
journal = j-MATH-COMP,
volume = "19",
number = "90",
pages = "297--301",
year = "1965",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Cooley:1993:OPF,
author = "James W. Cooley and John W. Tukey",
title = "On the Origin and Publication of the {FFT} Paper",
journal = "Current Contents",
number = "51--52",
pages = "8--9",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Cody:1980:SME,
author = "William J. {Cody, Jr.} and William Waite",
title = "Software Manual for the Elementary Functions",
publisher = pub-PH,
address = pub-PH:adr,
pages = "x + 269",
year = "1980",
ISBN = "0-13-822064-6",
ISBN-13 = "978-0-13-822064-8",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Coppersmith:1987:MMA,
author = "Don Coppersmith and Shmuel Winograd",
booktitle = "Proceedings of the Nineteenth Annual ACM Symposium on
Theory of Computing",
title = "Matrix Multiplication via Arithmetic Progressions",
publisher = "ACM Press, New York",
pages = "1--6",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Chang:1996:NPA,
author = "{Xiao-Wen} Chang and Christopher C. Paige and G. W.
Stewart",
title = "New Perturbation Analyses for the {Cholesky}
Factorization",
journal = j-IMAJNA,
volume = "16",
number = "4",
pages = "457--484",
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Chang:1997:PAQ,
author = "{Xiao-Wen} Chang and Christopher C. Paige and G. W.
Stewart",
title = "Perturbation Analyses for the {QR} Factorization",
journal = j-SIMAX,
volume = "18",
number = "3",
pages = "775--791",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Crary:1979:VPN,
author = "Fred D. Crary",
title = "A Versatile Precompiler for Nonstandard Arithmetics",
journal = j-TOMS,
volume = "5",
number = "2",
pages = "204--217",
year = "1979",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Book{Inc:1989:UMS,
author = "Cray Research Inc.",
key = "Cray",
title = "{UNICOS} Math and Scientific Library Reference
Manual",
publisher = "Number SR-2081, Version 5.0",
address = "Eagan, MN, USA",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Crout:1941:SME,
author = "Prescott D. Crout",
title = "A Short Method for Evaluating Determinants and Solving
Systems of Linear Equations with Real or Complex
Coefficients",
journal = j-TRANS-AMER-INST-ELEC-ENG,
volume = "60",
pages = "1235--1241",
year = "1941",
CODEN = "TAEEA5",
ISSN = "0096-3860",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Transactions of the American Institute of Electrical Engineers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
}
@Article{Cryer:1968:PSG,
author = "Colin W. Cryer",
title = "Pivot Size in {Gaussian} Elimination",
journal = j-NUM-MATH,
volume = "12",
pages = "335--345",
year = "1968",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Cryer:1973:FTP,
author = "Colin W. Cryer",
title = "The {$LU$}-Factorization of Totally Positive
Matrices",
journal = j-LAA,
volume = "7",
pages = "83--92",
year = "1973",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Cryer:1976:SPT,
author = "Colin W. Cryer",
title = "Some Properties of Totally Positive Matrices",
journal = j-LAA,
volume = "15",
pages = "1--25",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Csanky:1976:FPM,
author = "L. Csanky",
title = "Fast Parallel Matrix Inversion Algorithms",
journal = j-SICOMP,
volume = "5",
number = "4",
pages = "618--623",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Curtis:1972:ASM,
author = "A. R. Curtis and J. K. Reid",
title = "On the Automatic Scaling of Matrices for {Gaussian}
Elimination",
journal = j-JIMA,
volume = "10",
pages = "118--124",
year = "1972",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Cybenko:1986:CME,
author = "George Cybenko and Charles F. {Van Loan}",
title = "Computing the Minimum Eigenvalue of a Symmetric
Positive Definite {Toeplitz} matrix",
journal = j-SISSC,
volume = "7",
number = "1",
pages = "123--131",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Dahlquist:1974:NM,
author = "Germund Dahlquist and {\AA}ke Bj{\"o}rck and Ned
Anderson",
title = "Numerical Methods",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xviii + 573",
year = "1974",
ISBN = "0-13-627315-7",
ISBN-13 = "978-0-13-627315-8",
LCCN = "QA297 .D131 1969",
bibdate = "Tue Dec 14 22:44:59 1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "Translated by Ned Anderson.",
series = "Prentice-Hall Series in Automatic Computation",
acknowledgement = ack-nhfb,
shorttableofcontents = "1: Some General Principles of Numerical
Calculation / 1 \\
2: How to Obtain and Estimate Accuracy in Numerical
Calculations / 21 \\
3: Numerical Uses of Series / 60 \\
4: Approximation of Functions / 81 \\
5: Numerical Linear Algebra / 137 \\
6: Nonlinear Equations / 218 \\
7: Finite Differences with Applications to Numerical
Integration, Differentiation, and Interpolation / 255
\\
8: Differential Equations / 330 \\
9: Fourier Methods / 405 \\
10: Optimization / 422 \\
11: The Monte Carlo Method and Simulation / 448 \\
12: Solutions to Problems / 465 \\
13: Bibliography and Published Algorithms / 536 \\
Index by Subject to Algorithms, 1960--1970 / 548 \\
Appendix Tables / 563 \\
Index / 565",
tableofcontents = "Preface / xvii \\
Conventions / xix \\
1: Some General Principles of Numerical Calculation / 1
\\
1.1. Introduction / 1 \\
1.2. Some Common Ideas and Concepts in Numerical
Methods / 2 \\
1.3. Numerical Problems and Algorithms / 13 \\
1.3.1. Definitions / 13 \\
1.3.2. Recursive Formulas; Homer's Rule / 14 \\
1.3.3. An Example of Numerical Instability / 16 \\
2: How to Obtain and Estimate Accuracy in Numerical
Calculations / 21 \\
2.1. Basic Concepts in Error Estimation / 21 \\
2.1.1. Introduction / 21 \\
2.1.2. Sources of Error / 22 \\
2.1.3. Absolute and Relative Errors / 23 \\
2.1.4. Rounding and Chopping / 24 \\
2.2 Propagation of Errors / 26 \\
2.2.1. Simple Examples of Error Analysis / 26 \\
2.2.2. The General Formula for Error Propagation;
Maximum Error and Standard Error / 29 \\
2.2.3. On the Practical Application of Error Estimation
/ 34 \\
2.2.4. The Use of Experimental Perturbations / 36 \\
2.2.5. Automatic Control of Accuracy / 37 \\
2.3. Number Systems; Floating and Fixed Representation
/ 42 \\
2.3.1. The Position System / 42 \\
2.3.2. Floating and Fixed Representation / 43 \\
2.3.3. Floating Decimal Point / 44 \\
2.3.4. Fixed Decimal Point / 46 \\
2.3.5. Round-off Errors in Computation with Floating
Arithmetic Operations / 46 \\
2.4. Backward Error Analysis; Condition Numbers / 51
\\
2.4.1. Backward Error Analysis / 51 \\
2.4.2. Condition Numbers for Problems and Algorithms /
53 \\
2.4.3. Geometrical Illustration of Error Analysis / 56
\\
3: Numerical Uses of Series / 60 \\
3.1. Elementary Uses of Series / 60 \\
3.1.1. Simple Examples / 60 \\
3.1.2. Estimating the Remainder / 62 \\
3.1.3. Power Series / 65 \\
3.2. Acceleration of Convergence / 71 \\
3.2.1. Slowly Converging Alternating Series / 71 \\
3.2.2. Slowly Converging Series with Positive Terms /
73 \\
3.2.3. Other Simple Ways to Accelerate Convergence / 74
\\
3.2.4. Ill-Conditioned Series / 75 \\
3.2.5. Numerical Use of Divergent Series / 77 \\
4: Approximation of Functions / 81 \\
4.1. Basic Concepts in Approximation / 81 \\
4.1.1. Introduction / 81 \\
4.1.2. The Idea of a Function Space / 84 \\
4.1.3. Norms and Seminorms / 85 \\
4.1.4. Approximation of Functions as a Geometric
Problem in Function Space / 87 \\
4.2. The Approximation of Functions by the Method of
Least Squares / 88 \\
4.2.t. Statement of the Problems / 88 \\
4.2.2. Orthogonal Systems / 89 \\
4.2.3. Solution of the Approximation Problem / 92 \\
4.3. Polynomials / 97 \\
4.3.1. Basic Terminology; the Weierstrass Approximation
Theorem / 97 \\
4.3.2. Triangle Families of Polynomials / 98 \\
4.3.3. A Triangle Family and Its Application to
Interpolation / 99 \\
4.3.4. Equidistant Interpolation and the Runge
Phenomenon / 101 \\
4.4. Orthogonal Polynomials and Applications / 104 \\
4.4.1. Tchebycheff Polynomials / 104 \\
4.4.2. Tchebycheff Interpolation and Smoothing / 106
\\
4.4.3. General Theory of Orthogonal Polynomials / 108
\\
4.4.4. Legendre Polynomials and Gram Polynomials / 113
\\
4.5. Complementary Observations on Polynomial
Approximation / 117 \\
4.5.1. Summary of the Use of Polynomials / 117 \\
4.5.2. Some Inequalities for $E_n(f)$ with Applications
to the Computation of Linear Functionals / 120 \\
4.5.3. Approximation in the Maximum Norm / 124 \\
4.5.4. Economization of Power Series; Standard
Functions / 125 \\
4.5.5. Some Statistical Aspects of the Method of Least
Squares / 126 \\
4.6. Spline Functions / 131 \\
5: Numerical Linear Algebra / 137 \\
5,1. Introduction / 137 \\
5.2. Basic Concepts of Linear Algebra / 138 \\
5.2.1. Fundamental Definitions / 138 \\
5.2.2. Partitioned Matrices / 140 \\
5.2.3. Linear Vector Spaces / 141 \\
5.2.4. Eigenvalues and Similarity Transformations / 142
\\
5.2.5. Singular-Value Decomposition and Pseudo-Inverse
/ 143 \\
5.3. Direct Methods for Solving Systems of Linear
Equations / 146 \\
5.3.1. Triangular Systems / 146 \\
5.3.2. Gaussian Elimination / 147 \\
5.3.3. Pivoting Strategies / 150 \\
5.3.4. $L U$-Decomposition / 152 \\
5.3.5. Compact Schemes for Gaussian Elimination / 157
\\
5.3.6. Inverse Matrices / 159 \\
5.4. Special Matrices / 162 \\
5.4.1. Symmetric Positive-Definite Matrices / 162 \\
5.4.2. Band Matrices / 165 \\
5.4.3. Large-Scale Linear Systems / 168 \\
5.4.4. Other Sparse Matrices / 169 \\
5.5. Error Analysis for Linear Systems / 174 \\
5.5.1. An Ill-Conditioned Example / 174 \\
5.5.2. Vector and Matrix Norms / 175 \\
5.5.3. Perturbation Analysis / 176 \\
5.5.4. Rounding Errors in Gaussian Elimination / 177
\\
5.5.5. Scaling of Linear Systems / 181 \\
5.5.6. Iterative Improvement of a Solution / 183 \\
5.6. Iterative Methods / 188 \\
5.7. Overdetermined Linear Systems / 196 \\
5.7.1. The Normal Equations / 197 \\
5.7.2. Orthogonalization Methods / 201 \\
5.7.3. Improvement of Least-Squares Solutions / 204 \\
5.7.4. Least-Squares Problems with Linear Constraints /
205 \\
5.8. Computation of Eigenvalues and Eigenvectors / 208
\\
5.8.1. The Power Method / 209 \\
5.8.2. Methods Based on Similarity Transformations /
211 \\
5.8.3. Eigenvalues by Equation Solving / 215 \\
5.8.4. The $Q R$-Algorithm / 216 \\
6: Nonlinear Equations / 218 \\
6.1. Introduction / 218 \\
6.2. Initial Approximations; Starting Methods / 219 \\
6.2.1. Introduction / 219 \\
6.2.2. The Bisection Method / 220 \\
6.3. Newton--Raphson's Method / 222 \\
6.4. The Secant Method / 227 \\
6.4.1. Description of the Method / 227 \\
6.4.2. Error Analysis for the Secant Method / 228 \\
6.4.3. Regula Falsi / 230 \\
6.4.4. Other Related Methods / 230 \\
6.5. General Theory of Iteration Methods / 233 \\
6.6. Error Estimation and Attainable Accuracy in
Iteration Methods / 238 \\
6.6.1. Error Estimation / 238 \\
6.6.2. Attainable Accuracy; Termination Criteria / 240
\\
6.7. Multiple Roots / 242 \\
6.8. Algebraic Equations / 243 \\
6.8.1. Introduction / 243 \\
6.8.2. Deflation / 245 \\
6.8.3. Ill-Conditioned Algebraic Equations / 246 \\
6.9. Systems of Nonlinear Equations / 248 \\
6.9.1. Iteration / 249 \\
6.9.2. Newton--Raphson's Method and Some Modifications
/ 249 \\
6.9.3. Other Methods / 251 \\
7: Finite Differences with Applications to Numerical
Integration, Differentiation, and Interpolation / 255
\\
7.1. Difference Operators and Their Simplest Properties
/ 255 \\
7.2. Simple Methods for Deriving Approximation Formulas
and Error Estimates / 263 \\
7.2.1. Statement of the Problems and Some Typical
Examples / 263 \\
7.2.2, Repeated Richardson Extrapolation / 269 \\
7.3. Interpolation / 275 \\
7.3.1. Introduction / 275 \\
7.3.2. When is Linear Interpolation Sufficient? / 276
\\
7.3.3. Newton's General Interpolation Formula / 277 \\
7.3.4. Formulas for Equidistant Interpolation / 279 \\
7.3.5. Complementary Remarks on Interpolation / 282 \\
7.3.6. Lagrange's Interpolation Formula / 284 \\
7.3.7. Hermite Interpolation / 285 \\
7.3.8. Inverse Interpolation / 286 \\
7.4. Numerical Integration / 290 \\
7.4.1. The Rectangle Rule, Trapezoidal Rule, and
Romberg's Method / 291 \\
7.4.2. The Truncation Error of the Trapezoidal Rule /
293 \\
7.4.3. Some Difficulties and Possibilities in Numerical
Integration / 294 \\
7.4.4. The Euler--Maclaurin Summation Formula / 297 \\
7.4.5. Uses of the Euler--Maclaurin Formula / 300 \\
7.4.6. Other Methods for Numerical Integration / 302
\\
7.5. Numerical Differentiation / 307 \\
7.6. The Calculus of Operators / 311 \\
7.6.1. Operator Algebra / 311 \\
7.6.2. Operator Series with Applications / 312 \\
7.7. Functions of Several Variables / 318 \\
7.7.1. Working with One Variable at a Time / 319 \\
7.7.2. Rectangular Grids / 319 \\
7.7.3. Irregular Triangular Grids / 322 \\
8: Differential Equations / 330 \\
8.1. Theoretical Background / 330 \\
8.1.1. Initial-Value Problems for Ordinary Differential
Equations / 330 \\
8.1.2. Error Propagation / 333 \\
8.1.3. Other Differential Equation Problems / 337 \\
8.2. Euler's Method, with Repeated Richardson
Extrapolation / 338 \\
8.3. Other Methods for Initial-Value Problems in
Ordinary Differential Equations / 342 \\
8.3.1. The Modified Midpoint Method / 342 \\
8.3.2. The Power-Series Method / 345 \\
8.3.3. Runge--Kutta Methods / 346 \\
8.3.4. Implicit Methods / 347 \\
8.3.5. Stiff Problems / 349 \\
8.3.6. Control of Step Size / 350 \\
8.3.7. A Finite-Difference Method for a Second-Order
Equation / 352 \\
8.4. Orientation on Boundary and Eigenvalue Problems
for Ordinary Differential Equations / 359 \\
8.4.1. Introduction / 359 \\
8.4.2. The Shooting Method / 359 \\
8.4.3. The Band Matrix Method / 361 \\
8.4.4. Numerical Example of an Eigenvalue Problem / 363
\\
8.5. Difference Equations / 367 \\
8.5.1. Homogeneous Linear Difference Equations with
Constant Coefficients / 368 \\
8.5.2. General Linear Difference Equations / 370 \\
8.5.3. Analysis of a Numerical Method with the Help of
a Test Problem / 372 \\
8.5.4. Linear Multistep Methods / 375 \\
8.6. Partial Differential Equations / 383 \\
8.6.1. Introduction / 383 \\
8.6.2. An Example of an Initial-Value Problem / 384 \\
8.6.3. An Example of a Boundary-Value Problem / 389 \\
8.6.4. Methods of Undetermined Coefficients and
Variational Methods / 392 \\
8.6.5. Finite-Element Methods / 395 \\
8.6.6. Integral Equations / 397 \\
9: Fourier Methods / 405 \\
9.1. Introduction / 405 \\
9.2. Basic Formulas and Theorems in Fourier Analysis /
406 \\
9.2.1. Functions of One Variable / 406 \\
9.2.2. Functions of Several Variables / 411 \\
9.3. Fast Fourier Analysis / 413 \\
9.3.1. An Important Special Case / 413 \\
9.3.2. Fast Fourier Analysis, General Case / 414 \\
9.4. Periodic Continuation of a Nonperiodic Function /
417 \\
9.5. The Fourier Integral Theorem / 419 \\
10: Optimization / 422 \\
10.1. Statement of the Problem, Definitions, and Normal
Form / 422 \\
10.2. The Simplex Method / 426 \\
10.3. Duality / 435 \\
10.4. The Transportation Problem and Some Other
Optimization Problems / 436 \\
10.5. Nonlinear Optimization Problems / 438 \\
10.5.1. Basic Concepts and Introductory Examples / 438
\\
10.5.2. Line Search / 440 \\
10.5.3. Algorithms for Unconstrained Optimization / 441
\\
10.5.4. Overdetermined Nonlinear Systems / 443 \\
10.5.5. Constrained Optimization / 444 \\
11: The Monte Carlo Method and Simulation / 448 \\
11.1. Introduction / 448 \\
11.2. Random Digits and Random Numbers / 449 \\
11.3. Applications; Reduction of Variance / 455 \\
11.4. Pseudorandom Numbers / 463 \\
12: Solutions to Problems / 465 \\
13: Bibliography and Published Algorithms / 536 \\
13.1. Introduction / 536 \\
13.2. General Literature in Numerical Analysis / 536
\\
13.3. Tables, Collections of Formulas, and Problems /
539 \\
13.4. Error Analysis and Approximation of Functions /
540 \\
13.5. Linear Algebra and Nonlinear Systems of Equations
/ 541 \\
13.6. Interpolation, Numerical Integration, and
Numerical Treatment of Differential Equations / 543 \\
13.7. Optimization; Simulation / 545 \\
13.8. Reviews, Abstracts and Other Periodicals / 547
\\
13.9. Survey of Published Algorithms / 548 \\
Index by Subject to Algorithms, 1960--1970 / 548 \\
Appendix Tables / 563 \\
Index / 565",
}
@Article{Davies:2000:NSG,
author = "Philip I. Davies and Nicholas J. Higham",
title = "Numerically Stable Generation of Correlation Matrices
and their Factors",
journal = j-BIT,
volume = "40",
number = "4",
pages = "640--651",
year = "2000",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Dahlquist:1983:MMM,
author = "G. Dahlquist",
title = "On matrix majorants and minorants, with applications
to differential equations",
journal = j-LAA,
volume = "52/53",
pages = "199--216",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Dax:1977:PTS,
author = "Achiya Dax and S. Kaniel",
title = "Pivoting Techniques for Symmetric {Gaussian}
Elimination",
journal = j-NUM-MATH,
volume = "28",
pages = "221--241",
year = "1977",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Danloy:1976:CSH,
author = "B. Danloy",
title = "On the Choice of Signs for {Householder's} Matrices",
journal = j-JCAM,
volume = "2",
number = "1",
pages = "67--69",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Day:1988:GGE,
author = "Jane M. Day and Brian Peterson",
title = "Growth in {Gaussian} Elimination",
journal = j-AMM,
volume = "95",
number = "6",
pages = "489--513",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Davis:1984:MNI,
author = "Philip J. Davis and Philip Rabinowitz",
title = "Methods of Numerical Integration",
publisher = pub-AP,
address = pub-AP:adr-L,
edition = "Second",
pages = "xiv + 612",
year = "1984",
ISBN = "0-12-206360-0",
ISBN-13 = "978-0-12-206360-2",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Datta:1988:MEA,
author = "Karabi Datta",
title = "The Matrix Equation {$XA-BX=R$} and Its Applications",
journal = j-LAA,
volume = "109",
pages = "91--105",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Davis:1979:CM,
author = "Philip J. Davis",
title = "Circulant Matrices",
publisher = pub-Wiley,
address = pub-Wiley:adr,
pages = "xv + 250",
year = "1979",
ISBN = "0-471-05771-1",
ISBN-13 = "978-0-471-05771-0",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Dax:1982:PPS,
author = "Achiya Dax",
title = "Partial Pivoting Strategies for Symmetric {Gaussian}
Elimination",
journal = j-MATH-PROG,
volume = "22",
pages = "288--303",
year = "1982",
CODEN = "MHPGA4",
ISSN = "0025-5610",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
}
@Article{Dax:1990:CLS,
author = "Achiya Dax",
title = "The Convergence of Linear Stationary Iterative
Processes for Solving Singular Unstructured Systems of
Linear Equations",
journal = j-SIREV,
volume = "32",
number = "4",
pages = "611--635",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Dongarra:1979:LUG,
author = "J. J. Dongarra and J. R. Bunch and C. B. Moler and G.
W. Stewart",
title = "{LINPACK} Users' Guide",
publisher = pub-SIAM,
address = pub-SIAM:adr,
year = "1979",
ISBN = "0-89871-172-X",
ISBN-13 = "978-0-89871-172-1",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Boor:1977:BEA,
author = "Carl de Boor and Allan Pinkus",
title = "Backward Error Analysis for Totally Positive Linear
Systems",
journal = j-NUM-MATH,
volume = "27",
pages = "485--490",
year = "1977",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Dongarra:19xx:SLB,
author = "J. J. Dongarra and J. J. Du Croz and I. S. Duff and S.
J. Hammarling",
title = "A Set of {Level 3} Basic Linear Algebra Subprograms",
journal = j-TOMS,
volume = "16",
pages = "1--17",
year = "{\noopsort{a}}1990",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Dongarra:19xx:ASL,
author = "J. J. Dongarra and J. J. Du Croz and I. S. Duff and S.
J. Hammarling",
title = "Algorithm 679. {A} set of {Level 3} Basic Linear
Algebra Subprograms: {Model} Implementation and Test
Programs",
journal = j-TOMS,
volume = "16",
pages = "18--28",
year = "{\noopsort{b}}1990",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Dongarra:19xx:ESF,
author = "Jack J. Dongarra and Jeremy J. Du Croz and Sven J.
Hammarling and Richard J. Hanson",
title = "An Extended Set of {Fortran} Basic Linear Algebra
Subprograms",
journal = j-TOMS,
volume = "14",
number = "1",
pages = "1--17",
year = "{\noopsort{a}}1988",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Dongarra:19xx:AES,
author = "Jack J. Dongarra and Jeremy J. Du Croz and Sven J.
Hammarling and Richard J. Hanson",
title = "Algorithm 656. {An} Extended Set of {Fortran} Basic
Linear Algebra Subprograms: {Model} Implementation and
Test Programs",
journal = j-TOMS,
volume = "14",
number = "1",
pages = "18--32",
year = "{\noopsort{b}}1988",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@InProceedings{Demmel:1992:DPH,
author = "James W. Demmel and J. J. Dongarra and W. Kahan",
editor = "D. F. Griffiths and G. A. Watson",
booktitle = "Numerical Analysis \textup{1991}, Proceedings of the
\textup{14}th Dundee Conference",
title = "On Designing Portable High Performance Numerical
Libraries",
volume = "260",
publisher = pub-Longman-ST # ", " # pub-Longman-ST:adr,
pages = "69--84",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Pitman Research Notes in Mathematics",
}
@Article{Demmel:2001:CCE,
author = "James W. Demmel and Benjamin Diament and Gregorio
Malajovich",
title = "On the Complexity of Computing Error Bounds",
journal = j-FOCM,
volume = "1",
number = "1",
pages = "101--125",
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Demmel:1995:CSB,
author = "James W. Demmel and Inderjit Dhillon and Huan Ren",
title = "On the Correctness of Some Bisection-Like Parallel
Eigenvalue Algorithms in Floating Point Arithmetic",
journal = j-ETNA,
volume = "3",
pages = "116--149",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Dongarra:1998:NLA,
author = "Jack J. Dongarra and Iain S. Duff and Danny C.
Sorensen and Henk A. van der Vorst",
title = "Numerical Linear Algebra for High-Performance
Computers",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xviii + 342",
year = "1998",
ISBN = "0-89871-428-1",
ISBN-13 = "978-0-89871-428-9",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Demmel:1992:SBA,
author = "James W. Demmel and Nicholas J. Higham",
title = "Stability of Block Algorithms with Fast Level-3
{BLAS}",
journal = j-TOMS,
volume = "18",
number = "3",
pages = "274--291",
month = sep,
year = "1992",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Demmel:1993:IEB,
author = "James W. Demmel and Nicholas J. Higham",
title = "Improved Error Bounds for Underdetermined System
Solvers",
journal = j-SIMAX,
volume = "14",
number = "1",
pages = "1--14",
month = jan,
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Dekker:1989:RGJ,
author = "T. J. Dekker and W. Hoffmann",
title = "Rehabilitation of the {Gauss--Jordan} Algorithm",
journal = j-NUM-MATH,
volume = "54",
pages = "591--599",
year = "1989",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Demmel:1987:CSE,
author = "James W. Demmel and Bo K{\aa}gstr{\"o}m",
title = "Computing Stable Eigendecompositions of Matrix
Pencils",
journal = j-LAA,
volume = "88/89",
pages = "139--186",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Demmel:1988:ASI,
author = "James W. Demmel and Bo K{\aa}gstr{\"o}m",
title = "Accurate Solutions of Ill-Posed Problems in Control
Theory",
journal = j-SIMAX,
volume = "9",
number = "1",
pages = "126--145",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Demmel:1990:ASV,
author = "James W. Demmel and W. Kahan",
title = "Accurate Singular Values of Bidiagonal Matrices",
journal = j-SISSC,
volume = "11",
number = "5",
pages = "873--912",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Dekker:1971:FPT,
author = "T. J. Dekker",
title = "A Floating-Point Technique for Extending the Available
Precision",
journal = j-NUM-MATH,
volume = "18",
pages = "224--242",
year = "1971",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Demmel:1985:IAS,
author = "James W. Demmel and F. Kr{\"u}ckeberg",
title = "An Interval Algorithm for Solving Systems of Linear
Equations to Prespecified Accuracy",
journal = j-COMPUTING,
volume = "34",
pages = "117--129",
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@InProceedings{Dongarra:2000:RAS,
author = "Jack Dongarra and Victor Eijkhout and Piotr Luszczek",
booktitle = "Proceedings of the 1st SGI Users Conference",
title = "Recursive Approach in Sparse Matrix {LU}
Factorization",
organization = "ACC Cyfronet UMM",
address = "Cracow, Poland",
pages = "409--418",
month = oct,
year = "2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Demmel:1994:FNA,
author = "James W. Demmel and Xiaoye Li",
title = "Faster Numerical Algorithms via Exception Handling",
journal = j-IEEE-C,
volume = "43",
number = "8",
pages = "983--992",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Demmel:1989:TMG,
author = "James W. Demmel and A. McKenney",
title = "A Test Matrix Generation Suite",
type = "Preprint",
number = "MCS-P69-0389",
institution = inst-MCS-Argonne,
address = inst-MCS-Argonne:adr,
pages = "16",
month = mar,
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "LAPACK Working Note 9",
}
@Article{Demeure:1989:FFV,
author = "C{\'e}dric J. Demeure",
title = "Fast {$QR$} Factorization of {Vandermonde} Matrices",
journal = j-LAA,
volume = "122/3/4",
pages = "165--194",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Demeure:1990:FCV,
author = "C{\'e}dric J. Demeure",
title = "{$QR$} Factorization of Confluent {Vandermonde}
Matrices",
journal = j-IEEE-ASSP,
volume = "38",
number = "10",
pages = "1799--1802",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Unpublished{Demmel:2001:NAF,
author = "James W. Demmel",
title = "A Note on Accurate Floating Point Summation",
pages = "5",
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Manuscript",
}
@Article{Demmel:1983:CNE,
author = "James W. Demmel",
title = "The Condition Number of Equivalence Transformations
that Block Diagonalize Matrix Pencils",
journal = j-SINUM,
volume = "20",
number = "3",
pages = "599--610",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Demmel:1984:URN,
author = "James W. Demmel",
title = "Underflow and the Reliability of Numerical Software",
journal = j-SISSC,
volume = "5",
number = "4",
pages = "887--919",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Demmel:1987:CND,
author = "James W. Demmel",
title = "On Condition Numbers and the Distance to the Nearest
Ill-Posed Problem",
journal = j-NUM-MATH,
volume = "51",
pages = "251--289",
year = "1987",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@InProceedings{Demmel:1987:EAA,
author = "James W. Demmel",
editor = "Mary Jane Irwin and Renato Stefanelli",
booktitle = "Proceedings of the Eighth Symposium on Computer
Arithmetic, Como, Italy",
title = "On Error Analysis in Arithmetic With Varying Relative
Precision",
publisher = "IEEE Computer Society, Washington, D.C.",
pages = "148--152",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Demmel:1989:FPE,
author = "James W. Demmel",
title = "On Floating Point Errors in {Cholesky}",
type = "Technical Report",
number = "CS-89-87",
institution = inst-CS-U-Tenn,
address = inst-CS-U-Tenn:adr,
pages = "6",
month = oct,
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "LAPACK Working Note 14",
}
@Article{Demmel:1991:OIA,
author = "James W. Demmel",
title = "On the Odor of {IEEE} Arithmetic",
journal = j-NA-DIGEST,
volume = "Volume 91, Issue 39",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "(Response to a message ``IEEE Arithmetic Stinks'' in
Volume 91, Issue 33)",
fjournal = "NA Digest",
}
@Article{demm92,
author = "James W. Demmel",
title = "The Componentwise Distance to the Nearest Singular
Matrix",
journal = j-SIMAX,
volume = "13",
number = "1",
pages = "10--19",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Demmel:1992:OPN,
author = "James W. Demmel",
title = "Open Problems in Numerical Linear Algebra",
type = "IMA Preprint Series",
number = "\#961",
institution = inst-IMA,
address = inst-IMA:adr,
pages = "21",
month = apr,
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "LAPACK Working Note 47",
}
@TechReport{Demmel:1992:SFP,
author = "James W. Demmel",
title = "A Specification for Floating Point Parallel Prefix",
type = "Technical Report",
number = "CS-92-167",
institution = inst-CS-U-Tenn,
address = inst-CS-U-Tenn:adr,
pages = "8",
month = jul,
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "LAPACK Working Note 49",
}
@InProceedings{Demmel:1993:TPN,
author = "James W. Demmel",
editor = "Marc S. Moonen and Gene H. Golub and Bart L. De Moor",
booktitle = "Linear Algebra for Large Scale and Real-Time
Applications",
title = "Trading Off Parallelism and Numerical Stability",
volume = "232",
publisher = pub-Kluwer # ", " # pub-Kluwer:adr,
pages = "49--68",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "NATO ASI Series E",
}
@Book{Demmel:1997:ANL,
author = "James W. Demmel",
title = "Applied Numerical Linear Algebra",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xi + 419",
year = "1997",
ISBN = "0-89871-389-7",
ISBN-13 = "978-0-89871-389-3",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Demmel:1999:ASV,
author = "James W. Demmel",
title = "Accurate Singular Value Decompositions of Structured
Matrices",
journal = j-SIMAX,
volume = "21",
number = "2",
pages = "562--580",
year = "1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Duff:1986:DMS,
author = "I. S. Duff and A. M. Erisman and J. K. Reid",
title = "Direct Methods for Sparse Matrices",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xiii + 341",
year = "1986",
ISBN = "0-19-853408-6 (hardcover), 0-19-853421-3 (paperback)",
ISBN-13 = "978-0-19-853408-2 (hardcover), 978-0-19-853421-1
(paperback)",
LCCN = "QA188 .D841 1986",
bibdate = "Tue Dec 14 22:47:43 1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$37.50",
acknowledgement = ack-nhfb,
shorttableofcontents = "1: Introduction \\
2: Sparse matrices: storage schemes and simple
Operations \\
3: Gaussian elimination for dense matrices: the
algebraic problem \\
4: Gaussian elimination for dense matrices: numerical
considerations \\
5: Gaussian elimination for sparse matrices: an
introduction \\
6: Reduction to block triangular form \\
7: Local pivotal strategies for sparse matrices \\
8: Ordering sparse matrices to special forms \\
9: Implementing Gaussian elimination: ANALYSE with
numerical values \\
10: Implementing Gaussian elimination with symbolic
ANALYSE \\
11: Partitioning, matrix modification, and tearing \\
12: Other sparsity-oriented issues \\
Appendix A: Matrix and vector norms / 281 \\
Appendix B: The LINPACK condition number estimate / 285
\\
Appendix C: Fortran Conventions / 287 \\
Appendix D: Pictures of sparse matrices / 289 \\
Solutions to selected exercises / 297 \\
References / 313 \\
Author index / 327 \\
Subject index / 331",
tableofcontents = "1: Introduction \\
1.1 Introduction / 1 \\
1.2 Graph theory / 2 \\
1.3 Example / 4 \\
1.4 Advanced Computer architectures / 9 \\
1.5 Problem formulation / 11 \\
1.6 A sparse matrix test collection / 14 \\
2: Sparse matrices: storage schemes and simple
Operations \\
2.1 Introduction / 19 \\
2.2 Sparse vector storage / 19 \\
2.3 Inner product of two packed vectors / 20 \\
2.4 Adding packed vectors / 21 \\
2.5 Use of full-sized arrays / 22 \\
2.6 Coordinate scheme for storing sparse matrices / 23
\\
2.7 Sparse matrix as a collection of sparse vectors /
24 \\
2.8 Linked lists / 25 \\
2.9 Sparse matrix in row-linked list / 28 \\
2.10 Generating collections of sparse vectors / 30 \\
2.11 Access by rows and columns / 31 \\
2.12 Matrix by vector products / 32 \\
2.13 Matrix by matrix products / 33 \\
2.14 Permutation matrices / 34 \\
2.15 Clique (or finite-element) storage / 36 \\
2.16 Comparisons between sparse matrix structures / 37
\\
3: Gaussian elimination for dense matrices: the
algebraic problem \\
3.1 Introduction / 41 \\
3.2 Solution of triangular Systems / 41 \\
3.3 Gaussian elimination / 43 \\
3.4 Required row interchanges / 45 \\
3.5 Relationship with $L U$ factorization / 46 \\
3.6 Equivalent factorization methods, including
Doolittle and Crout / 49 \\
3.7 Computational sequences / 51 \\
3.8 Symmetric matrices / 53 \\
3.9 Gauss--Jordan elimination / 55 \\
3.10 Multiple right-hand sides and inverses / 56 \\
3.11 Computational cost / 57 \\
3.12 Block factorization / 59 \\
4: Gaussian elimination for dense matrices: numerical
considerations \\
4.1 Introduction / 65 \\
4.2 Computer arithmetic error / 66 \\
4.3 Algorithm instability / 67 \\
4.4 Controlling algorithm stability / 69 \\
4.5 Monitoring the stability / 72 \\
4.6 Special stability considerations / 76 \\
4.7 Solving indefinite symmetric systems / 77 \\
4.8 Ill-conditioning: introduction / 78 \\
4.9 Ill-conditioning: theoretical discussion / 79 \\
4.10 Ill-conditioning: automatic detection / 81 \\
4.11 Iterative refinement / 85 \\
4.12 Scaling / 86 \\
4.13 Prevention of ill-conditioning / 88 \\
4.14 Overall error bound / 89 \\
5: Gaussian elimination for sparse matrices: an
introduction \\
5.1 Introduction / 93 \\
5.2 Features of a sparse matrix code / 94 \\
5.3 Orderings / 96 \\
5.4 Numerical stability in sparse computation / 98 \\
5.5 Estimating condition numbers in sparse computation
/ 100 \\
5.6 The ANALYSE phase / 101 \\
5.7 The FACTORIZE and SOLVE phases / 102 \\
5.8 Writing compared with using sparse matrix Software
/ 103 \\
6: Reduction to block triangular form \\
6.1 Introduction / 105 \\
6.2 Background for finding a transversal / 107 \\
6.3 A depth-first search algorithm for transversal
extension / 109 \\
6.4 Analysis of the depth-first search transversal
algorithm / 111 \\
6.5 Implementation of the transversal algorithm / 112
\\
6.6 Symmetric permutations to block triangular form /
113 \\
6.7 The algorithm of Sargent and Westerberg / 114 \\
6.8 Tarjan's algorithm / 117 \\
6.9 Implementation of Tarjan's algorithm / 120 \\
6.10 Essential uniqueness of the block triangular form
/ 121 \\
6.11 Experience with block triangular forms / 122 \\
6.12 Maximum transversals / 124 \\
7: Local pivotal strategies for sparse matrices \\
7.1 Introduction / 127 \\
7.2 The Markowitz criterion / 128 \\
7.3 Minimum degree (Tinney scheme 2) / 129 \\
7.4 Simpler strategies / 130 \\
7.5 Local minimum fill-in / 133 \\
7.6 Other local strategies / 135 \\
7.7 The effect of tie-breaking on the minimum degree
algorithm / 136 \\
7.8 Numerical pivoting / 139 \\
7.9 Sparsity in the right-hand side and partial
Solution / 140 \\
7.10 Variability-type ordering / 143 \\
7.11 The Symmetric indefinite case / 145 \\
7.12 Solution methods based on orthogonalization / 145
\\
8: Ordering sparse matrices to special forms \\
8.1 Introduction / 149 \\
8.2 Desirable forms / 149 \\
8.3 Band and variable-band matrices / 151 \\
8.4 Ordering for small bandwidth / 153 \\
8.5 Refined quotient trees / 157 \\
8.6 One-way dissection / 161 \\
8.7 Nested dissection / 163 \\
8.8 The Boeing version of the Hellerman--Rarick
algorithm / 168 \\
8.9 The Hellerman--Rarick ordering / 172 \\
9: Implementing Gaussian elimination: ANALYSE with
numerical values \\
9.1 Introduction / 177 \\
9.2 Markowitz ANALYSE / 178 \\
9.3 FACTORIZE / 183 \\
9.4 SOLVE / 186 \\
9.5 Switching to full form / 188 \\
9.6 Loop-free code / 191 \\
9.7 Interpretative code / 192 \\
9.8 A posteriori ordering for stability / 193 \\
9.9 The use of drop tolerances to preserve sparsity /
195 \\
10: Implementing Gaussian elimination with symbolic
ANALYSE 10.1 Introduction / 199 \\
10.2 Band methods / 200 \\
10.3 Variable-band (profile) methods / 204 \\
10.4 Special methods for banded Systems / 205 \\
10.5 Frontal methods for finite-element problems / 210
\\
10.6 Frontal methods for non-element problems / 216 \\
10.7 Multifrontal (substructuring) methods for
finite-element problems / 218 \\
10.8 Multifrontal methods for non-element problems /
222 \\
10.9 Minimum degree ordering / 226 \\
10.10 Generating static data structures for FACTORIZE /
229 \\
10.11 Numerical FACTORIZE and SOLVE using static data
structures / 232 \\
10.12 Accommodating numerical pivoting within static
data structures / 233 \\
10.13 Nested dissection, refined quotient tree, and
one-way dissection / 234 \\
10.14 Effects of Computer architecture / 234 \\
11: Partitioning, matrix modification, and tearing \\
11.1 Introduction / 239 \\
11.2 Exploiting the partitioned form / 240 \\
11.3 Using partitioning to handle low-rank
perturbations / 242 \\
11.4 The matrix modification formula / 243 \\
11.5 Low-rank modifications / 244 \\
11.6 Use of the modification formula to solve equations
/ 245 \\
11.7 Perturbations that are full-rank submatrices / 247
\\
11.8 The equivalence of modification and partitioning /
249 \\
11.9 Modifications that change the matrix Order / 250
\\
11.10 Artificial perturbations / 251 \\
11.11 Branch tearing / 252 \\
11.12 Node tearing / 254 \\
11.13 Implementation of node and branch tearing / 255
\\
11.14 Manual choice of partitions and tear sets / 255
\\
11.15 Automatic choice of partitions and tear sets /
257 \\
11.16 Nonlinear tearing / 259 \\
11.17 Conclusions / 260 \\
12: Other sparsity-oriented issues \\
12.1 Introduction / 265 \\
12.2 Sparsity in nonlinear computations / 266 \\
12.3 Estimating a sparse Jacobian matrix / 267 \\
12.4 Updating a sparse Hessian matrix / 269 \\
12.5 Approximating a sparse matrix by a
positive-definite one / 270 \\
12.6 The inverse of a sparse matrix / 271 \\
12.7 Computing entries of the inverse of a sparse
matrix / 273 \\
12.8 Sparsity constrained backward error analysis / 275
\\
12.9 Assembling large finite-element matrices to band
form / 277 \\
12.10 Hypermatrices / 278 \\
Appendix A: Matrix and vector norms / 281 \\
Appendix B: The LINPACK condition number estimate / 285
\\
Appendix C: Fortran Conventions / 287 \\
Appendix D: Pictures of sparse matrices / 289 \\
Solutions to selected exercises / 297 \\
References / 313 \\
Author index / 327 \\
Subject index / 331",
}
@Article{Dembo:1982:INM,
author = "Ron S. Dembo and Stanley C. Eisenstat and Trond
Steihaug",
title = "Inexact {Newton} Methods",
journal = j-SINUM,
volume = "19",
number = "2",
pages = "400--408",
year = "1982",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Descloux:1963:NRE,
author = "J. Descloux",
title = "Note on the Round-Off Errors in Iterative Processes",
journal = j-MATH-COMP,
volume = "17",
pages = "18--27",
year = "1963",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Dennis:1983:NMU,
author = "John E. {Dennis, Jr.} and Robert B. Schnabel",
title = "Numerical Methods for Unconstrained Optimization and
Nonlinear Equations",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xiii + 378",
year = "1983",
ISBN = "0-13-627216-9 (original), 0-89871-364-1 (reprint)",
ISBN-13 = "978-0-13-627216-8 (original), 978-0-89871-364-0
(reprint)",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted by SIAM (1996).",
}
@Article{Dennis:1991:DSM,
author = "John E. {Dennis, Jr.} and Virginia Torczon",
title = "Direct Search Methods on Parallel Machines",
journal = j-SIOPT,
volume = "1",
number = "4",
pages = "448--474",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Dennis:1984:IQN,
author = "John E. {Dennis, Jr.} and Homer F. Walker",
title = "Inaccuracy in Quasi-{Newton} Methods: {Local}
Improvement Theorems",
journal = j-MATH-PROG-STUDY,
volume = "22",
pages = "70--85",
year = "1984",
CODEN = "MPSTDF",
ISSN = "0303-3929",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Mathematical Programming Study",
}
@Article{Dennis:1993:SLC,
author = "John E. {Dennis, Jr.} and Henry Wolkowicz",
title = "Sizing and Least-Change Secant Methods",
journal = j-SINUM,
volume = "30",
number = "5",
pages = "1291--1314",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Demmel:1999:CSV,
author = "James W. Demmel and Ming Gu and Stanley Eisenstat and
Ivan Slapni\v{c}ar and Kre\v{s}imir Veseli{\'c} and
Zlatko Drma\v{c}",
title = "Computing the Singular Value Decomposition with High
Relative Accuracy",
journal = j-LAA,
volume = "299",
pages = "21--80",
year = "1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Dongarra:1984:ILA,
author = "J. J. Dongarra and F. G. Gustavson and A. Karp",
title = "Implementing Linear Algebra Algorithms for Dense
Matrices on a Vector Pipeline Machine",
journal = j-SIREV,
volume = "26",
number = "1",
pages = "91--112",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Daniel:1976:RSA,
author = "J. W. Daniel and W. B. Gragg and L. Kaufman and G. W.
Stewart",
title = "Reorthogonalization and Stable Algorithms for Updating
the {Gram--Schmidt} {QR} Factorization",
journal = j-MATH-COMP,
volume = "30",
number = "136",
pages = "772--795",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Duff:1989:SMT,
author = "Iain S. Duff and Roger G. Grimes and John G. Lewis",
title = "Sparse Matrix Test Problems",
journal = j-TOMS,
volume = "15",
number = "1",
pages = "1--14",
year = "1989",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@TechReport{Duff:1992:UGH,
author = "Iain S. Duff and Roger G. Grimes and John G. Lewis",
title = "Users' Guide for the {Harwell--Boeing} Sparse Matrix
Collection (Release 1)",
type = "Report",
number = "RAL-92-086",
institution = inst-RAL,
address = inst-RAL:adr,
pages = "84",
month = dec,
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Duff:1991:FSS,
author = "I. S. Duff and N. I. M. Gould and J. K. Reid and J. A.
Scott and K. Turner",
title = "The Factorization of Sparse Symmetric Indefinite
Matrices",
journal = j-IMAJNA,
volume = "11",
pages = "181--204",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Drkosova:1995:NSG,
author = "J. Drko{\v{s}}ov{\'a} and A. Greenbaum and M.
Rozlo{\v{z}}n{\'\i}k and Z. Strako{\u{s}}",
title = "Numerical Stability of {GMRES}",
journal = j-BIT,
volume = "35",
pages = "309--330",
year = "1995",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Dhillon:1998:RCC,
author = "Inderjit Dhillon",
title = "Reliable Computation of the Condition Number of a
Tridiagonal Matrix in {$O(n)$} Time",
journal = j-SIMAX,
volume = "19",
number = "3",
pages = "776--796",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Demmel:1995:SBF,
author = "James W. Demmel and Nicholas J. Higham and Robert S.
Schreiber",
title = "Stability of Block {$LU$} Factorization",
journal = j-NLAA,
volume = "2",
number = "2",
pages = "173--190",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Douglas:1994:GPL,
author = "Craig C. Douglas and Michael Heroux and Gordon
Slishman and Roger M. Smith",
title = "{GEMMW}: {A} Portable Level 3 {BLAS Winograd} Variant
of {Strassen's} Matrix--Matrix Multiply Algorithm",
journal = j-JCOMP-PHYS,
volume = "110",
pages = "1--10",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Diamond:1978:SRI,
author = "Harold G. Diamond",
title = "Stability of Rounded Off Inverses Under Iteration",
journal = j-MATH-COMP,
volume = "32",
number = "141",
pages = "227--232",
year = "1978",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Dixon:1983:EEE,
author = "John D. Dixon",
title = "Estimating Extremal Eigenvalues and Condition Numbers
of Matrices",
journal = j-SINUM,
volume = "20",
number = "4",
pages = "812--814",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Dongarra:1987:DMS,
author = "Jack J. Dongarra and Eric Grosse",
title = "Distribution of Mathematical Software Via Electronic
Mail",
journal = j-CACM,
volume = "30",
number = "5",
pages = "403--407",
year = "1987",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@TechReport{Dongarra:2001:PVC,
author = "Jack J. Dongarra",
title = "Performance of Various Computers Using Standard Linear
Equations Software",
type = "Technical Report",
number = "CS-89-85",
institution = inst-CS-U-Tenn,
address = inst-CS-U-Tenn:adr,
pages = "58",
month = aug,
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Douglas:1994:VMM,
author = "Craig C. Douglas and Gordon Slishman",
title = "Variants of Matrix-Matrix Multiplication for
{Fortran}-90",
journal = j-SIGNUM,
volume = "29",
pages = "4--6",
year = "1994",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
}
@Article{Douglas:1959:REN,
author = "Jim {Douglas, Jr.}",
title = "Round-Off Error in the Numerical Solution of the Heat
Equation",
journal = j-ACM,
volume = "6",
pages = "48--58",
year = "1959",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Drmac:1994:PCF,
author = "Zlatko Drma\v{c} and Matja\v{z} Omladi\v{c} and
Kre\v{s}imir Veseli{\'c}",
title = "On the Perturbation of the {Cholesky} Factorization",
journal = j-SIMAX,
volume = "15",
number = "4",
pages = "1319--1332",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Doyle:1957:ISC,
author = "Thomas C. Doyle",
title = "Inversion of Symmetric Coefficient Matrix of
Positive-Definite Quadratic Form",
journal = j-MTAC,
volume = "11",
pages = "55--58",
year = "1957",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Duff:1979:DSS,
author = "Iain S. Duff and John K. Reid and Neils Munskgaard and
Hans B. Nielsen",
title = "Direct Solution of Sets of Linear Equations Whose
Matrix is Sparse, Symmetric and Indefinite",
journal = j-JIMA,
volume = "23",
pages = "235--250",
year = "1979",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Dubrulle:1983:CNM,
author = "Augustin A. Dubrulle",
title = "A Class of Numerical Methods for the Computation of
{Pythagorean} Sums",
journal = j-IBM-JRD,
volume = "27",
number = "6",
pages = "582--589",
year = "1983",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Dubrulle:1994:MQI,
author = "Augustin A. Dubrulle and Gene H. Golub",
title = "A Multishift {QR} Iteration Without Computation of the
Shifts",
journal = j-NUM-ALG,
volume = "7",
pages = "173--181",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Croz:1992:SMM,
author = "Jeremy J. Du Croz and Nicholas J. Higham",
title = "Stability of Methods for Matrix Inversion",
journal = j-IMAJNA,
volume = "12",
pages = "1--19",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Dumitrescu:1998:IEA,
author = "Bogdan Dumitrescu",
title = "Improving and Estimating the Accuracy of {Strassen's}
Algorithm",
journal = j-NUM-MATH,
volume = "79",
pages = "485--499",
year = "1998",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{Dunham:1990:JTG,
author = "William Dunham",
title = "Journey Through Genius: {The} Great Theorems of
Mathematics",
publisher = pub-Penguin,
address = pub-Penguin:adr-NY,
pages = "xiii + 300",
year = "1990",
ISBN = "0-14-014739-X",
ISBN-13 = "978-0-14-014739-1",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Duff:1982:MSF,
author = "Iain S. Duff and John K. Reid",
title = "{MA27}---{A} Set of {Fortran} Subroutines for Solving
Sparse Symmetric Sets of Linear Equations",
number = "AERE R10533",
institution = inst-HARWELL,
month = jul,
year = "1982",
ISBN = "0-7058-0985-4",
ISBN-13 = "978-0-7058-0985-6",
note = "Published by " # pub-HMSO # ", " # pub-HMSO:adr,
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{dure95,
author = "Iain S. Duff and John K. Reid",
title = "{MA47}, a {Fortran} Code for Direct Solution of
Indefinite Sparse Symmetric Linear Systems",
type = "Report",
number = "RAL-95-001",
institution = inst-RAL,
address = inst-RAL:adr,
pages = "63",
month = jan,
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Dwyer:1951:LC,
author = "Paul S. Dwyer",
title = "Linear Computations",
publisher = pub-Wiley,
address = pub-Wiley:adr,
pages = "xi + 344",
year = "1951",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Eckart:1936:AOM,
author = "Carl Eckart and Gale Young",
title = "The Approximation of One Matrix by Another of Lower
Rank",
journal = j-PSYCHO,
volume = "1",
number = "3",
pages = "211--218",
year = "1936",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Edelman:1988:ECN,
author = "Alan Edelman",
title = "Eigenvalues and Condition Numbers of Random Matrices",
journal = j-SIMAX,
volume = "9",
number = "4",
pages = "543--560",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Edelman:1991:FAL,
author = "Alan Edelman",
title = "The First Annual Large Dense Linear System Survey",
journal = j-SIGNUM,
volume = "26",
pages = "6--12",
month = oct,
year = "1991",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
}
@Article{edel91a,
key = "Editor",
title = "Editor's Note",
journal = j-SIMAX,
volume = "12",
number = "3",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Edelman:1991:DMS,
author = "Alan Edelman",
title = "The Distribution and Moments of the Smallest
Eigenvalue of a Random Matrix of {Wishart} Type",
journal = j-LAA,
volume = "159",
pages = "55--80",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Edelman:1992:CPC,
author = "Alan Edelman",
title = "The Complete Pivoting Conjecture for {Gaussian}
Elimination is False",
journal = j-MATHEMATICA-J,
volume = "2",
pages = "58--61",
year = "1992",
ISSN = "1047-5974 (print), 1097-1610 (electronic)",
ISSN-L = "1047-5974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Mathematica Journal",
journal-URL = "http://www.mathematica-journal.com/",
}
@Article{Edelman:1992:DSC,
author = "Alan Edelman",
title = "On the Distribution of a Scaled Condition Number",
journal = j-MATH-COMP,
volume = "58",
number = "197",
pages = "185--190",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Edelman:1993:ERR,
author = "Alan Edelman",
editor = "Marc S. Moonen and Gene H. Golub and Bart L. De Moor",
booktitle = "Linear Algebra for Large Scale and Real-Time
Applications",
title = "Eigenvalue Roulette and Random Test Matrices",
volume = "232",
publisher = pub-Kluwer # ", " # pub-Kluwer:adr,
pages = "365--368",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "NATO ASI Series E",
}
@Article{Edelman:1993:LDN,
author = "Alan Edelman",
title = "Large Dense Numerical Linear Algebra in 1993: {The}
Parallel Computing Influence",
journal = j-IJSA,
volume = "7",
number = "2",
pages = "113--128",
year = "1993",
CODEN = "IJSAE9",
ISSN = "0890-2720",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "International Journal of Supercomputer Applications",
journal-URL = "http://hpc.sagepub.com/content/by/year",
}
@InProceedings{Edelman:1994:SDN,
author = "Alan Edelman",
editor = "John G. Lewis",
booktitle = "Proceedings of the Fifth SIAM Conference on Applied
Linear Algebra",
title = "Scalable Dense Numerical Linear Algebra in 1994: {The}
Multicomputer Influence",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "344--348",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Unpublished{Edelman:1994:W,
author = "Alan Edelman",
title = "When is {$x*(1/x) \ne 1$}?",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Manuscript",
}
@Article{Edelman:1997:MPD,
author = "Alan Edelman",
title = "The Mathematics of the {Pentium} Division Bug",
journal = j-SIREV,
volume = "39",
number = "1",
pages = "54--67",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Edelman:1995:CPC,
author = "Alan Edelman and Walter Mascarenhas",
title = "On the Complete Pivoting Conjecture for a {Hadamard}
Matrix of Order 12",
journal = j-LMA,
volume = "38",
number = "3",
pages = "181--188",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Edelman:1995:PRC,
author = "Alan Edelman and H. Murakami",
title = "Polynomial Roots from Companion Matrix Eigenvalues",
journal = j-MATH-COMP,
volume = "64",
number = "210",
pages = "763--776",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Edelman:1993:SO,
author = "Alan Edelman and G. W. Stewart",
title = "Scaling for Orthogonality",
journal = j-IEEE-SP,
volume = "41",
number = "4",
pages = "1676--1677",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Egecioglu:1990:PMF,
author = "{\"O}mer E\v{g}ecio\u{g}lu and E. Gallopoulos and
{\c{C}}. K. Ko{\c{c}}",
title = "A Parallel Method for Fast and Practical High-Order
{Newton} Interpolation",
journal = j-BIT,
volume = "30",
pages = "268--288",
year = "1990",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Erisman:1987:EOU,
author = "A. M. Erisman and R. G. Grimes and J. G. Lewis and W.
G. Poole and H. D. Simon",
title = "Evaluation of Orderings for Unsymmetric Sparse
Matrices",
journal = j-SISSC,
volume = "8",
number = "4",
pages = "600--624",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Eirola:1993:ABE,
author = "Timo Eirola",
title = "Aspects of Backward Error Analysis of Numerical
{ODE}s",
journal = j-JCAM,
volume = "45",
number = "1-2",
pages = "65--73",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Edelman:1994:HME,
author = "Alan Edelman and Eric Kostlan and Michael Shub",
title = "How Many Eigenvalues of a Random Matrix are Real?",
journal = j-JAMS,
volume = "7",
number = "1",
pages = "247--267",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Elden:1980:PTL,
author = "Lars Eld{\'e}n",
title = "Perturbation Theory for the Least Squares Problem with
Linear Equality Constraints",
journal = j-SINUM,
volume = "17",
number = "3",
pages = "338--350",
year = "1980",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Eldersveld:1992:BUL,
author = "Samuel K. Eldersveld and Michael A. Saunders",
title = "A Block-{$LU$} Update for Large-Scale Linear
Programming",
journal = j-SIMAX,
volume = "13",
number = "1",
pages = "191--201",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Enright:1989:NEC,
author = "W. H. Enright",
title = "A New Error-Control for Initial Value Solvers",
journal = j-APP-MATH-COMP,
volume = "31",
pages = "288--301",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Epton:1980:MSA,
author = "Michael A. Epton",
title = "Methods for the Solution of {$AXD-BXC=E$} and its
Application in the Numerical Solution of Implicit
Ordinary Differential Equations",
journal = j-BIT,
volume = "20",
pages = "341--345",
year = "1980",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Erisman:1974:MST,
author = "A. M. Erisman and J. K. Reid",
title = "Monitoring the Stability of the Triangular
Factorization of a Sparse Matrix",
journal = j-NUM-MATH,
volume = "22",
pages = "183--186",
year = "1974",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Espelid:1995:FPS,
author = "Terje O. Espelid",
title = "On Floating-Point Summation",
journal = j-SIREV,
volume = "37",
number = "4",
pages = "603--607",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Ewing:1991:PHC,
editor = "John H. Ewing and F. W. Gehring",
title = "{Paul Halmos}: {Celebrating} 50 Years of Mathematics",
publisher = pub-Springer,
address = pub-Springer:adr-NY,
pages = "viii + 320",
year = "1991",
ISBN = "3-540-97509-8",
ISBN-13 = "978-3-540-97509-0",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Ewing:1994:CMT,
editor = "John Ewing",
title = "A Century of Mathematics Through the Eyes of the
{Monthly}",
publisher = "Mathematical Association of America",
address = "Washington, D.C.",
pages = "xi + 323",
year = "1994",
ISBN = "0-88385-459-7",
ISBN-13 = "978-0-88385-459-4",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Faddeeva:1959:CML,
author = "V. N. Faddeeva",
title = "Computational Methods of Linear Algebra",
publisher = pub-Dover,
address = pub-Dover:adr,
pages = "x + 252",
year = "1959",
ISBN = "0-486-60424-1",
ISBN-13 = "978-0-486-60424-4",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Fan:1955:SMI,
author = "Ky Fan and A. J. Hoffman",
title = "Some Metric Inequalities in the Space of Matrices",
journal = j-PROC-AMS,
volume = "6",
pages = "111--116",
year = "1955",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Fallat:2001:BFT,
author = "Shaun M. Fallat",
title = "Bidiagonal Factorizations of Totally Nonnegative
Matrices",
journal = j-AMM,
volume = "108",
number = "8",
pages = "697--712",
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Farebrother:1987:MLM,
author = "R. W. Farebrother",
title = "A Memoir of the Life of {M. H. Doolittle}",
journal = j-IMA-BULL,
volume = "23",
number = "6/7",
pages = "102",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "IMA Bulletin",
}
@Book{Farebrother:1988:LLS,
author = "R. W. Farebrother",
title = "Linear Least Squares Computations",
publisher = "Marcel Dekker",
address = "New York",
pages = "xiii + 293",
year = "1988",
ISBN = "0-8247-7661-5",
ISBN-13 = "978-0-8247-7661-9",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Farnum:1988:CSF,
author = "Charles Farnum",
title = "Compiler Support for Floating-Point Computation",
journal = j-SPE,
volume = "18",
number = "7",
pages = "701--709",
year = "1988",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}
@Article{Fateman:1982:HLL,
author = "Richard J. Fateman",
title = "High-Level Language Implications of the Proposed
{IEEE} Floating-Point Standard",
journal = j-TOPLAS,
volume = "4",
number = "2",
pages = "239--257",
month = apr,
year = "1982",
CODEN = "ATPSDT",
DOI = "https://doi.org/10.1145/357162.357168",
ISSN = "0164-0925 (print), 1558-4593 (electronic)",
ISSN-L = "0164-0925",
bibdate = "Thu Nov 8 14:50:28 2007",
bibsource = "Compiler/bevan.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/fortran2.bib;
http://www.math.utah.edu/pub/tex/bib/toplas.bib",
abstract = "An IEEE Computer Society working group on
floating-point arithmetic has recommended a standard
for binary floating-point number formats, operations,
and semantics. This paper, which has evolved in part
during the deliberations of that committee, describes
the significance to languages and, in particular, to
FORTRAN and its variants, of various novel features of
the recommended standard.",
acknowledgement = ack-pb,
checked = "19940302",
fjournal = "ACM Transactions on Programming Languages and
Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J783",
keywords = "computer arithmetic; control structures; data types
and structures; error handling and recovery;
floating-point arithmetic; FORTRAN; run-time
environments",
source = "Dept. Library",
}
@InProceedings{Ferguson:1991:AMA,
author = "Warren E. {Ferguson, Jr.} and Tom Brightman",
editor = "Peter Kornerup and David W. Matula",
booktitle = "Proc. 10th IEEE Symposium on Computer Arithmetic",
title = "Accurate and Monotone Approximations of Some
Transcendental Functions",
publisher = "IEEE Computer Society Press, Los Alamitos, CA, USA",
pages = "237--244",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Feldstein:1982:LSF,
author = "Alan Feldstein and Richard Goodman",
title = "Loss of Significance in Floating Point Subtraction and
Addition",
journal = j-IEEE-C,
volume = "C-31",
number = "4",
pages = "328--335",
year = "1982",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Ferguson:1995:ECS,
author = "Warren E. {Ferguson, Jr.}",
editor = "Simon Knowles and William H. McAllister",
booktitle = "Proc. 12th IEEE Symposium on Computer Arithmetic,
Bath, England",
title = "Exact Computation of a Sum or Difference with
Applications to Argument Reduction",
publisher = "IEEE Computer Society Press, Los Alamitos, CA, USA",
pages = "216--221",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Feldstein:1986:OUS,
author = "Alan Feldstein and Peter Turner",
title = "Overflow, Underflow, and Severe Loss of Significance
in Floating-Point Addition and Subtraction",
journal = j-IMAJNA,
volume = "6",
pages = "241--251",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Feingold:1962:BDD,
author = "David G. Feingold and Richard S. Varga",
title = "Block Diagonally Dominant Matrices and Generalizations
of the {Gerschgorin} Circle Theorem",
journal = j-PAC-J-MATH,
volume = "12",
pages = "1241--1250",
year = "1962",
CODEN = "PJMAAI",
ISSN = "0030-8730 (print), 1945-5844 (electronic)",
ISSN-L = "0030-8730",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Pacific Journal of Mathematics",
journal-URL = "http://msp.org/pjm",
}
@Article{Forsgren:1995:CMN,
author = "Anders Forsgren and Philip E. Gill and Walter Murray",
title = "Computing Modified {Newton} Directions Using a Partial
{Cholesky} Factorization",
journal = j-SISC,
volume = "16",
number = "1",
pages = "139--150",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Ferng:1991:ALM,
author = "William R. Ferng and Gene H. Golub and Robert J.
Plemmons",
title = "Adaptive {Lanczos} Methods for Recursive Condition
Estimation",
journal = j-NUM-ALG,
volume = "1",
number = "1",
pages = "1--19",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Forsgren:1996:SSI,
author = "Anders Forsgren and Philip E. Gill and Joseph R.
Shinnerl",
title = "Stability of Symmetric Ill-Conditioned Systems Arising
in Interior Methods for Constrained Optimization",
journal = j-SIMAX,
volume = "17",
number = "1",
pages = "187--211",
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Fox:1978:PMS,
author = "P. A. Fox and A. D. Hall and N. L. Schryer",
title = "The {PORT} Mathematical Subroutine Library",
journal = j-TOMS,
volume = "4",
number = "2",
pages = "104--126",
year = "1978",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Fox:1948:NSA,
author = "L. Fox and H. D. Huskey and J. H. Wilkinson",
title = "Notes on the Solution of Algebraic Linear Simultaneous
Equations",
journal = j-QJMAM,
volume = "1",
pages = "149--173",
year = "1948",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Fike:1967:MEP,
author = "C. T. Fike",
title = "Methods of Evaluating Polynomial Approximations in
Function Evaluation Routines",
journal = j-CACM,
volume = "10",
number = "3",
pages = "175--178",
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Book{Fike:1968:CEM,
author = "C. T. Fike",
title = "Computer Evaluation of Mathematical Functions",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xii + 227",
year = "1968",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Fischer:1974:FSC,
author = "Patrick C. Fischer",
editor = "Jacques Loeckx",
booktitle = "Automata, Languages and Programming",
title = "Further Schemes for Combining Matrix Algorithms",
volume = "14",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
pages = "428--436",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Lecture Notes in Computer Science",
}
@Article{Fletcher:1976:FSI,
author = "R. Fletcher",
title = "Factorizing Symmetric Indefinite Matrices",
journal = j-LAA,
volume = "14",
pages = "257--272",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Fletcher:1985:EC,
author = "R. Fletcher",
title = "Expected Conditioning",
journal = j-IMAJNA,
volume = "5",
pages = "247--273",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Fletcher:1987:PMO,
author = "R. Fletcher",
title = "Practical Methods of Optimization",
publisher = pub-Wiley,
address = pub-Wiley:adr-C,
edition = "Second",
pages = "xiv + 436",
year = "1987",
ISBN = "0-471-91547-5",
ISBN-13 = "978-0-471-91547-8",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Fletcher:1974:MF,
author = "R. Fletcher and M. J. D. Powell",
title = "On the Modification of {$LDL^T$} Factorizations",
journal = j-MATH-COMP,
volume = "28",
number = "128",
pages = "1067--1087",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Forsythe:1977:CMM,
author = "George E. (George Elmer) Forsythe and Michael A.
Malcolm and Cleve B. Moler",
title = "Computer Methods for Mathematical Computations",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xi + 259",
year = "1977",
ISBN = "0-13-165332-6",
ISBN-13 = "978-0-13-165332-0",
LCCN = "QA297 .F5681",
MRclass = "65-01",
MRnumber = "MR0458783 (56 \#16983)",
MRreviewer = "Sven-{\AA}ke Gustafson",
bibdate = "Tue May 25 09:01:08 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
http://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/fortran1.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from
\path=math.liu.se= in \path=pub/references=",
price = "US\$16.95",
series = "Prentice-Hall series in automatic computation",
ZMnumber = "0361.65002",
acknowledgement = ack-nhfb,
classmath = "*65-01 Textbooks (numerical analysis) 68-01 Textbooks
(computer science)",
keywords = "Fortran (computer program language); numerical
analysis -- data processing",
remark = "Subroutines and exercises for the computer solution of
problems involving matrices, integrals, differential
equations, spline functions, zeros and extrema of
functions, least squares, and Monte Carlo techniques.",
subject = "Numerical analysis; Data processing; Computer
programs; Problems, exercises, etc; FORTRAN (Computer
program language)",
tableofcontents = "Introduction \\
Floating-point computation \\
Linear systems of equations \\
Interpolation \\
Numerical integration \\
Initial value problems in ordinary differential
equations \\
Solution of nonlinear equations \\
Optimization \\
Least squares and the singular value decomposition \\
Random number generation and Monte Carlo methods",
}
@Article{Funderlic:1982:DGD,
author = "R. E. Funderlic and M. Neumann and R. J. Plemmons",
title = "{$LU$} Decompositions of Generalized Diagonally
Dominant Matrices",
journal = j-NUM-MATH,
volume = "40",
pages = "57--69",
year = "1982",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{Forsythe:1967:CSL,
author = "George E. Forsythe and Cleve B. Moler",
title = "Computer Solution of Linear Algebraic Systems",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xi + 148",
year = "1967",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Ford:1978:PET,
author = "Brian Ford",
title = "Parameterization of the Environment for Transportable
Numerical Software",
journal = j-TOMS,
volume = "4",
number = "2",
pages = "100--103",
year = "1978",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Forsythe:1951:GGR,
author = "George E. Forsythe",
title = "Gauss to {Gerling} on Relaxation",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "5",
pages = "255--258",
year = "1951",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Forsythe:1953:SLA,
author = "George E. Forsythe",
title = "Solving Linear Algebraic Equations Can Be
Interesting",
journal = j-BAMS,
volume = "59",
number = "4",
pages = "299--329",
year = "1953",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Forsythe:1959:RNR,
author = "George E. Forsythe",
title = "Reprint of a Note on Rounding-Off Errors",
journal = j-SIREV,
volume = "1",
number = "1",
pages = "66--67",
year = "1959",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Forsythe:1960:ACP,
author = "George E. Forsythe",
title = "{Algorithm 16}: {Crout} with Pivoting",
journal = j-CACM,
volume = "3",
number = "9",
pages = "507--508",
month = sep,
year = "1960",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/367390.367406",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:28 MST 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Forsythe:1967:TCM,
author = "George E. Forsythe",
title = "Today's Computational Methods of Linear Algebra",
journal = j-SIREV,
volume = "9",
pages = "489--515",
year = "1967",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
nuber = "3",
}
@InCollection{Forsythe:1969:WSQ,
author = "George E. Forsythe",
editor = "Bruno Dejon and Peter Henrici",
booktitle = "Constructive Aspects of the Fundamental Theorem of
Algebra",
title = "What is a Satisfactory Quadratic Equation Solver?",
publisher = "Wiley-Interscience",
address = "London",
pages = "53--61",
year = "1969",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InCollection{Forsythe:1969:SQE,
author = "George E. Forsythe",
editor = "National Research Council's Committee on Support of
Research in the Mathematical Sciences",
booktitle = "The Mathematical Sciences: {A} Collection of Essays",
title = "Solving a Quadratic Equation on a Computer",
publisher = pub-MIT,
address = pub-MIT:adr,
pages = "138--152",
year = "1969",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Forsythe:1970:PCW,
author = "George E. Forsythe",
title = "Pitfalls in Computation, or Why a Math Book Isn't
Enough",
journal = j-AMM,
volume = "77",
pages = "931--956",
year = "1970",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Forsythe:1955:BCM,
author = "George E. Forsythe and E. G. Straus",
title = "On Best Conditioned Matrices",
journal = j-PROC-AMS,
volume = "6",
pages = "340--345",
year = "1955",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Foster:1991:MNE,
author = "Leslie Foster",
editor = "G. H. Golub and P. M. {Van Dooren}",
booktitle = "Numerical Linear Algebra, Digital Signal Processing
and Parallel Algorithms",
title = "Modifications of the Normal Equations Method That Are
Numerically Stable",
volume = "F70",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
pages = "501--512",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "NATO ASI Series",
}
@Article{Foster:1994:GEP,
author = "Leslie V. Foster",
title = "Gaussian Elimination with Partial Pivoting Can Fail in
Practice",
journal = j-SIMAX,
volume = "15",
number = "4",
pages = "1354--1362",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Foster:1997:GFE,
author = "Leslie V. Foster",
title = "The Growth Factor and Efficiency of {Gaussian}
Elimination with Rook Pivoting",
journal = j-JCAM,
volume = "86",
pages = "177--194",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Corrigendum in " # j-JCAM # ", 98:177, 1998",
}
@Book{Fox:1964:INL,
author = "L. Fox",
title = "An Introduction to Numerical Linear Algebra",
publisher = pub-OUP,
pages = "xi + 328",
year = "1964",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Fox:1971:HGM,
author = "L. Fox",
title = "How to Get Meaningless Answers in Scientific
Computation (and What to Do About It)",
journal = j-IMA-BULL,
volume = "7",
number = "10",
pages = "296--302",
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "IMA Bulletin",
}
@InProceedings{Fox:1978:AAJ,
author = "L. Fox",
booktitle = "The Contribution of {Dr. J. H. Wilkinson} to Numerical
Analysis",
title = "All About {Jim Wilkinson}, with a Commemorative
Snippet on Backward Error Analysis",
publisher = inst-IMA-UK # ", " # inst-IMA-UK:adr,
pages = "1--20",
year = "1978",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Symposium Proceedings Series No. 19",
}
@Article{Fox:1987:JHW,
author = "L. Fox",
title = "{James Hardy Wilkinson}, 1919--1986",
journal = j-BIOGRAPH-MEMOIRS-FELLOWS-ROY-SOC,
volume = "33",
pages = "671--708",
year = "1987",
CODEN = "BMFRA3",
ISSN = "0080-4606 (print), 1748-8494 (electronic)",
ISSN-L = "0080-4606",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Biographical Memoirs of Fellows of the Royal Society",
journal-URL = "http://www.jstor.org/journals/00804606.html",
}
@TechReport{fpv86,
key = "NAG",
title = "{FPV}: {A} Floating-Point Validation Package. {Release
I}. {User's} Guide",
type = "Technical Report",
number = "NP 1201",
institution = "NAG Ltd.",
address = "Oxford",
month = may,
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Frank:1958:CEC,
author = "Werner L. Frank",
title = "Computing Eigenvalues of Complex Matrices by
Determinant Evaluation and by Methods of {Danilewski}
and {Wielandt}",
journal = j-SIAM,
volume = "6",
number = "4",
pages = "378--392",
year = "1958",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@PhdThesis{Fraysse:1992:RCS,
author = "V. Frayss{\'e}",
title = "Reliability of Computer Solutions",
school = "L'Institut National Polytechnique de Toulouse",
address = "Toulouse, France",
month = jul,
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "CERFACS Report TH/PA/92/11",
}
@Article{Friedland:1991:RMS,
author = "Shmuel Friedland",
title = "Revisiting Matrix Squaring",
journal = j-LAA,
volume = "154--156",
pages = "59--63",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Frigo:1998:FAS,
author = "Matteo Frigo and Steven G. Johnson",
booktitle = "Proceedings of International Conference on Acoustics,
Speech and Signal Processing, Volume 3",
title = "{FFTW}: {An} Adaptive Software Architecture for the
{FFT}",
pages = "1381 +",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Francois:1991:SPM,
author = "Philippe Fran{\c{c}}ois and Jean-Michel Muller",
booktitle = "Proceedings of IMACS '91, 13th World Congress on
Computation and Applied Mathematics, Dublin, Volume 1",
title = "The {SCALP} Perturbation Method",
pages = "59--60",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InCollection{Frommer:2001:PCU,
author = "Andreas Frommer",
editor = "A. Facius and U. Kulisch and R. Lohner",
booktitle = "Perspectives on Enclosure Methods",
title = "Proving Conjectures by Use of Interval Arithmetic",
publisher = pub-Springer # ", " # pub-Springer:adr-NY,
pages = "1--13",
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Friedland:1980:GPN,
author = "Shmuel Friedland and Hans Schneider",
title = "The Growth of Powers of a Nonnegative Matrix",
journal = j-SIAD,
volume = "1",
number = "2",
pages = "185--200",
year = "1980",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gal:1991:AEM,
author = "Shmuel Gal and Boris Bachelis",
title = "An Accurate Elementary Mathematical Library for the
{IEEE} Floating Point Standard",
journal = j-TOMS,
volume = "17",
number = "1",
pages = "26--45",
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Book{Godunov:1993:GAN,
author = "S. K. Godunov and A. G. Antonov and O. P. Kiriljuk and
V. I. Kostin",
title = "Guaranteed Accuracy in Numerical Linear Algebra",
publisher = pub-Kluwer,
address = pub-Kluwer:adr,
pages = "xi + 535",
year = "1993",
ISBN = "0-7923-2352-1",
ISBN-13 = "978-0-7923-2352-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gardiner:1991:PAA,
author = "Judith D. Gardiner and Alan J. Laub",
title = "Parallel Algorithms for Algebraic {Riccati}
Equations",
journal = j-IJC,
volume = "54",
number = "6",
pages = "1317--1333",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Gantmacher:1959:TMa,
author = "F. R. Gantmacher",
title = "The Theory of Matrices",
volume = "one",
publisher = "Chelsea",
address = "New York",
pages = "x + 374",
year = "1959",
ISBN = "0-8284-0131-4",
ISBN-13 = "978-0-8284-0131-9",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Gantmacher:1959:TMb,
author = "F. R. Gantmacher",
title = "The Theory of Matrices",
volume = "two",
publisher = "Chelsea",
address = "New York",
pages = "ix + 276",
year = "1959",
ISBN = "0-8284-0133-0",
ISBN-13 = "978-0-8284-0133-3",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gasca:1992:TPN,
author = "M. Gasca and J. M. Pe{\~n}a",
title = "Total Positivity and {Neville} Elimination",
journal = j-LAA,
volume = "165",
pages = "25--44",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Gardner:1961:MMP,
author = "Martin Gardner",
title = "More Mathematical Puzzles and Diversions",
publisher = pub-Penguin,
address = pub-Penguin:adr-NY,
pages = "187",
year = "1961",
ISBN = "0-14-020748-1",
ISBN-13 = "978-0-14-020748-4",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Garner:1976:SSR,
author = "Harvey L. Garner",
title = "A Survey of Some Recent Contributions to Computer
Arithmetic",
journal = j-IEEE-C,
volume = "C-25",
number = "12",
pages = "1277--1282",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Gastinel:1983:LNA,
author = "Noel Gastinel",
title = "Linear Numerical Analysis",
publisher = "Kershaw Publishing",
address = "London",
pages = "ix + 341",
year = "1983",
ISBN = "0-901665-16-9",
ISBN-13 = "978-0-901665-16-4",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "First published in English by Academic Press, London,
1970",
}
@Article{Gautschi:1953:ABP,
author = "Walter Gautschi",
title = "The Asymptotic Behaviour of Powers of Matrices",
journal = j-DUKE-MATH-J,
volume = "20",
pages = "127--140",
year = "1953",
CODEN = "DUMJAO",
ISSN = "0012-7094 (print), 1547-7398 (electronic)",
ISSN-L = "0012-7094",
bibdate = "Thu Jan 19 07:49:45 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Duke Mathematical Journal",
journal-URL = "http://projecteuclid.org/info/euclid.dmj",
}
@Article{Gautschi:1962:IVC,
author = "Walter Gautschi",
title = "On Inverses of {Vandermonde} and Confluent
{Vandermonde} Matrices",
journal = j-NUM-MATH,
volume = "4",
pages = "117--123",
year = "1962",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Gautschi:1975:NEI,
author = "Walter Gautschi",
title = "Norm Estimates for Inverses of {Vandermonde}
Matrices",
journal = j-NUM-MATH,
volume = "23",
pages = "337--347",
year = "1975",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Gautschi:1978:IVC,
author = "Walter Gautschi",
title = "On Inverses of {Vandermonde} and Confluent
{Vandermonde} Matrices {III}",
journal = j-NUM-MATH,
volume = "29",
pages = "445--450",
year = "1978",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Gautschi:1983:CVL,
author = "Walter Gautschi",
title = "The Condition of {Vandermonde}-Like Matrices Involving
Orthogonal Polynomials",
journal = j-LAA,
volume = "52/53",
pages = "293--300",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Gautschi:1990:HSV,
author = "Walter Gautschi",
editor = "R. Wong",
booktitle = "Asymptotic and Computational Analysis",
title = "How (Un)stable are {Vandermonde} Systems?",
volume = "124",
publisher = pub-DEKKER,
address = pub-DEKKER:adr,
pages = "193--210",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Lecture Notes in Pure and Applied Mathematics",
mynote = "crossref Wong:1990:ACA",
}
@TechReport{Gay:1990:CRB,
author = "David M. Gay",
title = "Correctly Rounded Binary-Decimal and Decimal-Binary
Conversions",
type = "Numerical Analysis Manuscript",
number = "90-10",
institution = inst-ATT,
address = inst-ATT:adr,
pages = "16",
month = nov,
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{gaze24,
key = "Mathematical Gazette",
title = "Gleanings Far and Near",
journal = j-MATH-GAZ,
volume = "22",
number = "170",
pages = "95",
year = "1924",
CODEN = "MAGAAS",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Mathematical Gazette",
journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}
@Book{Garbow:1977:MER,
author = "B. S. Garbow and J. M. Boyle and J. J. Dongarra and C.
B. Moler",
title = "Matrix Eigensystem Routines---{EISPACK} Guide
Extension",
volume = "51",
publisher = pub-Springer,
address = pub-Springer:adr-B,
pages = "viii + 343",
year = "1977",
ISBN = "3-540-08254-9",
ISBN-13 = "978-3-540-08254-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Lecture Notes in Computer Science",
}
@TechReport{Gu:1994:ECS,
author = "Ming Gu and James W. Demmel and Inderjit Dhillon",
title = "Efficient Computation of the Singular Value
Decomposition with Applications to Least Squares
Problems",
type = "Technical Report",
number = "CS-94-257",
institution = inst-CS-U-Tenn,
address = inst-CS-U-Tenn:adr,
pages = "19",
month = oct,
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "LAPACK Working Note 88",
}
@Article{Guggenheimer:1995:SEC,
author = "Heinrich W. Guggenheimer and Alan S. Edelman and
Charles R. Johnson",
title = "A Simple Estimate of the Condition Number of a Linear
System",
journal = j-CMJ,
volume = "26",
number = "1",
pages = "2--5",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{George:1981:CSL,
author = "Alan George and Joseph W-H Liu",
title = "Computer Solution of Large Sparse Positive Definite
Systems",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xii + 324",
year = "1981",
ISBN = "0-13-165274-5",
ISBN-13 = "978-0-13-165274-3",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gentleman:1974:MAR,
author = "W. Morven Gentleman and Scott B. Marovich",
title = "More on Algorithms that Reveal Properties of Floating
Point Arithmetic Units",
journal = j-CACM,
volume = "17",
number = "5",
pages = "276--277",
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Geman:1986:SRL,
author = "Stuart Geman",
title = "The Spectral Radius of Large Random Matrices",
journal = j-ANN-PROBAB,
volume = "14",
number = "4",
pages = "1318--1328",
month = oct,
year = "1986",
CODEN = "APBYAE",
ISSN = "0091-1798 (print), 2168-894X (electronic)",
ISSN-L = "0091-1798",
bibdate = "Sun Apr 20 10:44:17 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/annprobab1980.bib",
URL = "http://projecteuclid.org/euclid.aop/1176992372",
acknowledgement = ack-nhfb,
fjournal = "Annals of Probability",
journal-URL = "http://projecteuclid.org/all/euclid.aop",
}
@Article{Gentleman:1969:EAG,
author = "W. M. Gentleman",
title = "An Error Analysis of {Goertzel's (Watt's)} Method for
Computing {Fourier} Coefficients",
journal = j-COMP-J,
volume = "12",
pages = "160--165",
year = "1969",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Gentleman:1973:LSC,
author = "W. Morven Gentleman",
title = "Least Squares Computations by {Givens} Transformations
Without Square Roots",
journal = j-JIMA,
volume = "12",
pages = "329--336",
year = "1973",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gentleman:1975:EAD,
author = "W. Morven Gentleman",
title = "Error Analysis of {$QR$} Decompositions by {Givens}
Transformations",
journal = j-LAA,
volume = "10",
pages = "189--197",
year = "1975",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Gentleman:1966:FFT,
author = "W. M. Gentleman and G. Sande",
booktitle = "Fall Joint Computer Conference",
title = "Fast {Fourier} Transforms---For Fun and Profit",
volume = "29",
publisher = "Spartan Books, Washington, D.C.",
pages = "563--578",
year = "1966",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "AFIPS Conference Proceedings",
}
@Article{Geurts:1982:CTC,
author = "A. J. Geurts",
title = "A Contribution to the Theory of Condition",
journal = j-NUM-MATH,
volume = "39",
pages = "85--96",
year = "1982",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Goodman:1985:REF,
author = "R. H. Goodman and A. Feldstein and J. Bustoz",
title = "Relative Error in Floating-Point Multiplication",
journal = j-COMPUTING,
volume = "35",
pages = "127--139",
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Ghavimi:1995:BES,
author = "Ali R. Ghavimi and Alan J. Laub",
title = "Backward Error, Sensitivity, and Refinement of
Computed Solutions of Algebraic {Riccati} Equations",
journal = j-NUM-LIN-ALG-APPL,
volume = "2",
number = "1",
pages = "29--49",
year = "1995",
CODEN = "NLAAEM",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
}
@Article{Ghavimi:1995:RBD,
author = "Ali R. Ghavimi and Alan J. Laub",
title = "Residual Bounds for Discrete-Time {Lyapunov}
Equations",
journal = j-IEEE-AC,
volume = "40",
number = "7",
pages = "1244--1249",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{George:2002:GFG,
author = "Alan George and Khakim D. Ikramov and Andrey B.
Kucherov",
title = "On the Growth Factor in {Gaussian} Elimination for
Generalized {Higham} Matrices",
journal = j-NLAA,
volume = "9",
pages = "107--114",
year = "2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gill:1951:PSS,
author = "S. Gill",
title = "A Process for the Step-By-Step Integration of
Differential Equations in an Automatic Digital
Computing Machine",
journal = j-PROC-CAMBRIDGE-PHIL-SOC,
volume = "47",
pages = "96--108",
year = "1951",
CODEN = "PCPSA4",
ISSN = "0008-1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Proceedings of the Cambridge Philosophical Society. Mathematical and physical sciences",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
}
@InCollection{Gillespie:1991:NVT,
author = "T. A. Gillespie",
editor = "John H. Ewing and F. W. Gehring",
booktitle = "{Paul Halmos}: {Celebrating} 50 Years of Mathematics",
title = "Noncommutative Variations on Theorems of {Marcel
Riesz} and Others",
publisher = pub-Springer,
address = pub-Springer:adr-B,
pages = "221--236",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gill:1973:NSF,
author = "P. E. Gill and W. Murray",
title = "A Numerically Stable Form of the Simplex Algorithm",
journal = j-LAA,
volume = "7",
pages = "99--138",
year = "1973",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Givens:1954:NCC,
author = "Wallace J. Givens",
title = "Numerical Computation of the Characteristic Values of
a Real Symmetric Matrix",
number = "ORNL-1574",
institution = inst-ORNL,
address = inst-ORNL:adr,
pages = "107",
year = "1954",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gudmundsson:1995:SSS,
author = "Thorkell Gudmundsson and Charles S. Kenney and Alan J.
Laub",
title = "Small-Sample Statistical Estimates for Matrix Norms",
journal = j-SIMAX,
volume = "16",
number = "3",
pages = "776--792",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Graham:1994:CM,
author = "Ronald L. Graham and Donald E. Knuth and Oren
Patashnik",
title = "Concrete Mathematics",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xiii + 657",
year = "1994",
ISBN = "0-201-55802-5",
ISBN-13 = "978-0-201-55802-9",
LCCN = "QA39.2 .G733 1994",
MRclass = "68-01 (00-01 00A05 05-01 68Rxx)",
MRnumber = "97d:68003",
bibdate = "Wed Jul 6 14:39:36 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
http://www.math.utah.edu/pub/tex/bib/texbook2.bib",
acknowledgement = ack-nhfb,
keywords = "computer science -- mathematics; mathematics",
shorttableofcontents = "1: Recurrent Problems / 1 \\
2: Sums / 21 \\
3: Integer Functions / 67 \\
4: Number Theory / 102 \\
5: Binomial Coefficients / 153 \\
6: Special Numbers / 257 \\
7: Generating Functions / 320 \\
8: Discrete Probability / 381 \\
9: Asymptotics / 439 \\
A: Answers to Exercises / 497 \\
B: Bibliography / 604 \\
C: Credits for Exercises / 632 \\
Index / 637 \\
List of Tables / 657",
tableofcontents = "1: Recurrent Problems / 1 \\
1.1 The Tower of Hanoi / 1 \\
1.2 Lines in the Plane / 4 \\
1.3 The Josephus Problem / 8 \\
Exercises / 17 \\
2: Sums / 21 \\
2.1 Notation / 21 \\
2.2 Sums and Recurrences / 25 \\
2.3 Manipulation of Sums / 30 \\
2.4 Multiple Sums / 34 \\
2.5 General Methods / 41 \\
2.6 Finite and Infinite Calculus / 47 \\
2.7 Infinite Sums / 56 \\
Exercises / 62 \\
3: Integer Functions / 67 \\
3.1 Floors and Ceilings / 67 \\
3.2 Floor/Ceiling Applications / 70 \\
3.3 Floor/Ceiling Recurrences / 78 \\
3.4 `mod': The Binary Operation / 81 \\
3.5 Floor/Ceiling Sums / 86 \\
Exercises / 95 \\
4: Number Theory / 102 \\
4.1 Divisibility / 102 \\
4.2 Primes / 105 \\
4.3 Prime Examples / 107 \\
4.4 Factorial Factors / 111 \\
4.5 Relative Primality / 115 \\
4.6 `mod': The Congruence Relation / 123 \\
4.7 Independent Residues / 126 \\
4.8 Additional Applications / 129 \\
4.9 Phi and Mu / 133 \\
Exercises / 144 \\
5: Binomial Coefficients / 153 \\
5.1 Basic Identities / 153 \\
5.2 Basic Practice / 172 \\
5.3 Tricks of the Trade / 186 \\
5.4 Generating Functions / 196 \\
5.5 Hypergeometric Functions / 204 \\
5.6 Hypergeometric Transformations / 216 \\
5.7 Partial Hypergeometric Sums / 223 \\
5.8 Mechanical Summation / 229 \\
Exercises / 242 \\
6: Special Numbers / 257 \\
6.1 Stirling Numbers / 257 \\
6.2 Eulerian Numbers / 267 \\
6.3 Harmonic Numbers / 272 \\
6.4 Harmonic Summation / 279 \\
6.5 Bernoulli Numbers / 283 \\
6.6 Fibonacci Numbers / 290 \\
6.7 Continuants / 301 \\
Exercises / 309 \\
7: Generating Functions / 320 \\
7.1 Domino Theory and Change / 320 \\
7.2 Basic Maneuvers / 331 \\
7.3 Solving Recurrences / 337 \\
7.4 Special Generating Functions / 350 \\
7.5 Convolutions / 353 \\
7.6 Exponential Generating Functions / 364 \\
7.7 Dirichlet Generating Functions / 370 \\
Exercises / 371 \\
8: Discrete Probability / 381 \\
8.1 Definitions / 381 \\
8.2 Mean and Variance / 387 \\
8.3 Probability Generating Functions / 394 \\
8.4 Flipping Coins / 401 \\
8.5 Hashing / 411 \\
Exercises / 427 \\
9: Asymptotics / 439 \\
9.1 A Hierarchy / 440 \\
9.2 O Notation / 443 \\
9.3 O Manipulation / 450 \\
9.4 Two Asymptotic Tricks / 463 \\
9.5 Euler's Summation Formula / 469 \\
9.6 Final Summations / 476 \\
Exercises / 489 \\
A: Answers to Exercises / 497 \\
B: Bibliography / 604 \\
C: Credits for Exercises / 632 \\
Index / 637 \\
List of Tables / 657",
}
@Article{Gardiner:1992:SSM,
author = "Judith D. Gardiner and Alan J. Laub and James J. Amato
and Cleve B. Moler",
title = "Solution of the {Sylvester} Matrix Equation
{$AXB^T+CXD^T=E$}",
journal = j-TOMS,
volume = "18",
number = "2",
pages = "223--231",
year = "1992",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Gardiner:1992:AFS,
author = "Judith D. Gardiner and Matthew R. Wette and Alan J.
Laub and James J. Amato and Cleve B. Moler",
title = "Algorithm 705: {A} {FORTRAN}-77 Software Package for
Solving the {Sylvester} Matrix Equation
{$AXB^T+CXD^T=E$}",
journal = j-TOMS,
volume = "18",
number = "2",
pages = "232--238",
year = "1992",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Glanz:1995:MLF,
author = "James Glanz",
title = "Mathematical Logic Flushes Out the Bugs in Chip
Designs",
journal = j-SCIENCE,
volume = "267",
pages = "332--333",
year = "1995",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "20 " # jan,
CODEN = "SCIEAS",
fjournal = "Science",
journal-URL = "http://www.sciencemag.org/archive/",
}
@Article{Gahinet:1990:SSD,
author = "Pascal M. Gahinet and Alan J. Laub and Charles S.
Kenney and Gary A. Hewer",
title = "Sensitivity of the Stable Discrete-Time {Lyapunov}
Equation",
journal = j-IEEE-AC,
volume = "AC-35",
number = "11",
pages = "1209--1217",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gluchowska:1990:SLL,
author = "J. Gluchowska and A. Smoktunowicz",
title = "Solving the Linear Least Squares Problem with Very
High Relative Accuracy",
journal = j-COMPUTING,
volume = "45",
pages = "345--354",
year = "1990",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Gill:1992:PIS,
author = "Philip E. Gill and Walter Murray and Dulce B.
Poncele{\'o}n and Michael A. Saunders",
title = "Preconditioners For Indefinite Systems Arising in
Optimization",
journal = j-SIMAX,
volume = "13",
number = "1",
pages = "292--311",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Gill:1986:UGN,
author = "Philip E. Gill and Walter Murray and Michael A.
Saunders and Margaret H. Wright",
title = "User's Guide for {NPSOL} (Version 4.0): {A} {Fortran}
Package for Nonlinear Programming",
type = "Technical Report",
number = "SOL 86-2",
institution = inst-OR-U-STANFORD,
address = inst-U-STANFORD:adr,
pages = "53",
month = jan,
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gill:1991:ICM,
author = "Philip E. Gill and Walter Murray and Michael A.
Saunders and Margaret H. Wright",
title = "Inertia-Controlling Methods for General Quadratic
Programming",
journal = j-SIREV,
volume = "33",
number = "1",
pages = "1--36",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Gill:1981:PO,
author = "Philip E. Gill and Walter Murray and Margaret H.
Wright",
title = "Practical Optimization",
publisher = pub-AP,
address = pub-AP:adr-L,
pages = "xvi + 401",
year = "1981",
ISBN = "0-12-283952-8",
ISBN-13 = "978-0-12-283952-8",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Golub:1979:HSM,
author = "G. H. Golub and S. Nash and C. F. {Van Loan}",
title = "A {Hessenberg--Schur} Method for the Problem
{$AX+XB=C$}",
journal = j-IEEE-AC,
volume = "AC-24",
number = "6",
pages = "909--913",
year = "1979",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Goodman:1975:REP,
author = "R. Goodman and A. Feldstein",
title = "Round-Off Error in Products",
journal = j-COMPUTING,
volume = "15",
pages = "263--273",
year = "1975",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Gohberg:1993:MCS,
author = "I. Gohberg and I. Koltracht",
title = "Mixed, Componentwise, and Structured Condition
Numbers",
journal = j-SIMAX,
volume = "14",
number = "3",
pages = "688--704",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Goldberg:1967:BED,
author = "I. Bennett Goldberg",
title = "$ 27 $ Bits Are Not Enough For $8$-Digit Accuracy",
journal = j-CACM,
volume = "10",
number = "2",
pages = "105--106",
month = feb,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363067.363112",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:11 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "From the inequality $ 10^8 < 2^{27} $, we are likely
to conclude that we can represent 8-digit decimal
floating-point numbers accurately by 27-bit [binary]
floating-point numbers. However, we need 28 significant
bits to represent some 8-digit numbers accurately. In
general, we can show that if $ 10^p < 2^{q - 1} $, then
$q$ significant bits are always enough for $p$-digit
decimal accuracy. Finally, we can define a compact
27-bit floating-point representation that will give 28
significant bits, for numbers of practical
importance.",
acknowledgement = ack-nj # " and " # ack-mfc # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floating-point arithmetic",
received = "August 1966 (revised October 1966)",
}
@Book{Goldstine:1972:CPN,
author = "Herman H. Goldstine",
title = "The Computer: {From Pascal} to {von Neumann}",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "xii + 378",
year = "1972",
ISBN = "0-691-02367-0",
ISBN-13 = "978-0-691-02367-0",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "1993 printing with new preface",
}
@Book{Goldstine:1977:HNA,
author = "Herman H. Goldstine",
title = "A History of Numerical Analysis from the 16th through
the 19th Century",
publisher = "Springer-Verlag",
address = "New York",
pages = "xiv + 348",
year = "1977",
ISBN = "0-387-90277-5",
ISBN-13 = "978-0-387-90277-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Goldberg:1991:WEC,
author = "David Goldberg",
title = "What Every Computer Scientist Should Know About
Floating-Point Arithmetic",
journal = j-COMP-SURV,
volume = "23",
number = "1",
pages = "5--48",
year = "1991",
CODEN = "CMSVAN",
ISSN = "0360-0300 (print), 1557-7341 (electronic)",
ISSN-L = "0360-0300",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}
@Article{Golub:1962:BRE,
author = "Gene H. Golub",
title = "Bounds for the Round-Off Errors in the {Richardson}
Second Order Method",
journal = j-BIT,
volume = "2",
pages = "212--223",
year = "1962",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Golub:1965:NMS,
author = "G. H. Golub",
title = "Numerical Methods for Solving Linear Least Squares
Problems",
journal = j-NUM-MATH,
volume = "7",
pages = "206--216",
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Goodnight:1979:TSO,
author = "James H. Goodnight",
title = "A Tutorial on the {SWEEP} Operator",
journal = j-AMER-STAT,
volume = "33",
number = "3",
pages = "149--158",
year = "1979",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Gohberg:1994:FIC,
author = "I. Gohberg and V. Olshevsky",
title = "Fast Inversion of {Chebyshev--Vandermonde} Matrices",
journal = j-NUM-MATH,
volume = "67",
number = "1",
pages = "71--92",
year = "1994",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Govaerts:1990:BEO,
author = "W. Govaerts and J. D. Pryce",
title = "Block elimination with one iterative refinement solves
bordered linear systems accurately",
journal = j-BIT,
volume = "30",
pages = "490--507",
year = "1990",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Goldberg:1983:MNM,
author = "Moshe Goldberg and E. G. Straus",
title = "Multiplicativity of {$l_p$} Norms for Matrices",
journal = j-LAA,
volume = "52/53",
pages = "351--360",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gould:1991:GGE,
author = "N. I. M. Gould",
title = "On Growth in {Gaussian} Elimination with Complete
Pivoting",
journal = j-SIMAX,
volume = "12",
number = "2",
pages = "354--361",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Govaerts:2000:NMB,
author = "Willy J. F. Govaerts",
title = "Numerical Methods for Bifurcations of Dynamical
Equilibria",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxii + 362",
year = "2000",
ISBN = "0-89871-442-7",
ISBN-13 = "978-0-89871-442-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Golub:1974:CBS,
author = "G. H. Golub and J. M. Varah",
title = "On a Characterization of the Best {$\ell_2$}-Scaling
of a Matrix",
journal = j-SINUM,
volume = "11",
number = "3",
pages = "472--479",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Golub:1979:UPD,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Unsymmetric Positive Definite Linear Systems",
journal = j-LAA,
volume = "28",
pages = "85--97",
year = "1979",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Golub:1996:MC,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Matrix Computations",
publisher = pub-JOHNS-HOPKINS,
address = pub-JOHNS-HOPKINS:adr,
edition = "Third",
pages = "xxvii + 694",
year = "1996",
ISBN = "0-8018-5413-X (hardcover), 0-8018-5414-8 (paperback)",
ISBN-13 = "978-0-8018-5413-2 (hardcover), 978-0-8018-5414-9
(paperback)",
LCCN = "QA188 .G65 1996",
MRclass = "65-02 (65Fxx)",
MRnumber = "1417720 (97g:65006)",
bibdate = "Fri Nov 21 06:49:56 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/numana1990.bib",
series = "Johns Hopkins Studies in the Mathematical Sciences",
URL = "http://www.loc.gov/catdir/bios/jhu052/96014291.html;
http://www.loc.gov/catdir/description/jhu051/96014291.html",
acknowledgement = ack-njh # " and " # ack-nhfb # " and " # ack-rah,
author-dates = "Gene H. Golub (1932--2007)",
tableofcontents = "Preface to the Third Edition / xi \\
Software / xiii \\
Selected References / xv \\
1: Matrix Multiplication Problems \\
1.1 Basic Algorithms and Notation / 2 \\
1.2 Exploiting Structure / 16 \\
1.3 Block Matrices and Algorithms / 24 \\
1.4 Vectorization and Re-Use Issues / 34 \\
2: Matrix Analysis 48 V 2.1 Basic Ideas from Linear
Algebra / 48 \\
2.2 Vector Norms / 52 \\
2.3 Matrix Norms / 54 \\
2.4 Finite Precision Matrix Computations / 59 \\
2.5 Orthogonality and the SVD / 69 \\
2.6 Projections and the $CS$ Decomposition / 75 \\
2.7 The Sensitivity of Square Linear Systems / 80 \\
3: General Linear Systems / 87 \\
3.1 Triangular Systems / 88 \\
3.2 The $L U$ Factorization / 94 \\
3.3 Roundoff Analysis of Gaussian Elimination / 104 \\
3.4 Pivoting / 109 \\
3.5 Improving and Estimating Accuracy / 123 \\
4: Special Linear Systems / 133 \\
4.1 The $L D M^T$ and $L D L^T$ Factorizations / 135
\\
4.2 Positive Definite Systems / 140 \\
4.3 Banded Systems / 152 \\
4.4 Symmetric Indefinite Systems / 161 \\
4.5 Block Systems / 174 \\
4.6 Vandermonde Systems and the FFT / 183 \\
4.7 Toeplitz and Related Systems / 193 \\
5: Orthogonalization and Least Squares / 206 \\
5.1 Householder and Givens Matrices / 208 \\
5.2 The $Q R$ Factorization / 223 \\
5.3 The Full Rank LS Problem / 236 \\
5.4 Other Orthogonal Factorizations / 248 \\
5.5 The Rank Deficient LS Problem / 256 \\
5.6 Weighting and Iterative Improvement / 264 \\
5.7 Square and Underdetermined Systems / 270 \\
6: Parallel Matrix Computations / 275 \\
6.1 Basic Concepts / 276 \\
6.2 Matrix Multiplication / 292 \\
6.3 Factorizations / 300 \\
7: The Unsymmetric Eigenvalue Problem / 308 \\
7.1 Properties and Decompositions / 310 \\
7.2 Perturbation Theory / 320 \\
7.3 Power Iterations / 330 \\
7.4 The Hessenberg and Real Schur Forms / 341 \\
7.5 The Practical $Q R$ Algorithm / 352 \\
7.6 Invariant Subspace Computations / 362 \\
7.7 The $Q Z$ Method for $A x = \lambda B x$ / 375 \\
8: The Symmetric Eigenvalue Problem / 391 \\
8.1 Properties and Decompositions / 393 \\
8.2 Power Iterations / 405 \\
8.3 The Symmetric $Q R$ Algorithm / 414 \\
8.4 Jacobi Methods / 426 \\
8.5 Tridiagonal Methods / 439 \\
8.6 Computing the SVD / 448 \\
8.7 Some Generalized Eigenvalue Problems / 461 \\
9: Lanczos Methods / 470 \\
9.1 Derivation and Convergence Properties / 471 \\
9.2 Practical Lanczos Procedures / 479 \\
9.3 Applications to $A x = b$ and Least Squares / 490
\\
9.4 Arnoldi and Unsymmetric Lanczos / 499 \\
10: Iterative Methods for Linear Systems / 508 \\
10.1 The Standard Iterations / 509 \\
10.2 The Conjugate Gradient Method / 520 \\
10.3 Preconditioned Conjugate Gradients / 532 \\
10.4 Other Krylov Subspace Methods / 544 \\
11: Functions of Matrices / 555 \\
11.1 Eigenvalue Methods / 556 \\
11.2 Approximation Methods / 562 \\
11.3 The Matrix Exponential / 572 \\
12: Special Topics / 579 \\
12.1 Constrained Least Squares / 580 \\
12.2 Subset Selection Using the SVD / 590 \\
12.3 Total Least Squares / 595 \\
12.4 Computing Subspaces with the SVD / 601 \\
12.5 Updating Matrix Factorizations / 606 \\
12.6 Modified/Structured Eigenproblems / 621 \\
Bibliography / 637 \\
Index / 687",
}
@Article{Goldstine:1951:NIM,
author = "Herman H. Goldstine and John von Neumann",
title = "Numerical Inverting of Matrices of High Order {II}",
journal = j-PROC-AMS,
volume = "2",
pages = "188--202",
year = "1951",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted in \cite[pp.~558--572]{Taub:1963:JNC}",
}
@Article{Golub:1966:NIR,
author = "G. H. Golub and J. H. Wilkinson",
title = "Note on the iterative refinement of least squares
solution",
journal = j-NUM-MATH,
volume = "9",
pages = "139--148",
year = "1966",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Golub:1976:ICE,
author = "G. H. Golub and J. H. Wilkinson",
title = "Ill-Conditioned Eigensystems and the Computation of
the {Jordan} Canonical Form",
journal = j-SIREV,
volume = "18",
number = "4",
pages = "578--619",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gallivan:1990:PAD,
author = "K. A. Gallivan and R. J. Plemmons and A. H. Sameh",
title = "Parallel Algorithms for Dense Linear Algebra
Computations",
journal = j-SIREV,
volume = "32",
number = "1",
pages = "54--135",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Granville:1992:ZBB,
author = "Andrew Granville",
title = "{Zaphod Beeblebrox's} Brain and the Fifty-Ninth Row of
{Pascal's} Triangle",
journal = j-AMM,
volume = "99",
pages = "318--331",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Greenbaum:1989:BSP,
author = "Anne Greenbaum",
title = "Behavior of Slightly Perturbed {Lanczos} and
Conjugate-Gradient Recurrences",
journal = j-LAA,
volume = "113",
pages = "7--63",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Greenbaum:1994:LCG,
author = "Anne Greenbaum",
editor = "J. David Brown and Moody T. Chu and Donald C. Ellison
and Robert J. Plemmons",
booktitle = "Proceedings of the {Cornelius Lanczos} International
Centenary Conference",
title = "The {Lanczos} and Conjugate Gradient Algorithms in
Finite Precision Arithmetic",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "49--60",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Greenbaum:1997:IMS,
author = "Anne Greenbaum",
title = "Iterative Methods for Solving Linear Systems",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xiii + 220",
year = "1997",
ISBN = "0-89871-396-X",
ISBN-13 = "978-0-89871-396-1",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Greenbaum:1997:EAA,
author = "Anne Greenbaum",
title = "Estimating the Attainable Accuracy of Recursively
Computed Residual Methods",
journal = j-SIMAX,
volume = "18",
number = "3",
pages = "535--551",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Griewank:1985:SNE,
author = "Andreas Griewank",
title = "On Solving Nonlinear Equations with Simple
Singularities or Nearly Singular Solutions",
journal = j-SIREV,
volume = "27",
number = "4",
pages = "537--563",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Gregory:1969:CMT,
author = "Robert T. Gregory and David L. Karney",
title = "A Collection of Matrices for Testing Computational
Algorithms",
publisher = pub-Wiley,
address = pub-Wiley:adr,
pages = "ix + 154",
year = "1969",
ISBN = "0-88275-649-4",
ISBN-13 = "978-0-88275-649-3",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted with corrections by Robert E. Krieger,
Huntington, New York, 1978",
}
@Article{Grimes:1981:CNE,
author = "Roger G. Grimes and John G. Lewis",
title = "Condition Number Estimation for Sparse Matrices",
journal = j-SISSC,
volume = "2",
number = "4",
pages = "384--388",
year = "1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gragg:1976:SVS,
author = "W. B. Gragg and G. W. Stewart",
title = "A Stable Variant of the Secant Method for Solving
Nonlinear Equations",
journal = j-SINUM,
volume = "13",
number = "6",
pages = "889--903",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Greenbaum:1992:PBF,
author = "Anne Greenbaum and Zden{\u{e}}k Strako{\u{s}}",
title = "Predicting the Behavior of Finite Precision {Lanczos}
and Conjugate Gradient Computations",
journal = j-SIMAX,
volume = "13",
number = "1",
pages = "121--137",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gill:1996:SCF,
author = "Philip E. Gill and Michael A. Saunders and Joseph R.
Shinnerl",
title = "On the Stability of {Cholesky} Factorization for
Symmetric Quasidefinite Systems",
journal = j-SIMAX,
volume = "17",
number = "1",
pages = "35--46",
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gu:1998:BPB,
author = "Ming Gu",
title = "Backward Perturbation Bounds for Linear Least Squares
Problems",
journal = j-SIMAX,
volume = "20",
number = "2",
pages = "363--372",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gustafson:1996:MPS,
author = "John L. Gustafson and Srinivas Aluru",
title = "Massively Parallel Searching for Better Algorithms or,
How to Do a Cross Product with Five Multiplications",
journal = j-SCI-PROG,
volume = "",
pages = "203--213",
year = "1996",
CODEN = "SCIPEV",
ISSN = "1058-9244 (print), 1875-919X (electronic)",
ISSN-L = "1058-9244",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Scientific Programming",
journal-URL = "http://iospress.metapress.com/content/1058-9244",
}
@Article{Gulliksson:1994:IRC,
author = "M{\aa}rten Gulliksson",
title = "Iterative Refinement for Constrained and Weighted
Linear Least Squares",
journal = j-BIT,
volume = "34",
pages = "239--253",
year = "1994",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Gulliksson:1995:BEA,
author = "M{\aa}rten Gulliksson",
title = "Backward Error Analysis for the Constrained and
Weighted Linear Least Squares Problem When Using the
Weighted {$QR$} Factorization",
journal = j-SIMAX,
volume = "16",
number = "2",
pages = "675--687",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Gustavson:1997:RLA,
author = "F. G. Gustavson",
title = "Recursion Leads to Automatic Variable Blocking for
Dense Linear-Algebra Algorithms",
journal = j-IBM-JRD,
volume = "41",
number = "6",
pages = "737--755",
month = nov,
year = "1997",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Gulliksson:1992:MQD,
author = "M{\aa}rten Gulliksson and Per-{\AA}ke Wedin",
title = "Modifying the {QR}-Decomposition to Constrained and
Weighted Linear Least Squares",
journal = j-SIMAX,
volume = "13",
number = "4",
pages = "1298--1313",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Hull:1985:NT,
author = "T. E. Hull and A. Abraham and M. S. Cohen and A. F. X.
Curley and C. B. Hall and D. A. Penny and J. T. M.
Sawchuk",
title = "Numerical {TURING}",
journal = j-SIGNUM,
volume = "20",
number = "3",
pages = "26--34",
year = "1985",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
}
@Article{Hager:1984:CE,
author = "William W. Hager",
title = "Condition Estimates",
journal = j-SISSC,
volume = "5",
number = "2",
pages = "311--316",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Hall:1967:CT,
author = "Marshall {Hall, Jr.}",
title = "Combinatorial Theory",
publisher = pub-Blaisdell,
address = pub-Blaisdell:adr-MA,
pages = "x + 310",
year = "1967",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Hamada:1987:NRN,
author = "Hozumi Hamada",
editor = "Mary Jane Irwin and Renato Stefanelli",
booktitle = "Proceedings of the Eighth Symposium on Computer
Arithmetic, Como, Italy",
title = "A New Real Number Representation and its Operation",
publisher = "IEEE Computer Society, Washington, D.C.",
pages = "153--157",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Hamming:1973:NMS,
author = "R. W. Hamming",
title = "Numerical Methods for Scientists and Engineers",
publisher = pub-MH,
address = pub-MH:adr,
edition = "Second",
pages = "ix + 721",
year = "1973",
ISBN = "0-07-025887-2",
ISBN-13 = "978-0-07-025887-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Hammarling:1974:NMG,
author = "Sven Hammarling",
title = "A Note on Modifications to the {Givens} Plane
Rotation",
journal = j-JIMA,
volume = "13",
pages = "215--218",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Hammarling:1982:NSS,
author = "S. J. Hammarling",
title = "Numerical Solution of the Stable, Non-Negative
Definite {Lyapunov} Equation",
journal = j-IMAJNA,
volume = "2",
pages = "303--323",
year = "1982",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Hammarling:1987:NSG,
author = "Sven J. Hammarling",
editor = "T. S. Durrani and J. B. Abbiss and J. E. Hudson",
booktitle = "Mathematics in Signal Processing",
title = "The Numerical Solution of the General {Gauss--Markov}
Linear Model",
publisher = pub-OUP,
pages = "451--456",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Unpublished{Hanson:1997:AML,
author = "Richard J. Hanson",
title = "{Aasen's} Method for Linear Systems with Self-Adjoint
Matrices",
month = jul,
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Visual Numerics, Inc.,
\path|http://www.vni.com/books/whitepapers/Aasen.html|",
}
@Book{Hardy:1967:CPM,
author = "G. H. Hardy",
title = "A Course of Pure Mathematics",
publisher = pub-CUP,
edition = "Tenth",
pages = "xii + 509",
year = "1967",
ISBN = "0-521-09227-2",
ISBN-13 = "978-0-521-09227-2",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Harter:1972:OWF,
author = "Richard Harter",
title = "The Optimality of {Winograd's} Formula",
journal = j-CACM,
volume = "15",
number = "5",
pages = "352",
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Hartfiel:1980:CSS,
author = "D. J. Hartfiel",
title = "Concerning the Solution Set of {$Ax = b$} where {$P
\le A \le Q$} and {$p \le b \le q$}",
journal = j-NUM-MATH,
volume = "35",
pages = "355--359",
year = "1980",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Hauser:1996:HFP,
author = "John R. Hauser",
title = "Handling Floating-Point Exceptions in Numeric
Programs",
journal = j-TPLS,
volume = "18",
number = "2",
pages = "139--174",
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Hairer:1991:SOD,
author = "E. Hairer and G. Wanner",
title = "Solving Ordinary Differential Equations {II}",
publisher = pub-Springer,
address = pub-Springer:adr-B,
pages = "xv + 601",
year = "1991",
ISBN = "3-540-53775-9",
ISBN-13 = "978-3-540-53775-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Hammarling:1976:PBL,
author = "S. J. Hammarling and J. H. Wilkinson",
title = "The Practical Behaviour of Linear Iterative Methods
with Particular Reference to {S.O.R.}",
type = "Report",
number = "NAC 69",
institution = inst-NPL,
address = inst-NPL:adr,
pages = "19",
month = sep,
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Hearon:1977:NS,
author = "John Z. Hearon",
title = "Nonsingular Solutions of {$TA-BT=C$}",
journal = j-LAA,
volume = "16",
pages = "57--63",
year = "1977",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Heath:1984:NML,
author = "Michael T. Heath",
title = "Numerical Methods for Large Sparse Linear Least
Squares Problems",
journal = j-SISSC,
volume = "5",
number = "3",
pages = "497--513",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Hein:1992:G,
author = "Piet Hein",
title = "Grooks",
number = "85",
publisher = "Borgens Forlag",
address = "Copenhagen, Denmark",
edition = "Second",
pages = "53",
year = "1992",
ISBN = "87-418-1079-1",
ISBN-13 = "978-87-418-1079-9",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Borgens Pocketbooks",
}
@Article{Hewer:1988:SSL,
author = "Gary Hewer and Charles Kenney",
title = "The Sensitivity of the Stable {Lyapunov} Equation",
journal = j-SICOPT,
volume = "26",
number = "2",
pages = "321--344",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Henrici:1962:BII,
author = "Peter Henrici",
title = "Bounds for Iterates, Inverses, Spectral Variation and
Fields of Values of Non-Normal Matrices",
journal = j-NUM-MATH,
volume = "4",
pages = "24--40",
year = "1962",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{Henrici:1962:DVM,
author = "Peter Henrici",
title = "Discrete Variable Methods in Ordinary Differential
Equations",
publisher = "John Wiley",
address = "New York",
pages = "xi + 407",
year = "1962",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Henrici:1963:EPD,
author = "Peter Henrici",
title = "Error Propagation for Difference Methods",
publisher = "John Wiley",
address = "New York",
pages = "vi + 73",
year = "1963",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Henrici:1964:ENA,
author = "Peter Henrici",
title = "Elements of Numerical Analysis",
publisher = pub-Wiley,
address = pub-Wiley:adr,
pages = "xv + 328",
year = "1964",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Henrici:1966:TPM,
author = "Peter Henrici",
title = "Test of Probabilistic Models for the Propagation of
Roundoff Errors",
journal = j-CACM,
volume = "9",
number = "6",
pages = "409--410",
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@InProceedings{Henrici:1980:MPR,
author = "Peter Henrici",
editor = "Karl L. E. Nickel",
booktitle = "Interval Mathematics 1980",
title = "A Model for the Propagation of Rounding Error in
Floating Arithmetic",
publisher = pub-AP # ", " # pub-AP:adr-NY,
pages = "49--73",
year = "1980",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Hennessy:1996:CAQ,
author = "John L. Hennessy and David A. Patterson",
title = "Computer Architecture: {A} Quantitative Approach",
publisher = "Morgan Kaufmann",
address = "San Francisco, CA, USA",
edition = "Second",
pages = "xxiii + 760 + appendices",
year = "1996",
ISBN = "1-55860-329-8",
ISBN-13 = "978-1-55860-329-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Henderson:1981:DIS,
author = "H. V. Henderson and S. R. Searle",
title = "On Deriving the Inverse of a Sum of Matrices",
journal = j-SIREV,
volume = "23",
number = "1",
pages = "53--60",
year = "1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Henderson:1981:VPM,
author = "Harold V. Henderson and S. R. Searle",
title = "The Vec-Permutation Matrix, the Vec Operator and
{Kronecker} Products: {A} Review",
journal = j-LMA,
volume = "9",
pages = "271--288",
year = "1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Hull:1994:ICE,
author = "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter
Tang",
title = "Implementing Complex Elementary Functions Using
Exception Handling",
journal = j-TOMS,
volume = "20",
number = "2",
pages = "215--244",
year = "1994",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@TechReport{Heath:1990:EEI,
author = "M. T. Heath and G. A. Geist and J. B. Drake",
title = "Early Experience with the {Intel iPSC/860} at {Oak
Ridge National Laboratory}",
type = "Report",
number = "ORNL/TM-11655",
institution = inst-ORNL,
address = inst-ORNL:adr,
pages = "26",
month = sep,
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Hammer:1993:NTV,
author = "Rolf Hammer and Matthias Hocks and Ulrich Kulisch and
Dietmar Ratz",
title = "Numerical Toolbox for Verified Computing {I}. {Basic}
Numerical Problems: Theory, Algorithms, and
{Pascal-XSC} Programs",
publisher = pub-Springer,
address = pub-Springer:adr-B,
pages = "xiii + 337",
year = "1993",
ISBN = "3-540-57118-3",
ISBN-13 = "978-3-540-57118-6",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:2000:QFC,
author = "Nicholas J. Higham",
title = "{QR} Factorization with Complete Pivoting and Accurate
Computation of the {SVD}",
journal = j-LAA,
volume = "309",
pages = "153--174",
year = "2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:2001:EPA,
author = "Nicholas J. Higham",
title = "Evaluating {Pad\'e} Approximants of the Matrix
Logarithm",
journal = j-SIMAX,
volume = "22",
number = "4",
pages = "1126--1135",
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1986:CPD,
author = "Nicholas J. Higham",
title = "Computing the Polar Decomposition---with
Applications",
journal = j-SISSC,
volume = "7",
number = "4",
pages = "1160--1174",
month = oct,
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1986:EAC,
author = "Nicholas J. Higham",
title = "Efficient Algorithms for Computing the Condition
Number of a Tridiagonal Matrix",
journal = j-SISSC,
volume = "7",
number = "1",
pages = "150--165",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1987:CRS,
author = "Nicholas J. Higham",
title = "Computing Real Square Roots of a Real Matrix",
journal = j-LAA,
volume = "88/89",
pages = "405--430",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1987:SCN,
author = "Nicholas J. Higham",
title = "A Survey of Condition Number Estimation for Triangular
Matrices",
journal = j-SIREV,
volume = "29",
number = "4",
pages = "575--596",
month = dec,
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1987:EAB,
author = "Nicholas J. Higham",
title = "Error Analysis of the {Bj\"orck}-{Pereyra} Algorithms
for Solving {Vandermonde} Systems",
journal = j-NUM-MATH,
volume = "50",
number = "5",
pages = "613--632",
year = "1987",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Higham:1988:CNS,
author = "Nicholas J. Higham",
title = "Computing a Nearest Symmetric Positive Semidefinite
Matrix",
journal = j-LAA,
volume = "103",
pages = "103--118",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1988:FCE,
author = "Nicholas J. Higham",
title = "{FORTRAN} Codes for Estimating the One-norm of a Real
or Complex Matrix, with Applications to Condition
Estimation ({Algorithm} 674)",
journal = j-TOMS,
volume = "14",
number = "4",
pages = "381--396",
month = dec,
year = "1988",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Higham:1988:FSV,
author = "Nicholas J. Higham",
title = "Fast Solution of {Vandermonde}-like Systems Involving
Orthogonal Polynomials",
journal = j-IMAJNA,
volume = "8",
pages = "473--486",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Higham:1989:MNP,
author = "Nicholas J. Higham",
editor = "M. J. C. Gover and S. Barnett",
booktitle = "Applications of Matrix Theory",
title = "Matrix Nearness Problems and Applications",
publisher = pub-OUP,
pages = "1--27",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1989:AST,
author = "Nicholas J. Higham",
title = "The Accuracy of Solutions to Triangular Systems",
journal = j-SINUM,
volume = "26",
number = "5",
pages = "1252--1265",
month = oct,
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Higham:1990:ACD,
author = "Nicholas J. Higham",
editor = "M. G. Cox and S. J. Hammarling",
booktitle = "Reliable Numerical Computation",
title = "Analysis of the {Cholesky} Decomposition of a
Semi-definite Matrix",
publisher = pub-OUP,
pages = "161--185",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1990:EMN,
author = "Nicholas J. Higham",
title = "Experience with a Matrix Norm Estimator",
journal = j-SISSC,
volume = "11",
number = "4",
pages = "804--809",
month = jul,
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Higham:1990:HAG,
author = "Nicholas J. Higham",
editor = "D. F. Griffiths and G. A. Watson",
booktitle = "Numerical Analysis \textup{1989}, Proceedings of the
\textup{13}th Dundee Conference",
title = "How Accurate is {Gaussian} Elimination?",
volume = "228",
publisher = pub-Longman-ST # ", " # pub-Longman-ST:adr,
pages = "137--154",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Pitman Research Notes in Mathematics",
}
@TechReport{Higham:1990:IRE,
author = "Nicholas J. Higham",
title = "Iterative Refinement Enhances the Stability of {$QR$}
Factorization Methods for Solving Linear Equations",
type = t-NAREP,
number = "No. 182",
institution = inst-U-MANCHESTER,
address = inst-U-MANCHESTER:adr,
month = apr,
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Higham:1990:CEB,
author = "Nicholas J. Higham",
editor = "Philip J. Brown and Wayne A. Fuller",
booktitle = "Statistical Analysis of Measurement Error Models and
Applications, Contemporary Mathematics 112",
title = "Computing Error Bounds for Regression Problems",
publisher = pub-AMS # ", " # pub-AMS:adr,
pages = "195--208",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1990:EFM,
author = "Nicholas J. Higham",
title = "Exploiting Fast Matrix Multiplication within the Level
3 {BLAS}",
journal = j-TOMS,
volume = "16",
number = "4",
pages = "352--368",
month = dec,
year = "1990",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Higham:1990:BEG,
author = "Nicholas J. Higham",
title = "Bounding the Error in {Gaussian} Elimination for
Tridiagonal Systems",
journal = j-SIMAX,
volume = "11",
number = "4",
pages = "521--530",
month = oct,
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1990:SAA,
author = "Nicholas J. Higham",
title = "Stability Analysis of Algorithms for Solving Confluent
{Vandermonde}-like Systems",
journal = j-SIMAX,
volume = "11",
number = "1",
pages = "23--41",
month = jan,
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1991:TMP,
author = "Nicholas J. Higham",
title = "Three Measures of Precision in Floating Point
Arithmetic",
journal = j-NA-DIGEST,
volume = "Volume 91, Issue 16",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Electronic mail magazine:
\path|na.help@na-net.ornl.gov|",
fjournal = "NA Digest",
}
@Article{Higham:1991:IRE,
author = "Nicholas J. Higham",
title = "Iterative Refinement Enhances the Stability of {$QR$}
Factorization Methods for Solving Linear Equations",
journal = j-BIT,
volume = "31",
pages = "447--468",
year = "1991",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Higham:1992:EMN,
author = "Nicholas J. Higham",
title = "Estimating the Matrix {$p$}-norm",
journal = j-NUM-MATH,
volume = "62",
pages = "539--555",
year = "1992",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Higham:1992:SMM,
author = "Nicholas J. Higham",
title = "Stability of a Method for Multiplying Complex Matrices
with Three Real Matrix Multiplications",
journal = j-SIMAX,
volume = "13",
number = "3",
pages = "681--687",
month = jul,
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1993:ODS,
author = "Nicholas J. Higham",
title = "Optimization by Direct Search in Matrix Computations",
journal = j-SIMAX,
volume = "14",
number = "2",
pages = "317--333",
month = apr,
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1993:AFP,
author = "Nicholas J. Higham",
title = "The Accuracy of Floating Point Summation",
journal = j-SISC,
volume = "14",
number = "4",
pages = "783--799",
month = jul,
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1993:PTB,
author = "Nicholas J. Higham",
title = "Perturbation Theory and Backward Error for
{$AX-XB=C$}",
journal = j-BIT,
volume = "33",
pages = "124--136",
year = "1993",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@InProceedings{Higham:1994:SCP,
author = "Nicholas J. Higham",
editor = "Walter Gautschi",
booktitle = "{Mathematics of Computation} \textup{1943--1993}: {A}
Half Century of Computational Mathematics",
title = "A Survey of Componentwise Perturbation Theory in
Numerical Linear Algebra",
volume = "48",
publisher = pub-AMS # ", " # pub-AMS:adr,
pages = "49--77",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Proceedings of Symposia in Applied Mathematics",
}
@Article{Higham:1994:MSD,
author = "Nicholas J. Higham",
title = "The Matrix Sign Decomposition and Its Relation to the
Polar Decomposition",
journal = j-LAA,
volume = "212/213",
pages = "3--20",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1995:CNT,
author = "Desmond J. Higham",
title = "Condition Numbers and Their Condition Numbers",
journal = j-LAA,
volume = "214",
pages = "193--213",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Higham:1995:TMT,
author = "Nicholas J. Higham",
title = "The {Test Matrix Toolbox} for {MATLAB} (Version 3.0)",
type = t-NAREP,
number = "No. 276",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "70",
month = sep,
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1995:SPT,
author = "Nicholas J. Higham",
title = "Stability of Parallel Triangular System Solvers",
journal = j-SISC,
volume = "16",
number = "2",
pages = "400--413",
month = mar,
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1997:SDP,
author = "Nicholas J. Higham",
title = "Stability of the Diagonal Pivoting Method with Partial
Pivoting",
journal = j-SIMAX,
volume = "18",
number = "1",
pages = "52--65",
month = jan,
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1997:IRL,
author = "Nicholas J. Higham",
title = "Iterative Refinement for Linear Systems and {LAPACK}",
journal = j-IMAJNA,
volume = "17",
number = "4",
pages = "495--509",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1997:SIM,
author = "Nicholas J. Higham",
title = "Stable Iterations for the Matrix Square Root",
journal = j-NUM-ALG,
volume = "15",
number = "2",
pages = "227--242",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1998:FCS,
author = "Nicholas J. Higham",
title = "Factorizing Complex Symmetric Matrices with Positive
Definite Real and Imaginary Parts",
journal = j-MATH-COMP,
volume = "67",
number = "224",
pages = "1591--1599",
month = oct,
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1999:SBF,
author = "Nicholas J. Higham",
title = "Stability of Block $\mathrm{LDL^T}$ Factorization of a
Symmetric Tridiagonal Matrix",
journal = j-LAA,
volume = "287",
pages = "181--189",
year = "1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Higham:1999:NAS,
author = "Nicholas J. Higham",
editor = "Mark Ainsworth and Jeremy Levesley and Marco
Marletta",
booktitle = "The Graduate Student's Guide to Numerical Analysis
'\textup{98}",
title = "Notes on Accuracy and Stability of Algorithms in
Numerical Linear Algebra",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
pages = "48--82",
year = "1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Higham:1998:HWM,
author = "Nicholas J. Higham",
title = "Handbook of Writing for the Mathematical Sciences",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Second",
pages = "xvi + 302",
year = "1998",
ISBN = "0-89871-420-6",
ISBN-13 = "978-0-89871-420-3",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Higham:2002:ASN,
author = "Nicholas J. Higham",
title = "Accuracy and Stability of Numerical Algorithms",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Second",
pages = "xxx + 680",
year = "2002",
ISBN = "0-89871-521-0",
ISBN-13 = "978-0-89871-521-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1989:LGF,
author = "Nicholas J. Higham and Desmond J. Higham",
title = "Large Growth Factors in {Gaussian} Elimination with
Pivoting",
journal = j-SIMAX,
volume = "10",
number = "2",
pages = "155--164",
month = apr,
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1992:BEC,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "Backward Error and Condition of Structured Linear
Systems",
journal = j-SIMAX,
volume = "13",
number = "1",
pages = "162--175",
month = jan,
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1992:CPT,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "Componentwise Perturbation Theory for Linear Systems
with Multiple Right-Hand Sides",
journal = j-LAA,
volume = "174",
pages = "111--129",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Higham:2000:MG,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "{MATLAB} Guide",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxii + 283",
year = "2000",
ISBN = "0-89871-516-4",
ISBN-13 = "978-0-89871-516-3",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:2000:NAQ,
author = "Nicholas J. Higham and Hyun-Min Kim",
title = "Numerical Analysis of a Quadratic Matrix Equation",
journal = j-IMAJNA,
volume = "20",
number = "4",
pages = "499--519",
year = "2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Higham:1993:CEA,
author = "Nicholas J. Higham and Philip A. Knight",
editor = "Carl D. Meyer and Robert J. Plemmons",
booktitle = "Linear Algebra, Markov Chains, and Queueing Models",
title = "Componentwise Error Analysis for Stationary Iterative
Methods",
volume = "48",
publisher = pub-Springer # ", " # pub-Springer:adr-NY,
pages = "29--46",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "IMA Volumes in Mathematics and Its Applications",
}
@Article{Higham:1993:FPB,
author = "Nicholas J. Higham and Philip A. Knight",
title = "Finite Precision Behavior of Stationary Iteration for
Solving Singular Systems",
journal = j-LAA,
volume = "192",
pages = "165--186",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1995:MPF,
author = "Nicholas J. Higham and Philip A. Knight",
title = "Matrix Powers in Finite Precision Arithmetic",
journal = j-SIMAX,
volume = "16",
number = "2",
pages = "343--358",
month = apr,
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Hilbert:1894:BTL,
author = "David Hilbert",
title = "{Ein Beitrag zur Theorie des Legendre'schen
Polynoms}",
journal = j-ACTA-MATH,
volume = "18",
pages = "155--159",
year = "1894",
CODEN = "ACMAA8",
ISSN = "0001-5962 (print), 1871-2509 (electronic)",
ISSN-L = "0001-5962",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Acta Mathematica",
journal-URL = "http://link.springer.com/journal/11511",
}
@Book{Hildebrand:1974:INA,
author = "F. B. Hildebrand",
title = "Introduction to Numerical Analysis",
publisher = pub-MH,
address = pub-MH:adr,
edition = "Second",
pages = "xiii + 669",
year = "1974",
ISBN = "0-486-65363-3",
ISBN-13 = "978-0-486-65363-1",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted by Dover, New York, 1987",
}
@Article{Higham:1994:PAC,
author = "Nicholas J. Higham and Pythagoras Papadimitriou",
title = "A Parallel Algorithm for Computing the Polar
Decomposition",
journal = j-PAR-COMP,
volume = "20",
number = "8",
pages = "1161--1173",
month = aug,
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1994:SPI,
author = "Nicholas J. Higham and Alex Pothen",
title = "Stability of the Partitioned Inverse Method for
Parallel Solution of Sparse Triangular Systems",
journal = j-SISC,
volume = "15",
number = "1",
pages = "139--148",
month = jan,
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Higham:1987:NLA,
author = "Nicholas J. Higham and G. W. Stewart",
editor = "A. Iserles and M. J. D. Powell",
booktitle = "The State of the Art in Numerical Analysis",
title = "Numerical Linear Algebra in Statistical Computing",
publisher = pub-OUP,
pages = "41--57",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:2000:BAM,
author = "Nicholas J. Higham and Fran\c{c}oise Tisseur",
title = "A Block Algorithm for Matrix 1-Norm Estimation, with
an Application to 1-Norm Pseudospectra",
journal = j-SIMAX,
volume = "21",
number = "4",
pages = "1185--1201",
year = "2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Higham:2001:BEM,
author = "Nicholas J. Higham and Fran\c{c}oise Tisseur",
title = "Bounds for Eigenvalues of Matrix Polynomials",
type = t-NAREP,
number = "371",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "16",
month = jan,
year = "2001",
note = "To appear in " # j-LAA,
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Higham:1993:SO,
author = "Desmond J. Higham and Lloyd N. Trefethen",
title = "Stiffness of {ODE}s",
journal = j-BIT,
volume = "33",
pages = "285--303",
year = "1993",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@InProceedings{Hida:2001:AQD,
author = "Yozo Hida and Xiaoye S. Li and David H. Bailey",
editor = "",
booktitle = "Proc. 15th IEEE Symposium on Computer Arithmetic",
title = "Algorithms for Quad-Double Precision Floating Point
Arithmetic",
publisher = "IEEE Computer Society Press, Los Alamitos, CA, USA",
pages = "155--162",
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Hardy:1952:I,
author = "G. H. Hardy and J. E. Littlewood and G. P{\'o}lya",
title = "Inequalities",
publisher = pub-CUP,
edition = "Second",
pages = "xii + 324",
year = "1952",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Holt:1988:TPL,
author = "R. C. Holt and J. R. Cordy",
title = "The {Turing} Programming Language",
journal = j-CACM,
volume = "31",
number = "12",
pages = "1410--1423",
year = "1988",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@InProceedings{Hodel:1992:RAL,
author = "A. Scottedward Hodel",
editor = "R. Beauwens and P. de Groen",
booktitle = "Iterative Methods in Linear Algebra",
title = "Recent Applications of the {Lyapunov} Equation in
Control Theory",
publisher = "Elsevier Science Publishers B.V. (North-Holland)",
address = pub-NH:adr,
pages = "217--227",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Hodges:1983:ATE,
author = "Andrew Hodges",
title = "{Alan Turing}: {The} Enigma",
publisher = "Burnett Books",
address = "London",
pages = "xix + 586",
year = "1983",
ISBN = "0-09-911641-3",
ISBN-13 = "978-0-09-911641-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "1992 edition with preface, Vintage, London",
}
@Article{Hoffmann:1987:SLS,
author = "W. Hoffmann",
title = "Solving Linear Systems on a Vector Computer",
journal = j-JCAM,
volume = "18",
pages = "353--367",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Hoffmann:1989:IAG,
author = "W. Hoffmann",
title = "Iterative Algorithms for {Gram--Schmidt}
Orthogonalization",
journal = j-COMPUTING,
volume = "41",
pages = "335--348",
year = "1989",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Hoffmann:1989:PAR,
author = "Christoph M. Hoffmann",
title = "The Problems of Accuracy and Robustness in Geometric
Computation",
journal = j-COMPUTER,
volume = "March",
pages = "31--41",
year = "1989",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computer",
journal-URL = "http://www.computer.org/portal/web/csdl/magazines/computer",
}
@Book{Hockney:1988:PCA,
author = "Roger W. Hockney and Chris R. Jesshope",
title = "Parallel Computers: Architecture, Programming, and
Algorithms",
publisher = pub-ADAM-HILGER,
address = pub-ADAM-HILGER:adr,
edition = "Second",
pages = "xv + 625",
year = "1988",
ISBN = "0-85274-811-6 (hardcover), 0-85274-812-4 (paperback)",
ISBN-13 = "978-0-85274-811-4 (hardcover), 978-0-85274-812-1
(paperback)",
LCCN = "QA76.5 .H57 1988",
MRclass = "68-02, 65-04, 65Y05, 68N25",
bibdate = "Sun Jul 10 01:08:36 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
ZMnumber = "0641.68001",
abstract = "Parallel Computers 2 follows the development of large
fast supercomputers and provides a thorough guide to
all aspects of the subject; technology, computer
architecture, languages and algorithms using successful
commercially available products as examples. Of
interest to computer scientists, electronics engineers
and physicists in academia and industry, students on
MSc courses and final year undergraduates in computer
science, parallel computers, supercomputers, parallel
architectures, etc.",
acknowledgement = ack-nhfb,
libnote = "Not yet in my library.",
}
@Book{Horn:1985:MA,
author = "Roger A. Horn and Charles R. Johnson",
title = "Matrix Analysis",
publisher = pub-CUP,
pages = "xiii + 561",
year = "1985",
ISBN = "0-521-30586-1",
ISBN-13 = "978-0-521-30586-0",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Horn:1991:TMA,
author = "Roger A. Horn and Charles R. Johnson",
title = "Topics in Matrix Analysis",
publisher = pub-CUP,
pages = "viii + 607",
year = "1991",
ISBN = "0-521-30587-X",
ISBN-13 = "978-0-521-30587-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Horning:1979:NPR,
author = "Jim Horning",
title = "Note on Program Reliability",
journal = j-ACM-SIGSOFT,
volume = "4",
number = "4",
pages = "6",
year = "1979",
CODEN = "SFENDP",
ISSN = "0163-5948 (print), 1943-5843 (electronic)",
ISSN-L = "0163-5948",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Cited in \cite{Tropp:1984:FA}",
fjournal = "ACM Sigsoft",
}
@Article{Hochbruck:1995:PKS,
author = "Marlis Hochbruck and Gerhard Starke",
title = "Preconditioned {Krylov} Subspace Methods for
{Lyapunov} Matrix Equations",
journal = j-SIMAX,
volume = "16",
number = "1",
pages = "156--171",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Hotelling:1943:SNM,
author = "Harold Hotelling",
title = "Some New Methods in Matrix Calculation",
journal = j-ANN-MATH-STAT,
volume = "14",
number = "1",
pages = "1--34",
year = "1943",
CODEN = "AASTAD",
ISSN = "0003-4851 (print), 2168-8990 (electronic)",
ISSN-L = "0003-4851",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Annals of Mathematical Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aoms/",
}
@Article{Hough:1981:API,
author = "David Hough",
title = "Applications of the Proposed {IEEE 754} Standard for
Floating-Point Arithmetic",
journal = j-COMPUTER,
volume = "14",
pages = "70--74",
year = "1981",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computer",
journal-URL = "http://www.computer.org/portal/web/csdl/magazines/computer",
}
@Article{Hough:1989:RS,
author = "David Hough",
title = "Random Story",
journal = j-NA-DIGEST,
volume = "Volume 89, Issue 1",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "NA Digest",
}
@Article{hous58,
author = "Alston S. Householder",
title = "Unitary Triangularization of a Nonsymmetric Matrix",
journal = j-ACM,
volume = "5",
pages = "339--342",
year = "1958",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Householder:1964:TMN,
author = "Alston S. Householder",
title = "The Theory of Matrices in Numerical Analysis",
publisher = pub-Blaisdell,
address = pub-Blaisdell:adr-NY,
pages = "xi + 257",
year = "1964",
ISBN = "0-486-61781-5",
ISBN-13 = "978-0-486-61781-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted by Dover, New York, 1975",
}
@Article{Hough:1997:COD,
author = "Patricia D. Hough and Stephen A. Vavasis",
title = "Complete Orthogonal Decomposition for Weighted Least
Squares",
journal = j-SIMAX,
volume = "18",
number = "2",
pages = "369--392",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{hp82,
key = "Hewlett--Packard",
title = "{HP-\textup{15}C} Advanced Functions Handbook",
publisher = "Hewlett--Packard",
address = "Portable Computer Division, Corvallis, OR, USA",
pages = "221",
year = "1982",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Part number 00015-90011 Rev.~C",
}
@Book{hp93,
key = "Hewlett--Packard",
title = "{HP \textup{48}G} Series User's Guide",
publisher = "Hewlett--Packard",
address = "Corvallis Division, Corvallis, OR, USA",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Part number 00048-90126, Edition 3",
}
@Article{Henderson:1983:HKP,
author = "Harold V. Henderson and Friedrich Pukelsheim and
Shayle R. Searle",
title = "On the History of the {Kronecker} Product",
journal = j-LMA,
volume = "14",
pages = "113--120",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Hedayat:1999:OAT,
author = "A. S. Hedayat and N. J. A. Sloane and John Stufken",
title = "Orthogonal Arrays: {Theory} and Applications",
publisher = pub-Springer,
address = pub-Springer:adr-NY,
pages = "xxiii + 416",
year = "1999",
ISBN = "0-387-98766-5",
ISBN-13 = "978-0-387-98766-8",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Hull:1979:CNS,
author = "T. E. Hull",
editor = "Lloyd D. Fosdick",
booktitle = "Performance Evaluation of Numerical Software",
title = "Correctness of Numerical Software",
publisher = pub-NH # ", " # pub-NH:adr,
pages = "3--15",
year = "1979",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Hull:1982:PCE,
author = "T. E. Hull",
editor = "G. A. Watson",
booktitle = "Numerical Analysis Proceedings, Dundee 1981",
title = "Precision Control, Exception Handling and {A} Choice
of Numerical Algorithms",
volume = "912",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
pages = "169--178",
year = "1982",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Lecture Notes in Mathematics",
}
@Article{Hunt:1997:ROA,
author = "Julian Hunt",
title = "Rounding and Other Approximations for Measurements,
Records and Targets",
journal = j-MATH-TODAY,
volume = "33",
pages = "73--77",
year = "1997",
ISSN = "1361-2042",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Mathematics Today",
journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
nuber = "3",
}
@Article{Hu:1992:KSM,
author = "D. Y. Hu and L. Reichel",
title = "Krylov Subspace Methods for the {Sylvester} Equation",
journal = j-LAA,
volume = "172",
pages = "283--313",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Hull:1966:TPM,
author = "T. E. Hull and J. R. Swenson",
title = "Tests of Probabilistic Models for Propagation of
Roundoff Errors",
journal = j-CACM,
volume = "9",
number = "2",
pages = "108--113",
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Misc{Hyman:1957:EEG,
author = "M. A. Hyman",
title = "Eigenvalues and Eigenvectors of General Matrices",
howpublished = "Presented at the 12th National Meeting of the
Association for Computing Machinery, Houston, Texas",
year = "1957",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Cited in \cite{Wilkinson:1963:REA}",
}
@Book{IBM:1988:ESS,
author = "IBM",
title = "Engineering and Scientific Subroutine Library, Guide
and Reference, Release 3",
publisher = "Fourth Edition (Program Number 5668-863)",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Group:1981:PSB,
author = "{IEEE Computer Society Microprocessor Standards
Committee, Floating-Point Working Group}",
title = "A Proposed Standard for Binary Floating-Point
Arithmetic, {Draft} 8.0 of {IEEE Task P754} (With
Introductory Comments by {David Stevenson})",
journal = j-COMPUTER,
volume = "14",
pages = "51--62",
year = "1981",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computer",
journal-URL = "http://www.computer.org/portal/web/csdl/magazines/computer",
}
@Book{ieee85,
key = "IEEE Computer Society",
title = "{IEEE} Standard for Binary Floating-Point Arithmetic,
{ANSI/IEEE} Standard 754-1985",
publisher = "Institute of Electrical and Electronics Engineers",
address = "New York",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted in SIGPLAN Notices, 22(2):9--25, 1987",
}
@Book{ieee87,
key = "IEEE Computer Society",
title = "A Radix-Independent Standard for Floating-Point
Arithmetic, {IEEE} Standard 854-1987",
publisher = "IEEE Computer Society",
address = "New York",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Ikebe:1979:IHM,
author = "Yasuhiko Ikebe",
title = "On Inverses of {Hessenberg} Matrices",
journal = j-LAA,
volume = "24",
pages = "93--97",
year = "1979",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Ikramov:2000:BGF,
author = "Khakim D. Ikramov and Andrey B. Kucherov",
title = "Bounding the Growth Factor in {Gaussian} Elimination
for {Buckley's} Class of Complex Symmetric Matrices",
journal = j-NLAA,
volume = "7",
number = "5",
pages = "269--274",
year = "2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Ikramov:1998:RNC,
author = "Khakim D. Ikramov",
title = "A Remark on ``{A} Note on Constructing a Symmetric
Matrix with Specified Diagonal Entries and
Eigenvalues''",
journal = j-BIT,
volume = "38",
number = "4",
pages = "807",
year = "1998",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Misc{Committee:1993:RGL,
author = "{ILAS Education Committee}",
title = "Report on Graduate Linear Algebra Courses",
howpublished = "Manuscript from the International Linear Algebra
Society",
pages = "4",
month = nov,
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "\path|http://gauss.technion.ac.il/iic/GRAD-ED.SYLLABI|",
}
@Article{Incertis:1985:FMC,
author = "F. Incertis",
title = "A Faster Method of Computing Matrix {Pythagorean}
Sums",
journal = j-IEEE-AC,
volume = "AC-30",
number = "3",
pages = "273--275",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Ince:1992:CWM,
editor = "D. C. Ince",
title = "Collected Works of {A. M. Turing}: {Mechanical}
Intelligence",
publisher = pub-NH,
address = pub-NH:adr,
pages = "xix + 227",
year = "1992",
ISBN = "0-444-88058-5",
ISBN-13 = "978-0-444-88058-1",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Ipsen:1994:USM,
author = "Ilse C. F. Ipsen and Carl D. Meyer",
title = "Uniform Stability of {Markov} Chains",
journal = j-SIMAX,
volume = "15",
number = "4",
pages = "1061--1074",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Iri:1991:HAD,
author = "Masao Iri",
editor = "Andreas Griewank and George F. Corliss",
booktitle = "Automatic Differentiation of Algorithms: {Theory},
Implementation, and Application",
title = "History of Automatic Differentiation and Rounding
Error Estimation",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "3--16",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Isaacson:1966:ANM,
author = "Eugene Isaacson and Herbert Bishop Keller",
title = "Analysis of Numerical Methods",
publisher = pub-Wiley,
address = pub-Wiley:adr,
pages = "xv + 541",
year = "1966",
ISBN = "0-486-68029-0",
ISBN-13 = "978-0-486-68029-3",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted by Dover, New York, 1994",
}
@Article{Jang:1997:CLS,
author = "Ho-Jong Jang",
title = "A Constrained Least-Squares Approach to the Rapid
Reanalysis of Structures",
journal = j-LAA,
volume = "265",
pages = "185--202",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Jalby:1991:SAI,
author = "William Jalby and Bernard Philippe",
title = "Stability Analysis and Improvement of the Block
{Gram--Schmidt} Algorithm",
journal = j-SISSC,
volume = "12",
number = "5",
pages = "1058--1073",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Jansen:1986:HAA,
author = "Paul Jansen and Peter Weidner",
title = "High-Accuracy Arithmetic Software---Some Tests of the
{ACRITH} Problem-Solving Routines",
journal = j-TOMS,
volume = "12",
number = "1",
pages = "62--70",
year = "1986",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Jankowski:1977:IRI,
author = "M. Jankowski and H. Wo{\'z}niakowski",
title = "Iterative Refinement Implies Numerical Stability",
journal = j-BIT,
volume = "17",
pages = "303--311",
year = "1977",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Jankowski:1985:ASC,
author = "M. Jankowski and H. Wo{\'z}niakowski",
title = "The Accurate Solution of Certain Continuous Problems
Using Only Single Precision Arithmetic",
journal = j-BIT,
volume = "25",
pages = "635--651",
year = "1985",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Jennings:1982:BSV,
author = "A. Jennings",
title = "Bounds for the Singular Values of a Matrix",
journal = j-IMAJNA,
volume = "2",
pages = "459--474",
year = "1982",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Jennings:1974:DEA,
author = "L. S. Jennings and M. R. Osborne",
title = "A Direct Error Analysis for Least Squares",
journal = j-NUM-MATH,
volume = "22",
pages = "325--332",
year = "1974",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Jong:1977:TFD,
author = "Lieuwe Sytse de Jong",
title = "Towards a Formal Definition of Numerical Stability",
journal = j-NUM-MATH,
volume = "28",
pages = "211--219",
year = "1977",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Jones:1993:BKF,
author = "Mark T. Jones and Merrell L. Patrick",
title = "{Bunch--Kaufman} Factorization for Real Symmetric
Indefinite Banded Matrices",
journal = j-SIMAX,
volume = "14",
number = "2",
pages = "553--559",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Jones:1994:FSI,
author = "Mark T. Jones and Merrell L. Patrick",
title = "Factoring Symmetric Indefinite Matrices on
High-Performance Architectures",
journal = j-SIMAX,
volume = "15",
number = "1",
pages = "273--283",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Jordan:1968:EEG,
author = "T. L. Jordan",
title = "Experiments on Error Growth Associated with Some
Linear Least-Squares Procedures",
journal = j-MATH-COMP,
volume = "22",
pages = "579--588",
year = "1968",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Joseph:1991:CPN,
author = "George Gheverghese Joseph",
title = "The Crest of the Peacock: {Non-European} Roots of
Mathematics",
publisher = pub-Penguin,
address = pub-Penguin:adr-L,
pages = "xv + 371",
year = "1991",
ISBN = "0-14-012529-9",
ISBN-13 = "978-0-14-012529-0",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Jones:1974:NSE,
author = "William B. Jones and W. J. Thron",
title = "Numerical Stability in Evaluating Continued
Fractions",
journal = j-MATH-COMP,
volume = "28",
number = "127",
pages = "795--810",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Jankowski:1983:NFP,
author = "M. Jankowski and A. Smoktunowicz and H.
Wo{\'z}niakowski",
title = "A Note on Floating-Point Summation of Very Many
Terms",
journal = j-J-INFO-PROC-CYBERNETICS-EIK,
volume = "19",
number = "9",
pages = "435--440",
year = "1983",
CODEN = "JICYE5",
ISSN = "0863-0593",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Journal of Information Processing and Cybernetics: EIK",
}
@Article{Kahan:1963:ANIa,
author = "W. Kahan and I. Farkas",
title = "Algorithm 168: {Newton} Interpolation with Backward
Divided Differences",
journal = j-CACM,
volume = "6",
number = "4",
pages = "165",
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Kahan:1963:ANIb,
author = "W. Kahan and I. Farkas",
title = "Algorithm 169: {Newton} Interpolation with Forward
Divided Differences",
journal = j-CACM,
volume = "6",
number = "4",
pages = "165",
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Kaagstrom:1994:PAG,
author = "Bo K{\aa}gstr{\"o}m",
title = "A Perturbation Analysis of the Generalized {Sylvester}
Equation {$(AR-LB, DR-LE) = (C,F)$}",
journal = j-SIMAX,
volume = "15",
number = "4",
pages = "1045--1060",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Unpublished{Kahan:2001:WVT,
author = "W. Kahan",
title = "What has the Volume of a Tetrahedron to do with
Computer Programming Languages?",
pages = "31",
month = apr,
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Manuscript",
}
@Article{Kahan:1965:FRR,
author = "W. Kahan",
title = "Further Remarks on Reducing Truncation Errors",
journal = j-CACM,
volume = "8",
number = "1",
pages = "40",
year = "1965",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363707.363723",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Kahan:1966:NLA,
author = "W. M. Kahan",
title = "Numerical Linear Algebra",
journal = j-CAN-MATH-BULL,
volume = "9",
number = "??",
pages = "757--801",
month = "????",
year = "1966",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-1966-083-2",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
bibdate = "Thu Sep 8 10:03:18 MDT 2011",
bibsource = "http://cms.math.ca/cmb/v9/;
http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian mathematical bulletin = Bulletin canadien de
math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
}
@InProceedings{Kahan:1972:SEA,
author = "W. Kahan",
booktitle = "Proc. IFIP Congress, Ljubljana",
title = "A Survey of Error Analysis",
publisher = pub-NH # ", " # pub-NH:adr,
pages = "1214--1239",
year = "1972",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Information Processing 71",
}
@TechReport{Kahan:1973:IAL,
author = "W. Kahan",
title = "Implementation of Algorithms (Lecture Notes by {W. S.
Haugeland} and {D. Hough})",
type = "Technical Report",
number = "20",
institution = inst-Berkeley-CS,
address = inst-Berkeley:adr,
year = "1973",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Kahan:1980:IAO,
author = "W. Kahan",
editor = "Karl L. E. Nickel",
booktitle = "Interval Mathematics 1980",
title = "Interval Arithmetic Options in the Proposed {IEEE}
Floating Point Arithmetic Standard",
publisher = pub-AP # ", " # pub-AP:adr-NY,
pages = "99--128",
year = "1980",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Kahan:1981:WDW,
author = "W. Kahan",
title = "Why Do We Need a Floating-Point Arithmetic Standard?",
type = "Technical Report",
institution = inst-Berkeley,
address = inst-Berkeley:adr,
pages = "41",
month = feb,
year = "1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Kahan:1983:MWS,
author = "W. Kahan",
booktitle = "Statistical Computing Section, Proceedings of the
American Statistical Association, Toronto",
title = "Mathematics Written in Sand---The {HP-15C}, {Intel}
8087, etc.",
pages = "12--26",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Kahan:1986:SRC,
author = "W. Kahan",
title = "To Solve a Real Cubic Equation",
type = "Technical Report",
number = "PAM-352",
institution = "Center for Pure and Applied Mathematics, University of
California",
address = inst-Berkeley:adr,
pages = "20",
month = nov,
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Kahan:1987:BCC,
author = "W. Kahan",
editor = "A. Iserles and M. J. D. Powell",
booktitle = "The State of the Art in Numerical Analysis",
title = "Branch Cuts for Complex Elementary Functions or Much
Ado About Nothing's Sign Bit",
publisher = pub-OUP,
pages = "165--211",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Unpublished{Kahan:1987:DPI,
author = "W. Kahan",
title = "Doubled-Precision {IEEE} Standard 754 Floating-Point
Arithmetic",
month = feb,
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Manuscript",
}
@Unpublished{Kahan:1990:HCA,
author = "W. Kahan",
title = "How {Cray}'s Arithmetic Hurts Scientific Computation
(and What Might be Done About It)",
pages = "42",
month = jun,
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Manuscript prepared for the Cray User Group meeting in
Toronto",
}
@Article{Kahan:1991:ARL,
author = "W. Kahan",
title = "Analysis and Refutation of the {LCAS}",
journal = j-SIGNUM,
volume = "26",
number = "3",
pages = "2--15",
year = "1991",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
}
@Unpublished{Kahan:1994:CBV,
author = "W. Kahan",
title = "Computer Benchmarks Versus Accuracy",
month = jun,
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Draft manuscript",
}
@Unpublished{Kahan:1996:IPE,
author = "W. Kahan",
title = "The Improbability of Probabilistic Error Analyses for
Numerical Computations",
pages = "34",
month = mar,
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Manuscript",
}
@Unpublished{Kahan:1996:LNS,
author = "W. Kahan",
title = "Lecture Notes on the Status of {IEEE Standard} 754 for
Binary Floating-Point Arithmetic",
pages = "30",
month = may,
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Manuscript",
}
@Unpublished{Kahan:1997:MAA,
author = "W. Kahan",
title = "Miscalculating Area and Angles of a Needle-Like
Triangle",
pages = "20",
month = jul,
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Manuscript",
}
@InProceedings{Kahan:1985:AIA,
author = "W. Kahan and E. LeBlanc",
editor = "Kai Hwang",
booktitle = "Proceedings of the 7th Symposium on Computer
Arithmetic",
title = "Anomalies in the {IBM ACRITH} Package",
publisher = "IEEE Computer Society Press, Silver Spring, MD, USA",
pages = "322--331",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Karp:1997:HPD,
author = "Alan H. Karp and Peter Markstein",
title = "High-Precision Division and Square Root",
journal = j-TOMS,
volume = "23",
number = "4",
pages = "561--589",
year = "1997",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Karatsuba:1963:MMN,
author = "A. Karatsuba and Yu. Ofman",
title = "Multiplication of Multidigit Numbers on Automata",
journal = j-SOVIET-PHYS-DOKL,
volume = "7",
number = "7",
pages = "595--596",
month = jan,
year = "1963",
CODEN = "SPHDA9",
ISSN = "0038-5689",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Soviet Physics---Doklady",
}
@Article{Kahan:1979:PFP,
author = "W. Kahan and J. Palmer",
title = "On a Proposed Floating-Point Standard",
journal = j-SIGNUM,
volume = "14",
pages = "13--21",
month = oct,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
}
@Article{Kaagstrom:1992:DSM,
author = "Bo K{\aa}gstr{\"o}m and Peter Poromaa",
title = "Distributed and Shared Memory Block Algorithms for the
Triangular {Sylvester} Equation with {${\rm sep}^{-1}$}
Estimators",
journal = j-SIMAX,
volume = "13",
number = "1",
pages = "90--101",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kaagstrom:1996:LSA,
author = "Bo K{\aa}gstr{\"o}m and Peter Poromaa",
title = "{LAPACK}-Style Algorithms and Software for Solving the
Generalized {Sylvester} Equation and Estimating the
Separation Between Regular Matrix Pairs",
journal = j-TOMS,
volume = "22",
number = "1",
pages = "78--103",
year = "1996",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Kaagstrom:1996:CES,
author = "Bo K{\aa}gstr{\"o}m and Peter Poromaa",
title = "Computing Eigenspaces with Specified Eigenvalues of a
Regular Matrix Pair {$(A,B)$} and Condition Estimation:
{Theory}, Algorithms and Software",
journal = j-NUM-ALG,
volume = "12",
pages = "369--407",
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kaporin:1999:PAF,
author = "Igor Kaporin",
title = "A Practical Algorithm for Faster Matrix
Multiplication",
journal = j-NLAA,
volume = "6",
pages = "687--700",
year = "1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Karasalo:1974:CTD,
author = "Ilkka Karasalo",
title = "A Criterion for Truncation of the {$QR$}-Decomposition
Algorithm for the Singular Linear Least Squares
Problem",
journal = j-BIT,
volume = "14",
pages = "156--166",
year = "1974",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Book{Karlin:1968:TP,
author = "Samuel Karlin",
title = "Total Positivity",
volume = "1",
publisher = "Stanford University Press",
address = inst-U-STANFORD:adr,
year = "1968",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Karpinski:1985:PFP,
author = "Richard Karpinski",
title = "Paranoia: {A} Floating-Point Benchmark",
journal = j-BYTE,
volume = "10",
number = "2",
pages = "223--235",
month = feb,
year = "1985",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BYTE Magazine",
}
@Book{Kato:1976:PTL,
author = "Tosio Kato",
title = "Perturbation Theory for Linear Operators",
publisher = pub-Springer,
address = pub-Springer:adr-B,
edition = "Second",
pages = "xxi + 619",
year = "1976",
ISBN = "3-540-97588-5",
ISBN-13 = "978-3-540-97588-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kaufman:1983:MMQ,
author = "Linda Kaufman",
title = "Matrix Methods for Queuing Problems",
journal = j-SISSC,
volume = "4",
number = "3",
pages = "525--552",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kao:2000:LTA,
author = "Ming-Yang Kao and Jie Wang",
title = "Linear-Time Approximation Algorithms for Computing
Numerical Summation with Provably Small Errors",
journal = j-SICOMP,
volume = "29",
number = "5",
pages = "1568--1576",
year = "2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Karlson:1997:EOB,
author = "Rune Karlson and Bertil Wald{\'e}n",
title = "Estimation of Optimal Backward Perturbation Bounds for
the Linear Least Squares Problem",
journal = j-BIT,
volume = "37",
number = "4",
pages = "862--869",
year = "1997",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Kaagstrom:1989:GSM,
author = "Bo K{\aa}gstr{\"o}m and Lars Westin",
title = "Generalized {Schur} Methods with Condition Estimators
for Solving the Generalized {Sylvester} Equation",
journal = j-IEEE-AC,
volume = "AC-34",
number = "7",
pages = "745--751",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kearfott:1996:AIF,
author = "R. Baker Kearfott",
title = "Algorithm 763: {INTERVAL\_ARITHMETIC}: {A Fortran 90}
Module for an Interval Data Type",
journal = j-TOMS,
volume = "22",
number = "4",
pages = "385--392",
year = "1996",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Kearfott:1996:ICI,
author = "R. Baker Kearfott",
title = "Interval Computations: {Introduction}, Uses, and
Resources",
journal = j-EUROMATH-BULL,
volume = "2",
number = "1",
pages = "95--112",
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "\path|http://interval.louisiana.edu/preprints.html|",
fjournal = "Euromath Bulletin",
}
@Book{Kennedy:1980:SC,
author = "William J. {Kennedy, Jr.} and James E. Gentle",
title = "Statistical Computing",
publisher = "Marcel Dekker",
address = "New York",
pages = "xi + 591",
year = "1980",
ISBN = "0-8247-6898-1",
ISBN-13 = "978-0-8247-6898-0",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kenney:1990:SAD,
author = "Charles Kenney and Gary Hewer",
title = "The Sensitivity of the Algebraic and Differential
{Riccati} Equations",
journal = j-SICOPT,
volume = "28",
number = "1",
pages = "50--69",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kenney:1988:CSR,
author = "Charles Kenney and Alan J. Laub",
title = "Controllability and Stability Radii for Companion Form
Systems",
journal = j-MATH-CONTROL-SIGNALS-SYST,
volume = "1",
pages = "239--256",
year = "1988",
CODEN = "MCSYE8",
ISSN = "0932-4194 (print), 1435-568x (electronic)",
ISSN-L = "0932-4194",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Mathematics of control, signals, and systems: MCSS",
}
@Article{Kenney:1994:SSS,
author = "Charles S. Kenney and Alan J. Laub",
title = "Small-Sample Statistical Condition Estimates for
General Matrix Functions",
journal = j-SISC,
volume = "15",
number = "1",
pages = "36--61",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Keller:1965:SSS,
author = "Herbert B. Keller",
title = "On the Solution of Singular and Semidefinite Linear
Systems by Iteration",
journal = j-SINUM,
volume = "2",
number = "2",
pages = "281--290",
year = "1965",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Kelley:1995:IML,
author = "C. T. Kelley",
title = "Iterative Methods for Linear and Nonlinear Equations",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xiii + 165",
year = "1995",
ISBN = "0-89871-352-8",
ISBN-13 = "978-0-89871-352-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Kelley:1999:IMO,
author = "C. T. Kelley",
title = "Iterative Methods for Optimization",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xv + 180",
year = "1999",
ISBN = "0-89871-433-8",
ISBN-13 = "978-0-89871-433-3",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kerr:1990:FCT,
author = "Thomas H. Kerr",
title = "Fallacies in Computational Testing of Matrix Positive
Definiteness/Semidefiniteness",
journal = j-IEEE-TRANS-AEROSP-ELECTRON-SYST,
volume = "26",
number = "2",
pages = "415--421",
year = "1990",
CODEN = "IEARAX",
ISSN = "0018-9251 (print), 1557-9603 (electronic)",
ISSN-L = "0018-9251",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "IEEE Transactions on Aerospace and Electronic Systems",
}
@InProceedings{Krishnan:2001:PEM,
author = "Shankar Krishnan and Mark Foskey and Tim Culver and
John Keyser and Dinesh Manocha",
editor = "David Eppstein and Dan Halperin and Dinesh Manocha",
booktitle = "Proc. ACM Symposium on Computational Geometry",
title = "{PRECISE}: {Efficient} Multiprecision Evaluation of
Algebraic Roots and Predicates for Reliable Geometric
Computation",
publisher = "ACM Press",
pages = "274--283",
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kielbasinski:1973:SAC,
author = "Andrzej Kie{\l}basi{\'n}ski",
title = "Summation algorithm with corrections and some of its
applications",
journal = j-MATH-STOS,
volume = "1",
pages = "22--41",
year = "1973",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "(In Polish, cited in \cite{Jankowski:1983:NFP} and
\cite{Jankowski:1985:ASC})",
fjournal = "Math. Stos.",
}
@Article{Kielbasinski:1981:IRL,
author = "Andrzej Kie{\l}basi{\'n}ski",
title = "Iterative Refinement for Linear Systems in
Variable-Precision Arithmetic",
journal = j-BIT,
volume = "21",
pages = "97--103",
year = "1981",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Kielbasinski:1987:NRE,
author = "Andrzej Kie{\l}basi{\'n}ski",
title = "A Note on Rounding-Error Analysis of {Cholesky}
Factorization",
journal = j-LAA,
volume = "88/89",
pages = "487--494",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Kielbasinski:1988:NLA,
author = "Andrzej Kie{\l}basi{\'n}ski and Hubert Schwetlick",
title = "Numerische Lineare Algebra: {Eine} Computerorientierte
Einf{\"u}hrung",
publisher = "VEB Deutscher",
address = "Berlin",
pages = "472",
year = "1988",
ISBN = "3-87144-999-7",
ISBN-13 = "978-3-87144-999-4",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Kielbasinski:1992:NAL,
author = "Andrzej Kie{\l}basi{\'n}ski and Hubert Schwetlick",
title = "Numeryczna Algebra Liniowa: {Wprowadzenie} do
Oblicze{\'n} Zautomatyzowanych",
publisher = "Wydawnictwa Naukowo-Techniczne",
address = "Warszawa",
pages = "502",
year = "1992",
ISBN = "83-204-1260-9",
ISBN-13 = "978-83-204-1260-4",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kittaneh:1995:SVC,
author = "Fuad Kittaneh",
title = "Singular Values of Companion Matrices and Bounds on
Zeros of Polynomials",
journal = j-SIMAX,
volume = "16",
number = "1",
pages = "333--340",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Klatte:1993:CXC,
author = "R. Klatte and U. W. Kulisch and C. Lawo and M. Rauch
and A. Wiethoff",
title = "{C-XSC}: {A} {C++} Class Library for Extended
Scientific Computing",
publisher = pub-Springer,
address = pub-Springer:adr-B,
year = "1993",
ISBN = "0-387-56328-8",
ISBN-13 = "978-0-387-56328-2",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Klatte:1992:PXL,
author = "R. Klatte and U. W. Kulisch and M. Neaga and D. Ratz
and Ch. Ullrich",
title = "{PASCAL-XSC}---{Language} Reference with Examples",
publisher = pub-Springer,
address = pub-Springer:adr-B,
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kenney:1992:MSA,
author = "Charles S. Kenney and Alan J. Laub and Philip M.
Papadopoulos",
title = "Matrix-Sign Algorithms for {Riccati} Equations",
journal = "IMA J. Math. Control Inform.",
volume = "9",
pages = "331--344",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kenney:1998:SCEa,
author = "Charles Kenney and Alan J. Laub and M. S. Reese",
title = "Statistical Condition Estimation for Linear Systems",
journal = j-SISC,
volume = "19",
number = "2",
pages = "566--583",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kenney:1998:SCEb,
author = "Charles Kenney and Alan J. Laub and M. S. Reese",
title = "Statistical Condition Estimation for Linear Least
Squares",
journal = j-SIMAX,
volume = "19",
number = "4",
pages = "906--923",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Kahaner:1989:NMS,
author = "David K. Kahaner and Cleve B. Moler and Stephen G.
Nash",
title = "Numerical Methods and Software",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xii + 495",
year = "1989",
ISBN = "0-13-627258-4",
ISBN-13 = "978-0-13-627258-8",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@PhdThesis{Knight:1993:EAS,
author = "Philip A. Knight",
title = "Error Analysis of Stationary Iteration and Associated
Problems",
school = inst-U-Manchester,
address = inst-U-Manchester:adr,
pages = "135",
month = sep,
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Knight:1995:FRM,
author = "Philip A. Knight",
title = "Fast Rectangular Matrix Multiplication and {$QR$}
Decomposition",
journal = j-LAA,
volume = "221",
pages = "69--81",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Knuth:1962:EPC,
author = "Donald E. Knuth",
title = "Evaluation of polynomials by computer",
journal = j-CACM,
volume = "5",
number = "12",
pages = "595--599",
month = dec,
year = "1962",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355580.369074",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00 (12.00)",
MRnumber = "27 #970",
bibdate = "Thu Dec 08 11:11:03 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
MathSciNet database",
note = "See letter \cite{Knuth:1963:LEE}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
remark = "The author that Motzkin (1962) showed that Horner's
rule for polynomial evaluation may not be optimal, and
develops the idea further for arbitrary polynomials,
but also observes that the coefficients of the revised
polynomials may be difficult to find. He also asks
about, but does not answer, the question of error
analysis of the various methods.",
}
@Article{Knuth:1992:TNN,
author = "Donald E. Knuth",
title = "Two Notes on Notation",
journal = j-AMM,
volume = "99",
number = "5",
pages = "403--422",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Knuth:1999:DT,
author = "Donald E. Knuth",
title = "Digital Typography",
publisher = "Center for the Study of Language and Information",
address = "Stanford University, Stanford, CA, USA",
pages = "xv + 685",
year = "1999",
ISBN = "0-575-86010-4",
ISBN-13 = "978-0-575-86010-0",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "CSLI Lecture Notes Number 78",
}
@Book{Knuth:1997:FA,
author = "Donald E. Knuth",
title = "Fundamental Algorithms",
volume = "1",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Third",
pages = "xix + 650",
year = "1997",
ISBN = "0-201-89683-4",
ISBN-13 = "978-0-201-89683-1",
LCCN = "QA76.6 .K64 1997",
bibdate = "Fri Jul 11 15:41:22 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
http://www.math.utah.edu/pub/tex/bib/texbook2.bib",
price = "US\$49.50",
series = "The Art of Computer Programming",
acknowledgement = ack-nhfb,
keywords = "computer algorithms; electronic digital computers --
programming",
tableofcontents = "1: Basic Concepts / 1 \\
1.1. Algorithms / 1 \\
1.2. Mathematical Preliminaries / 10 \\
1.2.1. Mathematical Induction / 11 \\
1.2.2. Numbers, Powers, and Logarithms / 21 \\
1.2.3. Sums and Products / 27 \\
1.2.4. Integer Functions and Elementary Number Theory /
39 \\
1.2.5. Permutations and Factorials / 45 \\
1.2.6. Binomial Coefficients / 52 \\
1.2.7. Harmonic Numbers / 75 \\
1.2.8. Fibonacci Numbers / 79 \\
1.2.9. Generating Functions / 87 \\
1.2.10. Analysis of an Algorithm / 96 \\
* 1.2.11. Asymptotic Representations / 107 \\
*1.2.11.1. The $O$-notation / 107 \\
*1.2.11.2. Euler's summation formula / 111 \\
*1.2.11.3. Some asymptotic calculations / 116 \\
1.3. MIX / 124 \\
1.3.1. Description of MIX / 124 \\
1.3.2. The MIX Assembly Language / 144 \\
1.3.3. Applications to Permutations / 164 \\
1.4. Some Fundamental Programming Techniques / 186 \\
1.4.1. Subroutines / 186 \\
1.4.2. Coroutines / 193 \\
1.4.3. Interpretive Routines / 200 \\
1.4.3.1. A MIX simulator / 202 \\
*1.4.3.2. Trace routines / 212 \\
1.4.4. Input and Output / 215 \\
1.4.5. History and Bibliography / 229 \\
2: Information Structures / 232 \\
2.1. Introduction / 232 \\
2.2. Linear Lists / 238 \\
2.2.1. Stacks, Queues, and Deques / 238 \\
2.2.2. Sequential Allocation / 244 \\
2.2.3. Linked Allocation / 254 \\
2.2.4. Circular Lists / 273 \\
2.2.5. Doubly Linked Lists / 280 \\
2.2.6. Arrays and Orthogonal Lists / 298 \\
2.3. Trees / 308 \\
2.3.1. Traversing Binary Trees / 318 \\
2.3.2. Binary Tree Representation of Trees / 334 \\
2.3.3. Other Representations of Trees / 348 \\
2.3.4. Basic Mathematical Properties of Trees / 362 \\
2.3.4.1. Free trees / 363 \\
2.3.4.2. Oriented trees / 372 \\
*2.3.4.3. The ``infinity lemma'' / 382 \\
*2.3.4.4. Enumeration of trees / 386 \\
2.3.4.5. Path length / 399 \\
*2.3.4.6. History and bibliography / 406 \\
2.3.5. Lists and Garbage Collection / 408 \\
2.4. Multilinked Structures / 424 \\
2.5. Dynamic Storage Allocation / 435 \\
2.6. History and Bibliography / 457 \\
Answers to Exercises / 466 \\
Appendix A: Tables of Numerical Quantities / 619 \\
1. Fundamental Constants (decimal) / 619 \\
2. Fundamental Constants (octal) / 620 \\
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
Numbers / 621 \\
Appendix B: Index to Notations / 623 \\
Appendix C: Index to Algorithms and Theorems / 628 \\
Index and Glossary / 630",
}
@Book{Knuth:1998:SA,
author = "Donald E. Knuth",
title = "Seminumerical Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Third",
pages = "xiii + 762",
year = "1998",
ISBN = "0-201-89684-2",
ISBN-13 = "978-0-201-89684-8",
LCCN = "QA76.6 .K64 1997",
bibdate = "Fri Jul 11 15:41:22 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/css.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
http://www.math.utah.edu/pub/tex/bib/texbook2.bib",
price = "US\$52.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nhfb,
tableofcontents = "3: Random Numbers / 1 \\
3.1. Introduction / 1 \\
3.2. Generating Uniform Random Numbers / 10 \\
3.2.1. The Linear Congruential Method / 10 \\
3.2 1.1. Choice of modulus / 12 \\
3.2.1.2 Choice of multiplier / 16 \\
3.2.1.3. Potency / 23 \\
3.2.2. Other Methods / 26 \\
3.3. Statistical Tests / 41 \\
3.3.1. General Test Procedures for Studying Random Data
/ 41 \\
3.3.2. Empirical Tests / 61 \\
*3.3.3. Theoretical Tests / 80 \\
3.3.4. The Spectral Test / 93 \\
3.4. Other Types of Random Quantities / 119 \\
3.4 1. Numerical Distributions / 119 \\
3.4.2. Random Sampling and Shuffling / 142 \\
*3.5. What Is a Random Sequence? / 149 \\
3.6. Summary / 184 \\
4: Arithmetic / 194 \\
4.1. Positional Number Systems / 195 \\
4.2. Floating Point Arithmetic / 214 \\
4.2.1. Single-Precision Calculations / 214 \\
4.2 2. Accuracy of Floating Point Arithmetic / 229 \\
*4.2.3. Double-Precision Calculations / 246 \\
4.2.4. Distribution of Floating Point Numbers / 253 \\
4.3 Multiple Precision Arithmetic / 265 \\
4.3.1. The Classical Algorithms / 265 \\
*4.3.2. Modular Arithmetic / 284 \\
*4.3.3. How Fast Can We Multiply? / 294 \\
4.4. Radix Conversion / 319 \\
4.5. Rational Arithmetic / 330 \\
4.5.1. Fractions / 330 \\
4.5.2. The Greatest Common Divisor / 333 \\
*4.5.3. Analysis of Euclid's Algorithm / 356 \\
4.5.4. Factoring into Primes / 379 \\
4.6. Polynomial Arithmetic / 418 \\
4.6.1. Division of Polynomials / 420 \\
*4.6.2. Factorization of Polynomials / 439 \\
4.6.3. Evaluation of Powers / 461 \\
4.6.4. Evaluation of Polynomials / 485 \\
*4.7. Manipulation of Power Series / 525 \\
Answers to Exercises / 538 \\
Appendix A: Tables of Numerical Quantities / 726 \\
1. Fundamental Constants (decimal) / 726 \\
2; Fundamental Constants ( octal) / 727 \\
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
Numbers / 728 \\
Appendix B: Index to Notations / 730 \\
Index and Glossary / 735",
}
@Book{Korner:1988:FA,
author = "T. W. K{\"o}rner",
title = "Fourier Analysis",
publisher = pub-CUP,
address = pub-CUP:adr,
pages = "xii + 591",
year = "1988",
ISBN = "0-521-38991-7",
ISBN-13 = "978-0-521-38991-4",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kosowski:2000:CUT,
author = "Przemys{\l}aw Kosowski and Alicja Smoktunowicz",
title = "On Constructing Unit Triangular Matrices with
Prescribed Singular Values",
journal = j-COMPUTING,
volume = "64",
pages = "279--285",
year = "2000",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Kostlan:1992:SGM,
author = "Eric Kostlan",
title = "On the Spectra of {Gaussian} Matrices",
journal = j-LAA,
volume = "162--164",
pages = "385--388",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kovarik:1976:CAS,
author = "Z. V. Kovarik",
title = "Compatibility of Approximate Solutions of Inaccurate
Linear Equations",
journal = j-LAA,
volume = "15",
pages = "217--225",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Kreczmar:1976:MRS,
author = "Antoni Kreczmar",
title = "On Memory Requirements of {Strassen's} Algorithms",
volume = "45",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
pages = "404--407",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Lecture Notes in Computer Science",
}
@InProceedings{Kubota:1991:PFP,
author = "Koichi Kubota",
editor = "Andreas Griewank and George F. Corliss",
booktitle = "Automatic Differentiation of Algorithms: {Theory},
Implementation, and Application",
title = "{PADRE2}, a {Fortran} Precompiler Yielding Error
Estimates and Second Derivatives",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "251--262",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kuki:1973:SSA,
author = "H. Kuki and W. J. Cody",
title = "A Statistical Study of the Accuracy of Floating Point
Number Systems",
journal = j-CACM,
volume = "16",
number = "4",
pages = "223--230",
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Book{Kulisch:1981:CAT,
author = "Ulrich W. Kulisch and Willard L. Miranker",
title = "Computer Arithmetic in Theory and in Practice",
publisher = pub-AP,
address = pub-AP:adr-NY,
pages = "xiii + 249",
year = "1981",
ISBN = "0-12-428650-X",
ISBN-13 = "978-0-12-428650-4",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kulisch:1986:ADC,
author = "Ulrich W. Kulisch and Willard L. Miranker",
title = "The Arithmetic of the Digital Computer: {A} New
Approach",
journal = j-SIREV,
volume = "28",
number = "1",
pages = "1--40",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Kuperman:1971:ALA,
author = "I. B. Kuperman",
title = "Approximate Linear Algebraic Equations",
publisher = "Van Nostrand Reinhold",
address = "London",
pages = "xi + 225",
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Kuczynski:1992:ELE,
author = "J. Kuczy{\'n}ski and H. Wo{\'z}niakowski",
title = "Estimating the Largest Eigenvalue by the Power and
{Lanczos} Algorithms with a Random Start",
journal = j-SIMAX,
volume = "13",
number = "4",
pages = "1094--1122",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Laderman:1976:NAM,
author = "J. D. Laderman",
title = "A Noncommutative Algorithm for Multiplying {$3 \times
3$} Matrices Using 23 Multiplications",
journal = j-BAMS,
volume = "82",
number = "1",
pages = "126--128",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Lawson:1995:SLS,
author = "Charles L. Lawson and Richard J. Hanson",
title = "Solving Least Squares Problems",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xii + 337",
year = "1995",
ISBN = "0-89871-356-0",
ISBN-13 = "978-0-89871-356-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Revised republication of work first published in 1974
by Prentice-Hall",
}
@Article{Laszlo:1994:ALB,
author = "Lajos L{\'a}szl{\'o}",
title = "An Attainable Lower Bound for the Best Normal
Approximation",
journal = j-SIMAX,
volume = "15",
number = "3",
pages = "1035--1043",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Lay-Yong:1989:MSL,
author = "Lam Lay-Yong and Shen Kangshen",
title = "Methods of Solving Linear Equations in Traditional
{China}",
journal = j-HIST-MATH,
volume = "16",
number = "2",
pages = "107--122",
month = may,
year = "1989",
CODEN = "HIMADS",
ISSN = "0315-0860 (print), 1090-249X (electronic)",
ISSN-L = "0315-0860",
bibdate = "Wed Jun 26 06:18:18 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/histmath.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0315086089900335",
acknowledgement = ack-nhfb,
fjournal = "Historia Mathematica",
journal-URL = "http://www.sciencedirect.com/science/journal/03150860",
}
@Book{Lanczos:1956:AA,
author = "Cornelius Lanczos",
title = "Applied Analysis",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xx + 539",
year = "1956",
ISBN = "0-486-65656-X",
ISBN-13 = "978-0-486-65656-4",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted by Dover, New York, 1988",
}
@Article{Lancaster:1966:EAN,
author = "Peter Lancaster",
title = "Error Analysis for the {Newton--Raphson} Method",
journal = j-NUM-MATH,
volume = "9",
pages = "55--68",
year = "1966",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Lancaster:1970:ESL,
author = "Peter Lancaster",
title = "Explicit Solutions of Linear Matrix Equations",
journal = j-SIREV,
volume = "12",
number = "4",
pages = "544--566",
year = "1970",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Langlois:2001:ALC,
author = "Philippe Langlois",
title = "Automatic Linear Correction of Rounding Errors",
journal = j-BIT,
volume = "41",
number = "3",
pages = "515--539",
year = "2001",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Larson:1978:ECE,
author = "John L. Larson and Ahmed H. Sameh",
title = "Efficient Calculation of the Effects of Roundoff
Errors",
journal = j-TOMS,
volume = "4",
number = "3",
pages = "228--236",
year = "1978",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Errata 5(3):372, 1979",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Larson:1980:ARE,
author = "John L. Larson and Ahmed H. Sameh",
title = "Algorithms for Roundoff Error Analysis---{A} Relative
Error Approach",
journal = j-COMPUTING,
volume = "24",
pages = "275--297",
year = "1980",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Laub:1979:SMS,
author = "Alan J. Laub",
title = "A {Schur} Method for Solving Algebraic {Riccati}
Equations",
journal = j-IEEE-AC,
volume = "AC-24",
number = "6",
pages = "913--921",
year = "1979",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Lauchli:1961:JEA,
author = "Peter L{\"a}uchli",
title = "{Jordan-Elimination} und {Ausgleichung} nach kleinsten
{Quadraten}",
journal = j-NUM-MATH,
volume = "3",
pages = "226--240",
year = "1961",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Porte:1974:ESE,
author = "M. La Porte and J. Vignes",
title = "Etude Statistique des Erreurs Dans l'Arithm\'etique
des Ordinateurs; Application au Contr{\^o}le des
{R}\'esultats d'Algorithmes Num\'eriques",
journal = j-NUM-MATH,
volume = "23",
pages = "63--72",
year = "1974",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{Lavington:1980:EBC,
author = "Simon Lavington",
title = "Early {British} Computers: {The} Story of Vintage
Computers and the People Who Built Them",
publisher = "Manchester University Press",
pages = "139",
year = "1980",
ISBN = "0-7190-0803-4",
ISBN-13 = "978-0-7190-0803-0",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Li:2000:DIT,
author = "X. S. Li and J. W. Demmel and D. H. Bailey and G.
Henry and Y. Hida and J. Iskandar and W. Kahan and A.
Kapur and M. C. Martin and T. Tung and D. J. Yoo",
title = "Design, Implementation and Testing of {Extended and
Mixed Precision BLAS}",
type = "Technical Report",
number = "CS-00-451",
institution = inst-CS-U-Tenn,
address = inst-CS-U-Tenn:adr,
pages = "61",
month = oct,
year = "2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "LAPACK Working Note 149",
}
@Article{Lehmer:1943:TMP,
author = "D. H. Lehmer",
title = "Tables to Many Places of Decimals",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "1",
number = "1",
pages = "30--31",
year = "1943",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Lehoucq:1996:CEU,
author = "R. B. Lehoucq",
title = "The Computation of Elementary Unitary Matrices",
journal = j-TOMS,
volume = "22",
number = "4",
pages = "393--400",
year = "1996",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Lemeire:1975:BCN,
author = "Frans Lemeire",
title = "Bounds for Condition Numbers of Triangular and
Trapezoid Matrices",
journal = j-BIT,
volume = "15",
pages = "58--64",
year = "1975",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@InProceedings{Lefevre:2001:WCC,
author = "Vincent Lef{\`e}vre and Jean-Michel Muller",
editor = "",
booktitle = "Proc. 15th IEEE Symposium on Computer Arithmetic",
title = "Worst Cases for Correct Rounding of the Elementary
Functions in Double Precision",
publisher = "IEEE Computer Society Press, Los Alamitos, CA, USA",
pages = "",
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Leuprecht:1982:PAR,
author = "H. Leuprecht and W. Oberaigner",
title = "Parallel Algorithms for the Rounding Exact Summation
of Floating Point Numbers",
journal = j-COMPUTING,
volume = "28",
pages = "89--104",
year = "1982",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Lawson:1979:BLA,
author = "C. L. Lawson and R. J. Hanson and D. R. Kincaid and F.
T. Krogh",
title = "Basic Linear Algebra Subprograms for {Fortran} Usage",
journal = j-TOMS,
volume = "5",
number = "3",
pages = "308--323",
year = "1979",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Book{LIA94,
key = "IEC",
title = "{ISO\slash IEC \upshape 10967-1 (1994-12)}:
{Information} Technology---Language Independent
Arithmetic---Part {$1$}: {Integer} and Floating Point
Arithmetic",
publisher = pub-IEC,
address = pub-IEC:adr,
pages = "92",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Lickteig:1987:CCD,
author = "Thomas Lickteig",
title = "The Computational Complexity of Division in Quadratic
Extension Fields",
journal = j-SICOMP,
volume = "16",
number = "2",
pages = "278--311",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Li:1998:MSG,
author = "Xiaoye S. Li and James W. Demmel",
booktitle = "Proceedings of SC98: High Performance Networking and
Computing Conference, Orlando, Florida",
title = "Making Sparse {Gaussian} Elimination Scalable by
Static Pivoting",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "CD ROM",
}
@Article{Linnainmaa:1974:ASK,
author = "Seppo Linnainmaa",
title = "Analysis of Some Known Methods of Improving the
Accuracy of Floating-Point Sums",
journal = j-BIT,
volume = "14",
pages = "167--202",
year = "1974",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Linnainmaa:1975:TAS,
author = "Seppo Linnainmaa",
title = "Towards Accurate Statistical Estimation of Rounding
Errors in Floating-Point Computations",
journal = j-BIT,
volume = "15",
pages = "165--173",
year = "1975",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Linnainmaa:1976:TEA,
author = "Seppo Linnainmaa",
title = "Taylor Expansion of the Accumulated Rounding Error",
journal = j-BIT,
volume = "16",
pages = "146--160",
year = "1976",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Linnainmaa:1981:SDP,
author = "Seppo Linnainmaa",
title = "Software for Doubled-Precision Floating-Point
Computations",
journal = j-TOMS,
volume = "7",
number = "3",
pages = "272--283",
year = "1981",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Linz:1970:AFP,
author = "Peter Linz",
title = "Accurate Floating-Point Summation",
journal = j-CACM,
volume = "13",
number = "6",
pages = "361--362",
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Linzer:1992:STB,
author = "Elliot Linzer",
title = "On the Stability of Transform-Based Circular
Deconvolution",
journal = j-SINUM,
volume = "29",
number = "5",
pages = "1482--1492",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Liu:1987:PPS,
author = "Joseph W. H. Liu",
title = "A Partial Pivoting Strategy for Sparse Symmetric
Matrix Decomposition",
journal = j-TOMS,
volume = "13",
number = "2",
pages = "173--182",
year = "1987",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Li:1992:HDA,
author = "T. Y. Li and Zhonggang Zeng",
title = "Homotopy-Determinant Algorithm for Solving
Nonsymmetric Eigenvalue Problems",
journal = j-MATH-COMP,
volume = "59",
number = "200",
pages = "483--502",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Lefevre:1998:TCR,
author = "Vincent Lef{\`e}vre and Jean-Michel Muller and Arnaud
Tisserand",
title = "Toward Correctly Rounded Transcendentals",
journal = j-IEEE-C,
volume = "47",
number = "11",
pages = "1235--1243",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Loizou:1969:NJC,
author = "Georghios Loizou",
title = "Nonnormality and {Jordan} Condition Numbers of
Matrices",
journal = j-ACM,
volume = "16",
number = "4",
pages = "580--584",
year = "1969",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Longley:1967:ALS,
author = "J. W. Longley",
title = "An Appraisal of Least Squares Programs for the
Electronic Computer from the Point of View of the
User",
journal = j-ASA,
volume = "62",
pages = "819--841",
year = "1967",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Laderman:1992:PAA,
author = "Julian Laderman and Victor Pan and Xuan-He Sha",
title = "On Practical Algorithms for Accelerated Matrix
Multiplication",
journal = j-LAA,
volume = "162--164",
pages = "557--588",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Larson:1983:ASR,
author = "John L. Larson and Mary E. Pasternak and John A.
Wisniewski",
title = "Algorithm 594: {Software} for Relative Error
Analysis",
journal = j-TOMS,
volume = "9",
number = "1",
pages = "125--130",
year = "1983",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Lagarias:1998:CPN,
author = "Jeffrey C. Lagarias and James A. Reeds and Margaret H.
Wright and Paul E. Wright",
title = "Convergence Properties of the {Nelder--Mead} Simplex
Method in Low Dimensions",
journal = j-SIOPT,
volume = "9",
number = "1",
pages = "112--147",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Lewis:2000:DSM,
author = "Robert Michael Lewis and Virginia J. Torczon and
Michael W. Trossett",
title = "Direct Search Methods: {Then} and Now",
journal = j-JCAM,
volume = "124",
pages = "191--207",
year = "2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Lu:1994:FSC,
author = "Hao Lu",
title = "Fast Solution of Confluent {Vandermonde} Linear
Systems",
journal = j-SIMAX,
volume = "15",
number = "4",
pages = "1277--1289",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Lu:1995:FAC,
author = "Hao Lu",
title = "Fast Algorithms for Confluent {Vandermonde} Linear
Systems and Generalized {Trummer's} Problem",
journal = j-SIMAX,
volume = "16",
number = "2",
pages = "655--674",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Lu:1996:SVL,
author = "Hao Lu",
title = "Solution of {Vandermonde}-Like Systems and Confluent
{Vandermonde}-Like Systems",
journal = j-SIMAX,
volume = "17",
number = "1",
pages = "127--138",
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Barker:2001:LUG,
author = "V. A. Barker and L. S. Blackford and J. J. Dongarra
and J. J. Du Croz and S. J. Hammarling and M. Marinova
and J. Wa{\'s}niewski and P. Yalamov",
title = "{LAPACK95} Users' Guide",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xviii + 258",
year = "2001",
ISBN = "0-89871-504-0",
ISBN-13 = "978-0-89871-504-0",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Anderson:1999:LUG,
author = "E. Anderson and Z. Bai and C. H. Bischof and S.
Blackford and J. W. Demmel and J. J. Dongarra and J. J.
Du Croz and A. Greenbaum and S. J. Hammarling and A.
McKenney and D. C. Sorensen",
title = "{LAPACK} Users' Guide",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Third",
pages = "xxvi + 407",
year = "1999",
ISBN = "0-89871-447-8",
ISBN-13 = "978-0-89871-447-0",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Lyness:1976:CNA,
author = "J. N. Lyness and J. J. Kaganove",
title = "Comments on the Nature of Automatic Quadrature
Routines",
journal = j-TOMS,
volume = "2",
number = "1",
pages = "65--81",
year = "1976",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Lyness:1966:VMS,
author = "J. N. Lyness and C. B. Moler",
title = "{Van der Monde} Systems and Numerical
Differentiation",
journal = j-NUM-MATH,
volume = "8",
pages = "458--464",
year = "1966",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Lynn:1964:REM,
author = "M. Stuart Lynn",
title = "On the Round-Off Error in the Method of Successive
Over-Relaxation",
journal = j-MATH-COMP,
volume = "18",
number = "85",
pages = "36--49",
year = "1964",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Macleod:1989:SSG,
author = "Allan J. Macleod",
title = "Some Statistics on {Gaussian} Elimination with Partial
Pivoting",
journal = j-SIGNUM,
volume = "24",
number = "2/3",
pages = "10--14",
year = "1989",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
}
@Book{Maindonald:1984:SC,
author = "J. H. Maindonald",
title = "Statistical Computation",
publisher = pub-Wiley,
address = pub-Wiley:adr,
pages = "xviii + 370",
year = "1984",
ISBN = "0-471-86452-8",
ISBN-13 = "978-0-471-86452-3",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Matsui:1981:OUF,
author = "Shouichi Matsui and Masao Iri",
title = "An Overflow/Underflow-Free Floating-Point
Representation of Numbers",
journal = j-J-INF-PROCESS,
volume = "4",
number = "3",
pages = "123--133",
year = "1981",
CODEN = "JIPRDE",
ISSN = "0387-6101",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Journal of Information Processing",
}
@Article{Makhoul:1991:TDP,
author = "John Makhoul",
title = "{Toeplitz} Determinants and Positive
Semidefiniteness",
journal = j-IEEE-SP,
volume = "39",
number = "3",
pages = "743--746",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Matula:1985:FPR,
author = "David W. Matula and Peter Kornerup",
title = "Finite Precision Rational Arithmetic: {Slash} Number
Systems",
journal = j-IEEE-C,
volume = "C-34",
number = "1",
pages = "3--18",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Malcolm:1971:AFP,
author = "Michael A. Malcolm",
title = "On Accurate Floating-Point Summation",
journal = j-CACM,
volume = "14",
number = "11",
pages = "731--736",
month = nov,
year = "1971",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362854.362889",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65G05 (68-XX)",
MRnumber = "47 4434",
MRreviewer = "P. Brock",
bibdate = "Mon Jan 22 07:01:06 MST 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#Malcolm71;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Stanford Univ., CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "accurate floating-point summation; digital arithmetic;
error analysis",
oldlabel = "Malcolm71",
treatment = "P Practical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Malcolm71",
}
@Article{Malcolm:1972:ARP,
author = "Michael A. Malcolm",
title = "Algorithms to Reveal Properties of Floating-Point
Arithmetic",
journal = j-CACM,
volume = "15",
number = "11",
pages = "949--951",
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Malyshev:2000:NSG,
author = "Alexander N. Malyshev",
title = "A Note on the Stability of {Gauss--Jordan} Elimination
for Diagonally Dominant Matrices",
journal = j-COMPUTING,
volume = "65",
number = "3",
pages = "281--284",
year = "2000",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Malyshev:2001:OBP,
author = "Alexander N. Malyshev",
title = "Optimal Backward Perturbation Bounds for the {LSS}
Problem",
journal = j-BIT,
volume = "41",
number = "2",
pages = "430--432",
year = "2001",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Magnus:1979:CMS,
author = "Jan R. Magnus and Heinz Neudecker",
title = "The Commutation Matrix: {Some} Properties and
Applications",
journal = j-ANN-STAT,
volume = "7",
number = "2",
pages = "381--394",
year = "1979",
CODEN = "ASTSC7",
ISSN = "0090-5364 (print), 2168-8966 (electronic)",
ISSN-L = "0090-5364",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Annals of Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aos/",
}
@Book{Magnus:1999:MDC,
author = "Jan R. Magnus and Heinz Neudecker",
title = "Matrix Differential Calculus with Applications in
Statistics and Econometrics",
publisher = pub-Wiley,
address = pub-Wiley:adr-C,
edition = "Revised",
pages = "xviii + 395",
year = "1999",
ISBN = "0-471-98633-X",
ISBN-13 = "978-0-471-98633-1",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Manteuffel:1981:IAA,
author = "Thomas A. Manteuffel",
title = "An Interval Analysis Approach to Rank Determination in
Linear Least Squares Problems",
journal = j-SISSC,
volume = "2",
number = "3",
pages = "335--348",
year = "1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Malcolm:1974:FMS,
author = "Michael A. Malcolm and John Palmer",
title = "A Fast Method for Solving a Class of Tridiagonal
Linear Systems",
journal = j-CACM,
volume = "17",
number = "1",
pages = "14--17",
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Book{maple,
key = "Maple",
title = "Maple",
publisher = "Waterloo Maple Inc.",
address = "Waterloo, Ontario, Canada",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "\path|http://www.maplesoft.com|",
}
@Book{Char:1991:MVL,
author = "Bruce W. Char and Keith O. Geddes and Gaston H. Gonnet
and Benton L. Leong and Michael B. Monagan and Stephen
M. Watt",
title = "Maple {V} Library Reference Manual",
publisher = pub-Springer,
address = pub-Springer:adr-B,
pages = "xxv + 698",
year = "1991",
ISBN = "3-540-97592-6",
ISBN-13 = "978-3-540-97592-2",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Markoff:1994:CFC,
author = "John Markoff",
title = "Circuit Flaw Causes {Pentium} Chip to Miscalculate,
{Intel} Admits",
journal = j-NY-TIMES,
year = "1994",
CODEN = "NYTIAO",
ISSN = "0362-4331 (print), 1542-667X, 1553-8095",
ISSN-L = "0362-4331",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "24 November",
fjournal = "New York Times",
journal-URL = "http://www.nytimes.com/",
}
@Article{Malyshev:2002:COB,
author = "Alexander N. Malyshev and Miloud Sadkane",
title = "Computation of Optimal Backward Perturbation Bounds
for Large Sparse Linear Least Squares Problems",
journal = j-BIT,
volume = "41",
number = "4",
pages = "739--747",
year = "2002",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Mathias:1992:MPD,
author = "Roy Mathias",
title = "Matrices with Positive Definite {Hermitian} Part:
{Inequalities} and Linear Systems",
journal = j-SIMAX,
volume = "13",
number = "2",
pages = "640--654",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Mathias:1995:AEC,
author = "Roy Mathias",
title = "Accurate Eigensystem Computations by {Jacobi}
Methods",
journal = j-SIMAX,
volume = "16",
number = "3",
pages = "977--1003",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Mathias:1995:IPP,
author = "Roy Mathias",
title = "The Instability of Parallel Prefix Matrix
Multiplication",
journal = j-SISC,
volume = "16",
number = "4",
pages = "956--973",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Mathias:1996:AAO,
author = "Roy Mathias",
title = "Analysis of Algorithms for Orthogonalizing Products of
Unitary Matrices",
journal = j-NLAA,
volume = "3",
number = "2",
pages = "125--145",
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{mathematica,
key = "Mathematica",
title = "Mathematica",
publisher = "Wolfram Research, Inc.",
address = "Champaign, IL, USA",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "\path|http://www.wolfram.com|",
}
@Book{matlab,
key = "MathWorks, Inc.",
title = "{MATLAB}",
publisher = "The MathWorks, Inc.",
address = "Natick, MA, USA",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "\path|http://www.mathworks.com|",
}
@Book{matlab:SMT,
key = "MathWorks, Inc.",
title = "Symbolic Math Toolbox Version {$2$}: {User's} Guide",
publisher = "The MathWorks, Inc.",
address = "Natick, MA, USA",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Online version",
}
@Article{Mattheij:1984:SLD,
author = "R. M. M. Mattheij",
title = "The Stability of {LU}-Decompositions of Block
Tridiagonal Matrices",
journal = j-BULL-AUSTRAL-MATH-SOC,
volume = "29",
pages = "177--205",
year = "1984",
CODEN = "ALNBAB",
ISSN = "0004-9727 (print), 1755-1633 (electronic)",
ISSN-L = "0004-9727",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Bulletin of the Australian Mathematical Society",
}
@Article{Mattheij:1984:SBD,
author = "R. M. M. Mattheij",
title = "Stability of Block {$LU$}-Decompositions of Matrices
Arising From {BVP}",
journal = j-SIAD,
volume = "5",
number = "3",
pages = "314--331",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Matula:1968:C,
author = "David W. Matula",
title = "In-and-Out Conversions",
journal = j-CACM,
volume = "11",
number = "1",
pages = "47--50",
month = jan,
year = "1968",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362851.362887",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.80",
MRnumber = "39\#2360",
bibdate = "Fri Nov 25 18:20:17 MST 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib",
note = "See also \cite{Goldberg:1967:BED,Matula:1968:BCT}",
abstract = "By an in-and-out conversion we mean that a
floating-point number in one base is converted into a
floating-point number in another base and then
converted back to a floating-point number in the
original base. For all combinations of rounding and
truncation conversions the question is considered of
how many significant digits are needed in the
intermediate base to allow such in-and-out conversions
to return the original number (when possible), or at
least significant digit.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "floating-point numbers; number base conversion;
rounding error; significance; truncation error",
}
@Article{Matula:1970:FFP,
author = "David W. Matula",
title = "A Formalization of Floating-Point Numeric Base
Conversion",
journal = j-IEEE-C,
volume = "C-19",
number = "8",
pages = "681--692",
year = "1970",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{McCracken:1964:NMF,
author = "Daniel D. McCracken and William S. Dorn",
title = "Numerical Methods and {Fortran} Programming: {With}
Applications in Science and Engineering",
publisher = pub-Wiley,
address = pub-Wiley:adr,
pages = "xii + 457",
year = "1964",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{McKeeman:1962:ACE,
author = "William Marshall McKeeman",
title = "Algorithm 135: {Crout} with Equilibration and
Iteration",
journal = j-CACM,
volume = "5",
pages = "553--555",
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{McKinnon:1998:CNM,
author = "K. I. M. McKinnon",
title = "Convergence of the {Nelder--Mead} Simplex Method to a
Nonstationary Point",
journal = j-SIOPT,
volume = "9",
number = "1",
pages = "148--158",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{McCullagh:1989:GLM,
author = "P. McCullagh and J. A. Nelder",
title = "Generalized Linear Models",
publisher = "Chapman and Hall",
address = "London",
edition = "Second",
pages = "xix + 511",
year = "1989",
ISBN = "0-412-31760-5",
ISBN-13 = "978-0-412-31760-6",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{McCarthy:1974:OCM,
author = "Charles McCarthy and Gilbert Strang",
title = "Optimal Conditioning of Matrices",
journal = j-SINUM,
volume = "10",
number = "2",
pages = "370--388",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{McCullough:1999:NRE,
author = "B. D. McCullough and H. D. Vinod",
title = "The Numerical Reliability of Econometric Software",
journal = j-J-ECON-LIT,
volume = "37",
pages = "633--665",
year = "1999",
CODEN = "JECLB3",
ISSN = "0022-0515 (print), 1547-1101 (electronic)",
ISSN-L = "0022-0515",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Journal of Economic Literature",
}
@Article{Meyer:1957:MIL,
author = "H. I. Meyer and B. J. Hollingsworth",
title = "A Method of Inverting Large Matrices of Special Form",
journal = j-MTAC,
volume = "11",
pages = "94--97",
year = "1957",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Meinguet:1969:ES,
author = "Jean Meinguet",
editor = "Elden Hansen",
booktitle = "Topics in Interval Analysis",
title = "On the Estimation of Significance",
publisher = pub-OUP,
pages = "47--64",
year = "1969",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Meinguet:1983:REA,
author = "Jean Meinguet",
title = "Refined Error Analyses of {Cholesky} Factorization",
journal = j-SINUM,
volume = "20",
number = "6",
pages = "1243--1250",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Mendelsohn:1956:SEP,
author = "N. S. Mendelsohn",
title = "Some Elementary Properties of Ill Conditioned Matrices
and Linear Equations",
journal = j-AMM,
volume = "63",
number = "5",
pages = "285--295",
year = "1956",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Meyer:1977:CPM,
author = "Carl D. {Meyer, Jr.} and R. J. Plemmons",
title = "Convergent Powers of a Matrix With Applications to
Iterative Methods for Singular Linear Systems",
journal = j-SINUM,
volume = "14",
number = "4",
pages = "699--705",
year = "1977",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Metcalf:1999:FE,
author = "Michael Metcalf and John K. Reid",
title = "Fortran 90/95 Explained",
publisher = pub-OUP,
edition = "Second",
pages = "358",
year = "1999",
ISBN = "0-19-850558-2",
ISBN-13 = "978-0-19-850558-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Metropolis:1977:MSA,
author = "N. Metropolis",
editor = "David A. H. Jacobs",
booktitle = "The State of the Art in Numerical Analysis",
title = "Methods of Significance Arithmetic",
publisher = pub-AP # ", " # pub-AP:adr-L,
pages = "179--192",
year = "1977",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Meurant:1992:RIS,
author = "G{\'e}rard Meurant",
title = "A Review on the Inverse of Symmetric Tridiagonal and
Block Tridiagonal Matrices",
journal = j-SIMAX,
volume = "13",
number = "3",
pages = "707--728",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Milenkovic:1988:VIG,
author = "Victor J. Milenkovic",
title = "Verifiable Implementations of Geometric Algorithms
Using Finite Precision Arithmetic",
journal = j-ART-INTELL,
volume = "37",
pages = "377--401",
year = "1988",
CODEN = "AINTBB",
ISSN = "0004-3702 (print), 1872-7921 (electronic)",
ISSN-L = "0004-3702",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Artificial Intelligence",
}
@Article{Miller:1975:CCN,
author = "Webb Miller",
title = "Computational Complexity and Numerical Stability",
journal = j-SICOMP,
volume = "4",
number = "2",
pages = "97--107",
year = "1975",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Miller:1975:SRA,
author = "Webb Miller",
title = "Software for Roundoff Analysis",
journal = j-TOMS,
volume = "1",
number = "2",
pages = "108--128",
year = "1975",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Miller:1976:GTR,
author = "Webb Miller",
title = "Graph Transformations for Roundoff Analysis",
journal = j-SICOMP,
volume = "5",
number = "2",
pages = "204--216",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Miller:1984:ENS,
author = "Webb Miller",
title = "The Engineering of Numerical Software",
publisher = pub-PH,
address = pub-PH:adr,
pages = "viii + 167",
year = "1984",
ISBN = "0-13-279043-2",
ISBN-13 = "978-0-13-279043-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Miller:1988:ISM,
author = "D. F. Miller",
title = "The Iterative Solution of the Matrix Equation
{$XA+BX+C=0$}",
journal = j-LAA,
volume = "105",
pages = "131--137",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Mirsky:1961:ILA,
author = "L. Mirsky",
title = "An Introduction to Linear Algebra",
publisher = pub-OUP,
pages = "viii + 440",
year = "1961",
ISBN = "0-486-66434-1",
ISBN-13 = "978-0-486-66434-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted by Dover, New York, 1990",
}
@Article{Miller:19xx:SRA,
author = "Webb Miller and David Spooner",
title = "Software for Roundoff Analysis, {II}",
journal = j-TOMS,
volume = "4",
number = "4",
pages = "369--387",
year = "{\noopsort{a}}1978",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Miller:19xx:ASR,
author = "Webb Miller and David Spooner",
title = "Algorithm 532: {Software} for Roundoff Analysis",
journal = j-TOMS,
volume = "4",
number = "4",
pages = "388--390",
year = "{\noopsort{b}}1978",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Mitchell:1948:IMO,
author = "Herbert F. {Mitchell, Jr.}",
title = "Inversion of a Matrix of Order 38",
journal = j-MTAC,
volume = "3",
pages = "161--166",
year = "1948",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Miller:1980:SRA,
author = "Webb Miller and Celia Wrathall",
title = "Software for Roundoff Analysis of Matrix Algorithms",
publisher = pub-AP,
address = pub-AP:adr-NY,
pages = "x + 151",
year = "1980",
ISBN = "0-12-497250-0",
ISBN-13 = "978-0-12-497250-6",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Moore:1998:MCP,
author = "J. Strother Moore and Thomas W. Lynch and Matt
Kaufmann",
title = "A Mechanically Checked Proof of the
{$\mathrm{AMD}5_K86$} Floating-Point Division Program",
journal = j-IEEE-C,
volume = "47",
number = "9",
pages = "913--926",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Moler:1967:IRF,
author = "Cleve B. Moler",
title = "Iterative Refinement in Floating Point",
journal = j-ACM,
volume = "14",
number = "2",
pages = "316--321",
year = "1967",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Moler:1972:MCF,
author = "Cleve B. Moler",
title = "Matrix Computations with {Fortran} and Paging",
journal = j-CACM,
volume = "15",
number = "4",
pages = "268--270",
year = "1972{\noopsort{a}}",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Moler:1972:ALE,
author = "Cleve B. Moler",
title = "Algorithm 423: {Linear} Equation Solver",
journal = j-CACM,
volume = "15",
number = "4",
pages = "274",
year = "1972{\noopsort{b}}",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Moler:1974:CRS,
author = "Cleve B. Moler",
title = "Cramer's Rule on 2-by-2 Systems",
journal = j-SIGNUM,
volume = "9",
number = "4",
pages = "13--14",
year = "1974",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
}
@InCollection{Moler:1978:TRP,
author = "Cleve B. Moler",
editor = "G. H. Golub and J. Oliger",
booktitle = "Numerical Analysis",
title = "Three Research Problems in Numerical Linear Algebra",
volume = "22",
publisher = pub-AMS # ", " # pub-AMS:adr,
pages = "1--18",
year = "1978",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Proceedings of Symposia in Applied Mathematics",
}
@Article{Moler:1990:TND,
author = "Cleve B. Moler",
title = "Technical Note: {Double-rounding} and Implications for
Numeric Computations",
journal = j-MATHWORKS-NEWSLETTER,
volume = "4",
pages = "6",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "The MathWorks Newsletter",
}
@Article{Moler:1990:CCW,
author = "Cleve B. Moler",
title = "Cleve's Corner: {The} World's Simplest Impossible
Problem",
journal = j-MATHWORKS-NEWSLETTER,
volume = "4",
number = "2",
pages = "6--7",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "The MathWorks Newsletter",
}
@Article{Moler:1995:TTN,
author = "Cleve B. Moler",
title = "A Tale of Two Numbers",
journal = j-SIAM-NEWS,
volume = "28",
pages = "1,16",
month = jan,
year = "1995",
ISSN = "0036-1437",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Also in \emph{MATLAB News and Notes}, Winter 1995,
10--12",
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Article{Moller:1965:QDP,
author = "Ole M{\o}ller",
title = "Quasi Double-Precision in Floating Point Addition",
journal = j-BIT,
volume = "5",
pages = "37--50",
year = "1965",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "See also \cite{Moller:1965:NQD} for remarks on this
article",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Moller:1965:NQD,
author = "Ole M{\o}ller",
title = "Note on Quasi Double-Precision",
journal = j-BIT,
volume = "5",
pages = "251--255",
year = "1965",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Moler:1983:RSR,
author = "Cleve B. Moler and Donald Morrison",
title = "Replacing Square Roots by {Pythagorean} Sums",
journal = j-IBM-JRD,
volume = "27",
number = "6",
pages = "577--581",
year = "1983",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Moler:1983:SVA,
author = "Cleve B. Moler and Donald Morrison",
title = "Singular Value Analysis of Cryptograms",
journal = j-AMM,
volume = "90",
pages = "78--87",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Moore:1966:IA,
author = "Ramon E. Moore",
title = "Interval Analysis",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xi + 145",
year = "1966",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Moore:1979:MAI,
author = "Ramon E. Moore",
title = "Methods and Applications of Interval Analysis",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xi + 190",
year = "1979",
ISBN = "0-89871-161-4",
ISBN-13 = "978-0-89871-161-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Moler:1978:NDW,
author = "Cleve B. Moler and Charles F. {Van Loan}",
title = "Nineteen Dubious Ways to Compute the Exponential of a
Matrix",
journal = j-SIREV,
volume = "20",
number = "4",
pages = "801--836",
year = "1978",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Martin:1966:IRS,
author = "R. S. Martin and G. Peters and J. H. Wilkinson",
title = "Iterative Refinement of the Solution of a Positive
Definite System of Equations",
journal = j-NUM-MATH,
volume = "8",
pages = "203--216",
year = "1966",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Also in \cite[pp.~31--44]{Wilkinson:1971:LA},
Contribution I/2",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Mead:2001:SPS,
author = "J. L. Mead and R. E. Renaut and B. D. Welfert",
title = "Stability of a Pivoting Strategy for Parallel
{Gaussian} Elimination",
journal = j-BIT,
volume = "41",
number = "3",
pages = "633--639",
year = "2001",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Book{Muirhead:1982:AMS,
author = "Robb J. Muirhead",
title = "Aspects of Multivariate Statistical Theory",
publisher = pub-Wiley,
address = pub-Wiley:adr,
pages = "xix + 673",
year = "1982",
ISBN = "0-471-09442-0",
ISBN-13 = "978-0-471-09442-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Muller:1983:REA,
author = "K. H. M{\"u}ller",
title = "Rounding Error Analysis of {Horner's} Scheme",
journal = j-COMPUTING,
volume = "30",
pages = "285--303",
year = "1983",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Book{Muller:1989:AO,
author = "Jean-Michel Muller",
title = "Arithm{\'e}tique des Ordinateurs",
publisher = "Masson",
address = "Paris",
pages = "214",
year = "1989",
ISBN = "2-225-81689-1",
ISBN-13 = "978-2-225-81689-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "In French. Cited in \cite{Francois:1991:SPM}",
}
@Book{Muller:1997:EFA,
author = "Jean-Michel Muller",
title = "Elementary Functions: {Algorithms} and
Implementation",
publisher = pub-BH,
address = pub-BH:adr,
pages = "xv + 204",
year = "1997",
ISBN = "0-8176-3990-X",
ISBN-13 = "978-0-8176-3990-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Merikoski:1997:BUB,
author = "Jorma Kaarlo Merikoski and Uoti Arpala and Ari
Virtanen and Tin-Yau Tam and Frank Uhlig",
title = "A Best Upper Bound for the 2-Norm Condition Number of
a Matrix",
journal = j-LAA,
volume = "254",
pages = "355--365",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Nashed:1976:ABG,
author = "M. Zuhair Nashed and L. B. Rall",
editor = "M. Zuhair Nashed",
booktitle = "Generalized Inverses and Applications",
title = "Annotated Bibliography on Generalized Inverses and
Applications",
publisher = pub-AP # ", " # pub-AP:adr-NY,
pages = "771--1041",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Nelson:1998:PDM,
editor = "David Nelson",
title = "The Penguin Dictionary of Mathematics",
publisher = pub-Penguin,
address = pub-Penguin:adr-L,
edition = "Second",
pages = "461",
year = "1998",
ISBN = "0-14-051342-6",
ISBN-13 = "978-0-14-051342-4",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Nelder:1965:SMF,
author = "J. A. Nelder and R. Mead",
title = "A Simplex Method for Function Minimization",
journal = j-COMP-J,
volume = "7",
pages = "308--313",
year = "1965",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Neumann:1984:BEA,
author = "M. Neumann and R. J. Plemmons",
title = "Backward Error Analysis for Linear Systems Associated
with Inverses of {$H$}-Matrices",
journal = j-BIT,
volume = "24",
pages = "102--112",
year = "1984",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Neal:1992:GAG,
author = "Larry Neal and George Poole",
title = "A Geometric Analysis of {Gaussian} Elimination. {II}",
journal = j-LAA,
volume = "173",
pages = "239--264",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Newman:1958:EMI,
author = "Morris Newman and John Todd",
title = "The Evaluation of Matrix Inversion Programs",
journal = j-SIAM,
volume = "6",
number = "4",
pages = "466--476",
year = "1958",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Neumaier:1974:REV,
author = "A. Neumaier",
title = "Rundungsfehleranalyse einiger {Verfahren zur Summation
endlicher Summen}",
journal = j-ZAMM,
volume = "54",
pages = "39--51",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Neumaier:1985:IPR,
author = "A. Neumaier",
title = "Inner Product Rounding Error Analysis in the Presence
of Underflow",
journal = j-COMPUTING,
volume = "34",
pages = "365--373",
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Neumaier:1986:CMM,
author = "A. Neumaier",
title = "On the Comparison of {$H$}-Matrices with
{$M$}-Matrices",
journal = j-LAA,
volume = "83",
pages = "135--141",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Newbery:1973:EAF,
author = "A. C. R. Newbery",
title = "Error Analysis for {Fourier} Series Evaluation",
journal = j-MATH-COMP,
volume = "27",
number = "123",
pages = "639--644",
year = "1973",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Newbery:1974:EAP,
author = "A. C. R. Newbery",
title = "Error Analysis for Polynomial Evaluation",
journal = j-MATH-COMP,
volume = "28",
number = "127",
pages = "789--793",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Newcomb:1881:NFU,
author = "Simon Newcomb",
title = "Note on the Frequency of Use of the Different Digits
in Natural Numbers",
journal = j-AM-J-MATH,
volume = "4",
pages = "39--40",
year = "1881",
CODEN = "AJMAAN",
ISSN = "0002-9327 (print), 1080-6377 (electronic)",
ISSN-L = "0002-9327",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "American Journal of Mathematics",
}
@InCollection{Newman:1962:MC,
author = "Morris Newman",
editor = "John Todd",
booktitle = "Survey of Numerical Analysis",
title = "Matrix Computations",
publisher = pub-MH,
address = pub-MH:adr,
pages = "222--254",
year = "1962",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Nickel:1970:KBS,
author = "K. Nickel",
title = "Das {Kahan-Babu\u{s}kasche Summierungsverfahren in
Triplex-ALGOL} 60",
journal = j-ZAMM,
volume = "50",
pages = "369--373",
year = "1970",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Nickel:1977:IA,
author = "Karl Nickel",
editor = "David A. H. Jacobs",
booktitle = "The State of the Art in Numerical Analysis",
title = "Interval-Analysis",
publisher = pub-AP # ", " # pub-AP:adr-L,
pages = "193--225",
year = "1977",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Notay:1993:CRC,
author = "Yvan Notay",
title = "On the Convergence Rate of the Conjugate Gradients in
Presence of Rounding Errors",
journal = j-NUM-MATH,
volume = "65",
pages = "301--317",
year = "1993",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{Nocedal:1999:NO,
author = "Jorge Nocedal and Stephen J. Wright",
title = "Numerical Optimization",
publisher = pub-Springer,
address = pub-Springer:adr-NY,
pages = "xx + 636",
year = "1999",
ISBN = "0-387-98793-2",
ISBN-13 = "978-0-387-98793-4",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Oettli:1964:CAS,
author = "W. Oettli and W. Prager",
title = "Compatibility of Approximate Solution of Linear
Equations With Given Error Bounds for Coefficients and
Right-Hand Sides",
journal = j-NUM-MATH,
volume = "6",
pages = "405--409",
year = "1964",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Oettli:1965:SSL,
author = "W. Oettli",
title = "On the Solution Set of a Linear System with Inaccurate
Coefficients",
journal = j-SINUM,
volume = "2",
number = "1",
pages = "115--118",
year = "1965",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{OLeary:1980:EMC,
author = "Dianne Prost O'Leary",
title = "Estimating Matrix Condition Numbers",
journal = j-SISSC,
volume = "1",
number = "2",
pages = "205--209",
year = "1980",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Oliver:1977:EAM,
author = "J. Oliver",
title = "An Error Analysis of the Modified {Clenshaw} Method
for Evaluating {Chebyshev} and {Fourier} Series",
journal = j-JIMA,
volume = "20",
pages = "379--391",
year = "1977",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Oliver:1979:REP,
author = "J. Oliver",
title = "Rounding Error Propagation in Polynomial Evaluation
Schemes",
journal = j-JCAM,
volume = "5",
number = "2",
pages = "85--97",
year = "1979",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Olver:1978:NAE,
author = "F. W. J. Olver",
title = "A New Approach to Error Arithmetic",
journal = j-SINUM,
volume = "15",
number = "2",
pages = "368--393",
year = "1978",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Olver:1983:EAC,
author = "F. W. J. Olver",
booktitle = "Computational Aspects of Complex Analysis",
title = "Error Analysis of Complex Arithmetic",
volume = "102",
publisher = pub-reidel # ", " # pub-reidel:adr,
pages = "279--292",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "NATO Advanced Study Institute Series C",
editors = "H. Werner and L. Wuytack and E. Ng. and H. J.
B{\"u}nger",
}
@Article{Olver:1986:EBP,
author = "F. W. J. Olver",
title = "Error Bounds for Polynomial Evaluation and Complex
Arithmetic",
journal = j-IMAJNA,
volume = "6",
pages = "373--379",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Olver:1982:PEB,
author = "F. W. J. Olver and J. H. Wilkinson",
title = "{\em A posteriori\/} Error Bounds for {Gaussian}
Elimination",
journal = j-IMAJNA,
volume = "2",
pages = "377--406",
year = "1982",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Oettli:1965:ASL,
author = "W. Oettli and W. Prager and J. H. Wilkinson",
title = "Admissible Solutions of Linear Systems With Not
Sharply Defined Coefficients",
journal = j-SINUM,
volume = "2",
number = "2",
pages = "291--299",
year = "1965",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Ortega:1963:EAH,
author = "James M. Ortega",
title = "An Error Analysis of {Householder's} Method for the
Symmetric Eigenvalue Problem",
journal = j-NUM-MATH,
volume = "5",
pages = "211--225",
year = "1963",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{Ortega:1972:NAS,
author = "James M. Ortega",
title = "Numerical Analysis: {A} Second Course",
publisher = pub-AP,
address = pub-AP:adr-NY,
pages = "xiii + 201",
year = "1972",
ISBN = "0-89871-250-5 (original), 0-89871-250-5 (SIAM)",
ISBN-13 = "978-0-89871-250-6 (original), 978-0-89871-250-6
(SIAM)",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Republished by SIAM (1990).",
}
@Book{Ostrowski:1973:SEE,
author = "A. M. Ostrowski",
title = "Solution of Equations in {Euclidean and Banach}
Spaces",
publisher = pub-AP,
address = pub-AP:adr-NY,
pages = "xx + 412",
year = "1973",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Third edition of Solution of Equations and Systems of
Equations",
}
@Book{Overton:2001:NCI,
author = "Michael L. Overton",
title = "Numerical Computing with {IEEE} Floating Point
Arithmetic, Including One Theorem, One Rule of Thumb,
and One Hundred and One Exercises",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xiv + 104",
year = "2001",
ISBN = "0-89871-482-6 (hardcover), 0-89871-571-7 (paperback),
0-89871-807-4 (ebook)",
ISBN-13 = "978-0-89871-482-1 (hardcover), 978-0-89871-571-2
(print), 978-0-89871-807-2 (e-book)",
LCCN = "QA76.9.M35 O94 2001",
MRclass = "65-02 (65G30 68M07 68N99)",
MRnumber = "MR1828597 (2003b:65002)",
MRreviewer = "Jesse L. Barlow",
bibdate = "Fri Apr 27 16:50:46 2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
http://www.math.utah.edu/pub/tex/bib/numana2000.bib",
price = "US\$40.00",
URL = "http://www.cs.nyu.edu/cs/faculty/overton/book/;
http://www.siam.org/catalog/mcc07/ot76.htm",
abstract = "Are you familiar with the IEEE floating point
arithmetic standard? Would you like to understand it
better? This book gives a broad overview of numerical
computing, in a historical context, with a special
focus on the IEEE standard for binary floating point
arithmetic. Key ideas are developed step by step,
taking the reader from floating point representation,
correctly rounded arithmetic, and the IEEE philosophy
on exceptions, to an understanding of the crucial
concepts of conditioning and stability, explained in a
simple yet rigorous context. It gives technical details
that are not readily available elsewhere and includes
challenging exercises that go beyond the topics covered
in the text. Numerical Computing with IEEE Floating
Point Arithmetic provides an easily accessible yet
detailed discussion of IEEE Std 754-1985, arguably the
most important standard in the computer industry. The
result of an unprecedented cooperation between academic
computer scientists and the cutting edge of industry,
it is supported by virtually every modern computer.
Other topics include the floating point architecture of
the Intel microprocessors and a discussion of
programming language support for the standard.",
acknowledgement = ack-nhfb,
tableofcontents = "1: Introduction \\
2: The real numbers \\
3: Computer representation of numbers \\
4: IEEE floating point representation \\
5: Rounding \\
6: Correctly rounded floating point operations \\
7: Exceptions \\
8: The Intel microprocessors \\
9: Programming languages \\
10: Floating point in C \\
11: Cancellation \\
12: Conditioning of problems \\
13: Stability of algorithms \\
14: Conclusion",
}
@Article{Parlett:2000:RRR,
author = "Beresford N. Parlett and Inderjit S. Dhillon",
title = "Relatively Robust Representations of Symmetric
Tridiagonals",
journal = j-LAA,
volume = "309",
pages = "121--151",
year = "2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Patterson:1998:COD,
author = "David A. Patterson and John L. Hennessy",
title = "Computer Organization and Design: {The}
Hardware/Software Interface",
publisher = "Morgan Kaufmann",
address = "San Francisco, CA, USA",
edition = "Second",
pages = "xxix + 759 + appendices",
year = "1998",
ISBN = "1-55860-428-6",
ISBN-13 = "978-1-55860-428-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Paige:1973:EAM,
author = "C. C. Paige",
title = "An Error Analysis of a Method for Solving Matrix
Equations",
journal = j-MATH-COMP,
volume = "27",
number = "122",
pages = "355--359",
year = "1973",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Paige:1990:SAG,
author = "C. C. Paige",
editor = "M. G. Cox and S. J. Hammarling",
booktitle = "Reliable Numerical Computation",
title = "Some Aspects of Generalized {QR} Factorizations",
publisher = pub-OUP,
pages = "73--91",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Pan:2000:ECR,
author = "C.-T. Pan",
title = "On the Existence and Computation of Rank-Revealing
{LU} Factorizations",
journal = j-LAA,
volume = "316",
pages = "199--222",
year = "2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Pan:2001:SMP,
author = "Victor Y. Pan",
title = "Structured Matrices and Polynomials: {Unified}
Superfast Algorithms",
publisher = pub-BH,
address = pub-BH:adr,
pages = "xxiv + 278",
year = "2001",
ISBN = "0-8176-4240-4",
ISBN-13 = "978-0-8176-4240-2",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Pan:1978:SAO,
author = "Victor Y. Pan",
booktitle = "Proc. 19th Annual Symposium on the Foundations of
Computer Science",
title = "Strassen Algorithm is Not Optimal. {Trilinear}
Technique of Aggregating, Uniting and Canceling for
Constructing Fast Algorithms for Matrix
Multiplication",
publisher = "Ann Arbor, MI, USA",
pages = "166--176",
year = "1978",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Pan:1984:HCW,
author = "Victor Y. Pan",
title = "How Can We Speed up Matrix Multiplication?",
journal = j-SIREV,
volume = "26",
number = "3",
pages = "393--415",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Parhami:2000:CAA,
author = "Behrooz Parhami",
title = "Computer Arithmetic: Algorithms and Hardware Designs",
publisher = pub-OUP,
address = pub-OUP:adr-NY,
pages = "xx + 490",
year = "2000",
ISBN = "0-19-512583-5 (hardcover), 3-540-04907-X (print),
3-540-36246-0 (e-book)",
ISBN-13 = "978-0-19-512583-2 (hardcover), 978-3-540-04907-4
(print), 978-3-540-36246-3 (e-book)",
LCCN = "QA76.9.C62P37 1999",
bibdate = "Sat Jun 17 12:26:40 2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$85.00",
abstract = "The field of digital computer architecture has grown
explosively in the past two decades. Through a steady
stream of experimental research, tool-building efforts,
and theoretical studies, the design of an
instruction-set architecture has been transformed into
one of the most quantitative branches of computer
technology. However, this explosive growth has led to
unprecedented hardware complexity and almost
intolerable development costs. The challenge faxing
current and future computer designers is to institute
simplicity where we now have complexity; to use
fundamental theories being developed in this area to
gain performance and ease-of-use benefits from simpler
circuits; to understand the interplay between
technological capabilities/limitations and sound
architectural decisions. Computer arithmetic plays a
key role in the computer designers' quest for
user-friendliness, compactness, simplicity, high
performance, low cost, and low power. Parhami's
Computer Architecture emphasizes both the underlying
theory and actual hardware designs. and links computer
arithmetic to other subfields of computing. It is the
first computer arithmetic book to cover all topics
important for a balanced and complete view of the
field. IT will be accompanied by an instructor's
manual, with problem solutions and enlarged versions of
the figures/charts, suitable for reproduction as
transparencies. This is a textbook for senior/graduate
level courses in departments of computer science and
electrical and computer engineering. The course is
commonly called Computer Arithmetic. Students wishing
to enroll will usually have taken courses in computer
organization and advanced digital design before
enrolling. Computer Arithmetic is a sub-field of
digital computer organization. It deals with the
hardware realization of arithmetic functions to support
various computer architectures, as well as arithmetic
algorithms for firmware or software implementations. A
major thrust of digital computer arithmetic is the
design of hardware algorithms and circuits to enhance
the speed of numeric operations. Thus much of what is
presented in this book complements the architectural
and algorithmic speedup techniques studied in the
context of high performance computer architecture and
parallel processing.",
acknowledgement = ack-nhfb,
tableofcontents = "Part I: Number Representation \\
1: Numbers and Arithmetic \\
2: Representing Signed Numbers \\
3: Redundant Number Systems \\
4: Residue Number Systems \\
Part II: Addition/Subtraction \\
5: Basic Addition and Counting \\
6: Carry-Lookahead Adders \\
7: Variations in Fast Adders \\
8: Multioperand Addition \\
Part III: Multiplication \\
9: Basic Multiplication Schemes \\
10: High-Radix Multipliers \\
11: Tree and Array Multipliers \\
12: Variations in Multipliers \\
Part IV: Division \\
13: Basic Division Schemes \\
14: High-Radix Dividers \\
15: Variations in Dividers \\
16: Division by Convergence \\
Part V: Real Arithmetic \\
17: Floating-Point Representations \\
18: Floating-Point Operations \\
19: Errors and Error Control",
}
@Article{Parlett:1964:LMA,
author = "Beresford N. Parlett",
title = "{Laguerre's} Method Applied to the Matrix Eigenvalue
Problem",
journal = j-MATH-COMP,
volume = "18",
pages = "464--485",
year = "1964",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Parlett:1965:MEP,
author = "Beresford N. Parlett",
title = "Matrix Eigenvalue Problems",
journal = j-AMM,
volume = "72",
number = "2",
pages = "59--66",
month = feb,
year = "1965",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Parlett:1971:AAR,
author = "Beresford N. Parlett",
title = "Analysis of Algorithms for Reflections in Bisectors",
journal = j-SIREV,
volume = "13",
number = "2",
pages = "197--208",
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Parlett:1990:CJH,
author = "Beresford N. Parlett",
editor = "Stephen G. Nash",
booktitle = "A History of Scientific Computing",
title = "The Contribution of {J. H. Wilkinson} to Numerical
Analysis",
publisher = pub-AW # ", " # pub-AW:adr,
pages = "17--30",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Parlett:1998:SEP,
author = "Beresford N. Parlett",
title = "The Symmetric Eigenvalue Problem",
volume = "20",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxiv + 398",
year = "1998",
DOI = "https://doi.org/10.1137/1.9781611971163",
ISBN = "0-89871-402-8 (paperback), 1-61197-116-0 (e-book)",
ISBN-13 = "978-0-89871-402-9 (paperback), 978-1-61197-116-3
(e-book)",
LCCN = "QA188 .P37 1998",
MRclass = "65F15 (15A18)",
MRnumber = "MR1490034 (99c:65072)",
MRreviewer = "F. Szidarovszky",
bibdate = "Fri Nov 21 06:49:56 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Corrected reprint \cite{Parlett:1980:SEP}.",
series = "Classics in Applied Mathematics",
URL = "http://www.loc.gov/catdir/enhancements/fy0708/97040623-d.html",
ZMnumber = "0885.65039",
abstract = "According to Parlett, ``Vibrations are everywhere, and
so too are the eigenvalues associated with them. As
mathematical models invade more and more disciplines,
we can anticipate a demand for eigenvalue calculations
in an ever richer variety of contexts''. Anyone who
performs these calculations will welcome the reprinting
of Parlett's book (originally published in 1980). In
this unabridged, amended version, Parlett covers
aspects of the problem that are not easily found
elsewhere. The chapter titles convey the scope of the
material succinctly. The aim of the book is to present
mathematical knowledge that is needed in order to
understand the art of computing eigenvalues of real
symmetric matrices, either all of them or only a few.
The author explains why the selected information really
matters and he is not shy about making judgments. The
commentary is lively but the proofs are terse. The
first nine chapters are based on a matrix on which it
is possible to make similarity transformations
explicitly. The only source of error is inexact
arithmetic. The last five chapters turn to large sparse
matrices and the task of making approximations and
judging them.",
acknowledgement = ack-njh # " and " # ack-nhfb # " and " # ack-rah,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 15A18
Eigenvalues of matrices, etc. 15A23 Factorization of
matrices 15A57 Other types of matrices 15-02 Research
monographs (linear algebra) 65-02 Research monographs
(numerical analysis) 65F25 Orthogonalization (numerical
linear algebra)",
keywords = "bandmatrices; bounds for eigenvalues; eigenvalues;
generalized eigenvalue problem; Krylov sequences;
localization of eigenvalues; orthogonal
transformations; tridiagonal matrices; vector
iteration",
libnote = "Not yet in my library.",
remark = "Unabridged, corrected republication of the original
edition (1980; Zbl 0431.65017)",
tableofcontents = "Convergence theory for the Rayleigh quotient
iteration \\
Eigenvectors of tridiagonals \\
Convergence theory, simpler than Wilkinson's, for
Wilkinson's shift strategy in $Q L$ and $Q R$ \\
New proofs and sharper results for error bounds \\
Optimal properties of Rayleigh--Ritz approximations \\
Approximation theory from Krylov subspaces, Paige's
theorem for noisy Lanczos algorithms, and
semiorthogonality among Lanczos vectors \\
Four flavors of subspace iteration",
}
@Article{Pan:1991:INI,
author = "Victor Y. Pan and Robert Schreiber",
title = "An Improved {Newton} Iteration for the Generalized
Inverse of a Matrix, with Applications",
journal = j-SISSC,
volume = "12",
number = "5",
pages = "1109--1130",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Paterson:1973:NNM,
author = "Michael S. Paterson and Larry J. Stockmeyer",
title = "On the Number of Nonscalar Multiplications Necessary
to Evaluate Polynomials",
journal = j-SICOMP,
volume = "2",
number = "1",
pages = "60--66",
year = "1973",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{patriot92,
key = "United States General Accounting Office",
title = "Patriot Missile Defense: {Software} Problem Led to
System Failure at {Dhahran}, {Saudi Arabia}",
type = "Report",
number = "GAO/IMTEC-92-26",
institution = "Information Management and Technology Division, United
States General Accounting Office",
address = "Washington, D.C.",
pages = "16",
month = feb,
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Paige:1994:HGC,
author = "C. C. Paige and M. Wei",
title = "History and Generality of the {CS} Decomposition",
journal = j-LAA,
volume = "208/209",
pages = "303--326",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Unpublished{Paxson:1991:PTI,
author = "Vern Paxson",
title = "A Program for Testing {IEEE} Decimal--Binary
Conversion",
pages = "40",
month = may,
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Manuscript.
\path|ftp://ftp.ee.lbl.gov/testbase-report.ps.Z|",
}
@Article{Pan:2001:CNC,
author = "Victor Y. Pan and Y. Yu",
title = "Certification of Numerical Computation of the Sign of
the Determinant of a Matrix",
journal = j-ALGORITHMICA,
volume = "30",
number = "4",
pages = "708--724",
year = "2001",
CODEN = "ALGOEJ",
ISSN = "0178-4617 (print), 1432-0541 (electronic)",
ISSN-L = "0178-4617",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Algorithmica",
journal-URL = "http://link.springer.com/journal/453",
}
@InCollection{Pan:1999:NIS,
author = "Victor Y. Pan and Sheryl Branham and Rhys E. Rosholt
and Ai-Long Zheng",
editor = "Thomas Kailath and Ali H. Sayed",
booktitle = "Fast Reliable Algorithms for Matrices with Structure",
title = "Newton's Iteration for Structured Matrices",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "189--210",
year = "1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Pena:1996:PSL,
author = "J. M. Pe{\~n}a",
title = "Pivoting Strategies Leading to Small Bounds of the
Errors for Certain Linear Systems",
journal = j-IMAJNA,
volume = "16",
number = "2",
pages = "141--153",
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Pena:1998:PSL,
author = "J. M. Pe{\~n}a",
title = "Pivoting Strategies Leading to Diagonal Dominance by
Rows",
journal = j-NUM-MATH,
volume = "81",
pages = "293--304",
year = "1998",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Penzl:1998:NSG,
author = "Thilo Penzl",
title = "Numerical Solution of Generalized {Lyapunov}
Equations",
journal = j-Adv-Comp-Math,
volume = "8",
pages = "33--48",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Percival:2002:RMM,
author = "Colin Percival",
title = "Rapid Multiplication Modulo the Sum and Difference of
Highly Composite Numbers",
journal = j-MATH-COMP,
volume = "",
number = "",
pages = "",
year = "2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "To appear",
}
@Book{Petersen:1981:ET,
author = "Karl Petersen",
title = "Ergodic Theory",
publisher = pub-CUP,
address = pub-CUP:adr,
pages = "xi + 329",
year = "1981",
ISBN = "0-521-23632-0",
ISBN-13 = "978-0-521-23632-4",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Peters:1970:LSP,
author = "G. Peters and J. H. Wilkinson",
title = "The Least Squares Problem and Pseudo-Inverses",
journal = j-COMP-J,
volume = "13",
number = "3",
pages = "309--316",
year = "1970",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Peters:1971:PPA,
author = "G. Peters and J. H. Wilkinson",
title = "Practical Problems Arising in the Solution of
Polynomial Equations",
journal = j-JIMA,
volume = "8",
pages = "16--35",
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Peters:1975:SGJ,
author = "G. Peters and J. H. Wilkinson",
title = "On the Stability of {Gauss--Jordan} Elimination With
Pivoting",
journal = j-CACM,
volume = "18",
number = "1",
pages = "20--24",
year = "1975",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Tao:1984:CSM,
author = "Pham Dinh Tao",
title = "Convergence of a Subgradient Method for Computing the
Bound Norm of Matrices",
journal = j-LAA,
volume = "62",
pages = "163--182",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "In French",
}
@Article{Tao:1984:SMC,
author = "Pham Dinh Tao",
title = "Some Methods for Computing the Maximum of Quadratic
Form on the Unit Ball of the Maximum Norm",
journal = j-NUM-MATH,
volume = "45",
pages = "377--401",
year = "1984",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "In French",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Pichat:1972:CSA,
author = "M. Pichat",
title = "Correction d'une Somme en Arithm\'etique \`a Virgule
Flottante",
journal = j-NUM-MATH,
volume = "19",
pages = "400--406",
year = "1972",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Pierce:1992:FAC,
author = "Daniel J. Pierce and Robert J. Plemmons",
title = "Fast Adaptive Condition Estimation",
journal = j-SIMAX,
volume = "13",
number = "1",
pages = "274--291",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Peitgen:1992:FCP,
author = "Heinz-Otto Peitgen and Hartmut J{\"u}rgens and Dietmar
Saupe",
title = "Fractals for the Classroom. Part One: Introduction to
Fractals and Chaos",
publisher = pub-Springer,
address = pub-Springer:adr-NY,
pages = "xiv + 450",
year = "1992",
ISBN = "0-387-97041-X",
ISBN-13 = "978-0-387-97041-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Plauger:1988:PFP,
author = "P. J. Plauger",
title = "Properties of Floating-Point Arithmetic",
journal = j-COMP-LANG-MAG,
volume = "5",
number = "3",
pages = "17--22",
year = "1988",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computer Language Magazine",
}
@Article{Plemmons:1974:LLS,
author = "Robert J. Plemmons",
title = "Linear Least Squares by Elimination and {MGS}",
journal = j-ACM,
volume = "21",
number = "4",
pages = "581--585",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Plemmons:1976:RSD,
author = "R. J. Plemmons",
title = "Regular Splittings and the Discrete {Neumann}
Problem",
journal = j-NUM-MATH,
volume = "25",
pages = "153--161",
year = "1976",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Polman:1987:IBF,
author = "Ben Polman",
title = "Incomplete Blockwise Factorizations of (Block)
{$H$}-Matrices",
journal = j-LAA,
volume = "90",
pages = "119--132",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Poole:2000:RPS,
author = "George Poole and Larry Neal",
title = "The Rook's Pivoting Strategy",
journal = j-JCAM,
volume = "123",
pages = "353--369",
year = "2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Powell:1969:AHT,
author = "M. J. D. Powell and J. K. Reid",
booktitle = "Proc. IFIP Congress 1968",
title = "On Applying {Householder} Transformations to Linear
Least Squares Problems",
publisher = pub-NH # ", " # pub-NH:adr,
pages = "122--126",
year = "1969",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Poljak:1993:CRN,
author = "Svatopluk Poljak and Ji{\v{r}}{\'\i} Rohn",
title = "Checking Robust Nonsingularity is {NP}-Hard",
journal = j-MATH-CONTROL-SIGNALS-SYST,
volume = "6",
pages = "1--9",
year = "1993",
CODEN = "MCSYE8",
ISSN = "0932-4194 (print), 1435-568x (electronic)",
ISSN-L = "0932-4194",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Mathematics of control, signals, and systems: MCSS",
}
@Article{Powell:1970:SNM,
author = "M. J. D. Powell",
title = "A Survey of Numerical Methods for Unconstrained
Optimization",
journal = j-SIREV,
volume = "12",
number = "1",
pages = "79--97",
year = "1970",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Powell:1975:VUM,
author = "M. J. D. Powell",
title = "A View of Unconstrained Minimization Algorithms That
Do Not Require Derivatives",
journal = j-TOMS,
volume = "1",
number = "2",
pages = "97--107",
year = "1975",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Power:1986:CDH,
author = "Stephen Power",
title = "The {Cholesky} Decomposition in {Hilbert} Space",
journal = j-IMA-BULL,
volume = "22",
number = "11/12",
pages = "186--187",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "IMA Bulletin",
}
@Article{Powell:1998:DSA,
author = "M. J. D. Powell",
title = "Direct Search Algorithms for Optimization
Calculations",
journal = j-ACTA-NUMERICA,
volume = "7",
pages = "287--336",
year = "1998",
CODEN = "ANUMFU",
DOI = "https://doi.org/10.1017/S0962492900002841",
ISBN = "0-521-64316-3",
ISBN-13 = "978-0-521-64316-0",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
bibdate = "Sat Sep 24 10:23:37 MDT 2011",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
acknowledgement = ack-nhfb,
ajournal = "Acta Numer.",
fjournal = "Acta Numerica",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU",
onlinedate = "07 November 2008",
}
@InProceedings{Priest:1991:AAP,
author = "Douglas M. Priest",
editor = "Peter Kornerup and David W. Matula",
booktitle = "Proc. 10th IEEE Symposium on Computer Arithmetic",
title = "Algorithms for Arbitrary Precision Floating Point
Arithmetic",
publisher = "IEEE Computer Society Press, Los Alamitos, CA, USA",
pages = "132--143",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@PhdThesis{Priest:1992:PFP,
author = "Douglas M. Priest",
title = "On Properties of Floating Point Arithmetics:
{Numerical} Stability and the Cost of Accurate
Computations",
school = "Mathematics Department, University of California",
address = inst-Berkeley:adr,
pages = "126",
month = nov,
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "\path|ftp://ftp.icsi.berkeley.edu/pub/theory/priest-thesis.ps.Z|",
}
@Article{Pryce:1981:REA,
author = "J. D. Pryce",
title = "Round-Off Error Analysis with Fewer Tears",
journal = j-IMA-BULL,
volume = "17",
pages = "40--47",
year = "1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "IMA Bulletin",
}
@Article{Pryce:1984:NMR,
author = "J. D. Pryce",
title = "A New Measure of Relative Error for Vectors",
journal = j-SINUM,
volume = "21",
number = "1",
pages = "202--215",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Pryce:1985:MEA,
author = "J. D. Pryce",
title = "Multiplicative Error Analysis of Matrix Transformation
Algorithms",
journal = j-IMAJNA,
volume = "5",
pages = "437--445",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Misc{Embree:19xx:PG,
author = "Mark Embree and Lloyd N. Trefethen",
title = "Pseudospectra Gateway",
year = "19xx",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "\path|http://www.comlab.ox.ac.uk/pseudospectra/|",
}
@Book{Press:1992:NRF,
author = "William H. Press and Saul A. Teukolsky and William T.
Vetterling and Brian P. Flannery",
title = "Numerical Recipes in {FORTRAN}: {The} Art of
Scientific Computing",
publisher = pub-CUP,
edition = "Second",
pages = "xxvi + 963",
year = "1992",
ISBN = "0-521-43064-X",
ISBN-13 = "978-0-521-43064-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Puschmann:1983:CPR,
author = "Heinrich Puschmann and Joaqu{\'\i}n Cort\'es",
title = "The Coordinex Problem and its Relation to the
Conjecture of {Wilkinson}",
journal = j-NUM-MATH,
volume = "42",
pages = "291--297",
year = "1983",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Puglisi:1992:MHM,
author = "Chiara Puglisi",
title = "Modification of the {Householder} Method Based on the
Compact {WY} Representation",
journal = j-SISSC,
volume = "13",
number = "3",
pages = "723--726",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Puschmann:1985:ZUV,
author = "Heinrich Puschmann and Marcelo Nordio",
title = "Zwei {Unzal{\"a}ssige} {Verst{\"a}rkungen} der
{Vermutung} von {Wilkinson}",
journal = j-LAA,
volume = "72",
pages = "167--176",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "In German",
}
@Article{Quintana:2001:NPM,
author = "Enrique S. Quintana and Gregorio Quintana and Xiaobai
Sun and Robert van de Geijn",
title = "A Note on Parallel Matrix Inversion",
journal = j-SISC,
volume = "22",
number = "5",
pages = "1762--1771",
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Quinn:1991:TMY,
author = "Thomas R. Quinn and Scott Tremaine and Martin Duncan",
title = "A Three Million Year Integration of the Earth's
Orbit",
journal = j-ASTRON-J,
volume = "101",
number = "6",
pages = "2287--2305",
year = "1991",
CODEN = "ANJOAA",
ISSN = "0004-6256 (print), 1538-3881 (electronic)",
ISSN-L = "0004-6256",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Astronomical Journal",
journal-URL = "http://iopscience.iop.org/1538-3881",
}
@Article{Quinn:1983:EPR,
author = "Kevin Quinn",
title = "Ever Had Problems Rounding Off Figures? {This} Stock
Exchange Has",
journal = j-WALL-ST-J,
year = "1983",
CODEN = "WSJOAF",
ISSN = "0099-9660",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "8 November",
fjournal = "Wall Street Journal",
page = "37",
}
@Article{Quinlan:1994:REL,
author = "Gerald D. Quinlan",
title = "Round-Off Error in Long-Term Orbital Integrations
Using Multistep Methods",
journal = j-CELEST-MECH-DYN-ASTR,
volume = "58",
pages = "339--351",
year = "1994",
CODEN = "CLMCAV",
ISSN = "0923-2958 (print), 1572-9478 (electronic)",
ISSN-L = "0923-2958",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Celestial Mechanics and Dynamical Astronomy",
}
@Article{Quinn:1990:REL,
author = "Thomas Quinn and Scott Tremaine",
title = "Roundoff Error in Long-Term Planetary Orbit
Integrations",
journal = j-ASTRON-J,
volume = "99",
number = "3",
pages = "1016--1023",
year = "1990",
CODEN = "ANJOAA",
ISSN = "0004-6256 (print), 1538-3881 (electronic)",
ISSN-L = "0004-6256",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Astronomical Journal",
journal-URL = "http://iopscience.iop.org/1538-3881",
}
@Article{Raimi:1969:PDF,
author = "Ralph A. Raimi",
title = "The Peculiar Distribution of First Digits",
journal = j-SCI-AMER,
volume = "221",
number = "6",
pages = "109--120",
year = "1969",
CODEN = "SCAMAC",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Raimi:1976:FDP,
author = "Ralph A. Raimi",
title = "The First Digit Problem",
journal = j-AMM,
volume = "83",
pages = "521--538",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Rall:1981:ADT,
author = "Louis B. Rall",
title = "Automatic Differentiation: {Techniques} and
Applications",
volume = "120",
publisher = pub-Springer,
address = pub-Springer:adr-B,
pages = "viii + 165",
year = "1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Lecture Notes in Computer Science",
}
@InProceedings{Rall:1991:TMC,
author = "Louis B. Rall",
editor = "Kenneth R. Meyer and Dieter S. Schmidt",
booktitle = "Computer Aided Proofs in Analysis",
title = "Tools for Mathematical Computation",
volume = "28",
publisher = pub-Springer # ", " # pub-Springer:adr-NY,
pages = "217--228",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "IMA Volumes in Mathematics and Its Applications",
}
@Article{Ramos:1971:REA,
author = "George U. Ramos",
title = "Roundoff Error Analysis of the Fast {Fourier}
Transform",
journal = j-MATH-COMP,
volume = "25",
number = "116",
pages = "757--768",
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Randell:1975:ODC,
editor = "Brian Randell",
title = "The Origins of Digital Computers: {Selected} Papers",
publisher = pub-Springer,
address = pub-Springer:adr-B,
edition = "Third",
pages = "xvi + 580",
year = "1975",
ISBN = "3-540-11319-3",
ISBN-13 = "978-3-540-11319-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Rath:1982:FGR,
author = "Wolfgang Rath",
title = "Fast {Givens} Rotations for Orthogonal Similarity
Transformations",
journal = j-NUM-MATH,
volume = "40",
pages = "47--56",
year = "1982",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Reichel:1990:NIL,
author = "Lothar Reichel",
title = "Newton Interpolation at {Leja} Points",
journal = j-BIT,
volume = "30",
pages = "332--346",
year = "1990",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Reichel:1991:FQD,
author = "Lothar Reichel",
title = "Fast {QR} Decomposition of {Vandermonde}-Like Matrices
and Polynomial Least Squares Approximation",
journal = j-SIMAX,
volume = "12",
number = "3",
pages = "552--564",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Reid:2000:ISL,
author = "J. K. Reid",
title = "Implicit Scaling of Linear Least Squares Problems",
journal = j-BIT,
volume = "40",
number = "1",
pages = "146--157",
year = "2000",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Reid:1971:NSG,
author = "J. K. Reid",
title = "A Note on the Stability of {Gaussian} Elimination",
journal = j-JIMA,
volume = "8",
pages = "374--375",
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Reid:1987:SM,
author = "J. K. Reid",
editor = "A. Iserles and M. J. D. Powell",
booktitle = "The State of the Art in Numerical Analysis",
title = "Sparse Matrices",
publisher = pub-OUP,
pages = "59--85",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Reiser:1975:EDF,
author = "John F. Reiser and Donald E. Knuth",
title = "Evading the Drift in Floating-Point Addition",
journal = j-INFPL,
volume = "3",
number = "3",
pages = "84--87",
year = "1975",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Reichel:1991:CVS,
author = "Lothar Reichel and Gerhard Opfer",
title = "{Chebyshev}-{Vandermonde} Systems",
journal = j-MATH-COMP,
volume = "57",
number = "196",
pages = "703--721",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Reichel:1992:EPE,
author = "Lothar Reichel and Lloyd N. Trefethen",
title = "Eigenvalues and Pseudo-Eigenvalues of {Toeplitz}
Matrices",
journal = j-LAA,
volume = "162--164",
pages = "153--185",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Reddy:1992:SML,
author = "Satish C. Reddy and Lloyd N. Trefethen",
title = "Stability of the Method of Lines",
journal = j-NUM-MATH,
volume = "62",
pages = "235--267",
year = "1992",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Rheinboldt:1976:MIC,
author = "Werner C. Rheinboldt",
title = "On Measures of Ill-Conditioning for Nonlinear
Equations",
journal = j-MATH-COMP,
volume = "30",
number = "133",
pages = "104--111",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Rice:1966:TC,
author = "John R. Rice",
title = "A Theory of Condition",
journal = j-SINUM,
volume = "3",
number = "2",
pages = "287--310",
year = "1966",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Rice:1966:EGS,
author = "John R. Rice",
title = "Experiments on {Gram--Schmidt} Orthogonalization",
journal = j-MATH-COMP,
volume = "20",
pages = "325--328",
year = "1966",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Rigal:1967:CGS,
author = "J. L. Rigal and J. Gaches",
title = "On the Compatibility of a Given Solution with the Data
of a Linear System",
journal = j-ACM,
volume = "14",
number = "3",
pages = "543--548",
year = "1967",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Roberts:1980:LMR,
author = "J. D. Roberts",
title = "Linear Model Reduction and Solution of the Algebraic
{Riccati} Equation by Use of the Sign Function",
journal = j-IJC,
volume = "32",
number = "4",
pages = "677--687",
year = "1980",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "First issued as report CUED/B-Control/TR13, Department
of Engineering, University of Cambridge, 1971",
}
@Article{Rohn:1989:NCN,
author = "Ji{\v{r}}{\'\i} Rohn",
title = "New Condition Numbers for Matrices and Linear
Systems",
journal = j-COMPUTING,
volume = "41",
pages = "167--169",
year = "1989",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Rohn:1989:SLI,
author = "Ji{\v{r}}{\'\i} Rohn",
title = "Systems of Linear Interval Equations",
journal = j-LAA,
volume = "126",
pages = "39--78",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Rohn:1990:NUD,
author = "Ji{\v{r}}{\'\i} Rohn",
title = "Nonsingularity Under Data Rounding",
journal = j-LAA,
volume = "139",
pages = "171--174",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Rohn:1995:NHR,
author = "Ji{\v{r}}{\'\i} Rohn",
title = "{NP}-Hardness Results for Some Linear and Quadratic
Problems",
type = "Technical Report",
number = "No. 619",
institution = "Institute of Computer Science, Academy of Sciences of
the Czech Republic",
address = "Prague",
pages = "11",
month = jan,
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Robertazzi:1988:BOF,
author = "T. G. Robertazzi and S. C. Schwartz",
title = "Best ``Ordering'' for Floating-Point Addition",
journal = j-TOMS,
volume = "14",
number = "1",
pages = "101--110",
year = "1988",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Ross:1965:RTE,
author = "D. R. Ross",
title = "Reducing Truncation Errors Using Cascading
Accumulators",
journal = j-CACM,
volume = "8",
number = "1",
pages = "32--33",
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@PhdThesis{Rowan:1990:FSA,
author = "Thomas Harvey Rowan",
title = "Functional Stability Analysis of Numerical
Algorithms",
school = "University of Texas at Austin",
address = "Austin, TX, USA",
pages = "xii + 205",
month = may,
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Routh:1977:PSM,
author = "M. W. Routh and P. A. Swartz and M. B. Denton",
title = "Performance of the Super Modified Simplex",
journal = j-ANAL-CHEM,
volume = "49",
number = "9",
pages = "1422--1428",
year = "1977",
CODEN = "ANCHAM",
ISSN = "0003-2700 (print), 1520-6882 (electronic)",
ISSN-L = "0003-2700",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Analytical Chemistry (Washington, DC, USA)",
journal-URL = "http://pubs.acs.org/journal/ancham",
}
@Article{Ruhe:1983:NAG,
author = "Axel Ruhe",
title = "Numerical Aspects of {Gram--Schmidt} Orthogonalization
of Vectors",
journal = j-LAA,
volume = "52/53",
pages = "591--601",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Rump:2001:SVM,
author = "Siegfried M. Rump",
title = "Self-Validating Methods",
journal = j-LAA,
volume = "324",
pages = "3--13",
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Rump:2002:OSN,
author = "Siegfried M. Rump",
title = "Optimal Scaling for {$P$}-norms and Componentwise
Distance to Singularity",
journal = j-IMAJNA,
volume = "",
number = "",
pages = "",
year = "2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "To appear",
}
@Article{Rump:1998:SPS,
author = "Siegfried M. Rump",
title = "Structured Perturbations and Symmetric Matrices",
journal = j-LAA,
volume = "278",
pages = "121--132",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Rump:1999:ICM,
author = "Siegfried M. Rump",
title = "Ill-Conditioned Matrices Are Componentwise Near to
Singularity",
journal = j-SIREV,
volume = "41",
number = "1",
pages = "102--112",
year = "1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InCollection{Rump:1999:IIL,
author = "Siegfried M. Rump",
editor = "Tibor Csendes",
booktitle = "Developments~in~Reliable Computing",
title = "{INTLAB---INTerval LABoratory}",
publisher = pub-Kluwer,
address = pub-Kluwer:adr,
pages = "77--104",
year = "1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Rump:1999:FPI,
author = "Siegfried M. Rump",
title = "Fast and Parallel Interval Arithmetic",
journal = j-BIT,
volume = "39",
number = "3",
pages = "534--554",
year = "1999",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Russinoff:1998:MCP,
author = "David M. Russinoff",
title = "A Mechanically Checked Proof of {IEEE} Compliance of
the Floating Point Multiplication, Division and Square
Root Algorithms of the {AMD-K7} Processor",
journal = "LMS J. Computer Math.",
volume = "1",
pages = "148--200",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Rutherford:1947:SCD,
author = "D. E. Rutherford",
title = "Some Continuant Determinants Arising in Physics and
Chemistry",
journal = j-PROC-R-SOC-EDINB,
volume = "62,A",
pages = "229--236",
year = "1947",
CODEN = "PRSEAE",
ISSN = "0080-4541 (print), 2053-5902 (electronic)",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Proceedings of the Royal Society of Edinburgh",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PRE",
}
@Article{Rutherford:1952:SCD,
author = "D. E. Rutherford",
title = "Some Continuant Determinants Arising in Physics and
Chemistry---{II}",
journal = j-PROC-R-SOC-EDINB,
volume = "63,A",
pages = "232--241",
year = "1952",
CODEN = "PRSEAE",
ISSN = "0080-4541 (print), 2053-5902 (electronic)",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Proceedings of the Royal Society of Edinburgh",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PRE",
}
@InCollection{Rutishauser:1958:SEP,
author = "Heinz Rutishauser",
booktitle = "Further Contributions to the Solution of Simultaneous
Linear Equations and the Determination of Eigenvalues",
title = "Solution of Eigenvalue Problems With the
{LR}-Transformation",
number = "49",
publisher = "National Bureau of Standards, United States Department
of Commerce",
address = "Washington, D. C.",
pages = "47--81",
year = "1958",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Applied Mathematics Series",
}
@InProceedings{Rutishauser:1968:TM,
author = "H. Rutishauser",
booktitle = "Programmation en Math{\'e}matiques Num{\'e}riques,
Besan{\c{c}}on, 1966",
title = "On Test Matrices",
volume = "7 (no. 165)",
pages = "349--365",
year = "1968",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "{\'E}ditions Centre Nat. Recherche Sci., Paris",
}
@Article{Samelson:1953:ORR,
author = "Klaus Samelson and Friedrich L. Bauer",
title = "{Optimale Rechengenauigkeit} bei {Rechenanlagen} mit
gleitendem {Komma}",
journal = j-ZAMP,
volume = "4",
pages = "312--316",
year = "1953",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Sameh:1977:STS,
author = "Ahmed H. Sameh and Richard P. Brent",
title = "Solving Triangular Systems on a Parallel Computer",
journal = j-SINUM,
volume = "14",
number = "6",
pages = "1101--1113",
year = "1977",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Sanz-Serna:1993:SCS,
author = "J. M. Sanz-Serna and S. Larsson",
title = "Shadows, Chaos, and Saddles",
journal = j-APP-NUM-MATH,
volume = "13",
pages = "181--190",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InCollection{Savage:1954:TIF,
author = "I. Richard Savage and Eugene Lukacs",
editor = "Olga Taussky",
booktitle = "Contributions to the Solution of Systems of Linear
Equations and the Determination of Eigenvalues",
title = "Tables of Inverse of Finite Segments of the {Hilbert}
Matrix",
number = "39",
publisher = "National Bureau of Standards, United States Department
of Commerce",
address = "Washington, D. C.",
pages = "105--108",
year = "1954",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Applied Mathematics Series",
}
@TechReport{Saunders:1972:LSL,
author = "M. A. Saunders",
title = "Large-Scale Linear Programming Using the {Cholesky}
Factorization",
type = "Report",
number = "CS 252",
institution = inst-CS-U-STANFORD,
month = jan,
year = "1972",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Sautter:1978:EAG,
author = "Werner Sautter",
title = "Error Analysis of {Gauss} Elimination for the Best
Least Squares Problem",
journal = j-NUM-MATH,
volume = "30",
pages = "165--184",
year = "1978",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
germantitle = "Fehleranalyse f{\"ur} die {Gau\ss}-Elimination zur
Berechnung der L{\"o}sung minimaler L{\"a}nge",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{Smith:1976:MER,
author = "B. T. Smith and J. M. Boyle and J. J. Dongarra and B.
S. Garbow and Y. Ikebe and V. C. Klema and C. B.
Moler",
title = "Matrix Eigensystem Routines---{EISPACK} Guide",
volume = "6",
publisher = pub-Springer,
address = pub-Springer:adr-B,
edition = "Second",
pages = "vii + 551",
year = "1976",
ISBN = "3-540-06710-8",
ISBN-13 = "978-3-540-06710-8",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Lecture Notes in Computer Science",
}
@Book{Scarborough:1950:NMA,
author = "James B. Scarborough",
title = "Numerical Mathematical Analysis",
publisher = pub-JH,
address = pub-JH:adr,
edition = "Second",
pages = "xviii + 511",
year = "1950",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Schatzman:1996:ADF,
author = "James C. Schatzman",
title = "Accuracy of the Discrete {Fourier} Transform and the
Fast {Fourier} Transform",
journal = j-SISC,
volume = "17",
number = "5",
pages = "1150--1166",
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Schelin:1983:CFA,
author = "Charles W. Schelin",
title = "Calculator Function Approximation",
journal = j-AMM,
volume = "90",
number = "5",
pages = "317--325",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Schryer:1981:TCF,
author = "N. L. Schryer",
title = "A Test of a Computer's Floating-Point Arithmetic
Unit",
type = "Computing Science Technical Report",
number = "No. 89",
institution = inst-ATT,
address = inst-ATT:adr,
year = "1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Schryer:1984:DCF,
author = "N. L. Schryer",
editor = "Wayne R. Cowell",
booktitle = "Sources and Development of Mathematical Software",
title = "Determination of Correct Floating-Point Model
Parameters",
publisher = pub-PH # ", " # pub-PH:adr,
pages = "360--366",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Schreiber:1988:BAP,
author = "Robert S. Schreiber",
editor = "M. H. Schultz",
booktitle = "Numerical Algorithms for Modern Parallel Computer
Architectures",
title = "Block Algorithms for Parallel Machines",
number = "13",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
pages = "197--207",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "IMA Volumes In Mathematics and Its Applications",
}
@Article{Schreiber:1989:HRS,
author = "Robert S. Schreiber",
title = "{Hough's} Random Story Explained",
journal = j-NA-DIGEST,
volume = "Volume 89, Issue 3",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "NA Digest",
}
@Article{schu33,
author = "G{\"u}nther Schulz",
title = "{Iterative Berechnung} der Reziproken {Matrix}",
journal = j-ZAMM,
volume = "13",
pages = "57--59",
year = "1933",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Schreiber:1988:BRT,
author = "Robert S. Schreiber and Beresford N. Parlett",
title = "Block Reflectors: {Theory} and Computation",
journal = j-SINUM,
volume = "25",
number = "1",
pages = "189--205",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Schonfelder:1980:ECP,
author = "J. L. Schonfelder and M. Razaz",
title = "Error Control with Polynomial Approximations",
journal = j-IMAJNA,
volume = "1",
pages = "105--114",
year = "1980",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Schneider:1962:CTS,
author = "Hans Schneider and W. Gilbert Strang",
title = "Comparison Theorems for Supremum Norms",
journal = j-NUM-MATH,
volume = "4",
pages = "15--20",
year = "1962",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Schreiber:1989:SEW,
author = "Robert S. Schreiber and Charles F. {Van Loan}",
title = "A Storage Efficient {WY} Representation for Products
of {Householder} Transformations",
journal = j-SISSC,
volume = "10",
pages = "53--57",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Schneider:1998:MWN,
author = "Hans Schneider and Hans F. Weinberger",
title = "On Matrices for Which Norm Bounds Are Attained",
journal = j-LAA,
volume = "275--276",
pages = "563--577",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Scherer:1980:SNR,
author = "R. Scherer and K. Zeller",
title = "Shorthand Notation for Rounding Errors",
journal = j-COMPUTING,
volume = "Suppl. 2",
pages = "165--168",
year = "1980",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Book{Sedgewick:1988:A,
author = "Robert Sedgewick",
title = "Algorithms",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xii + 657",
year = "1988",
ISBN = "0-201-06673-4",
ISBN-13 = "978-0-201-06673-9",
LCCN = "QA76.6 .S435 1988",
MRclass = "68-01, 68N01, 68P05, 68P10, 68Q25, 68W10, 68W99",
bibdate = "Wed Dec 15 10:41:37 1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/hash.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
http://www.math.utah.edu/pub/tex/bib/texbook2.bib",
price = "US\$34.95",
ZMnumber = "0717.68005",
acknowledgement = ack-nhfb,
libnote = "Not yet in my library.",
remark = prep-tex,
}
@Misc{Severance:1998:IOM,
author = "Charles Severance",
title = "An Interview with the Old Man of Floating-Point.
{Reminiscences} Elicited from {William Kahan by Charles
Severance}",
month = feb,
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "\path|http://www.cs.berkeley.edu/~wkahan/ieee754status/754story.html|.
A shortened version appears in \emph{Computer},
31(3):114--115, March 1998.",
}
@Book{shal73,
author = "Lawrence F. Shampine and Richard C. {Allen, Jr.}",
title = "Numerical Computing: {An} Introduction",
publisher = "W. B. Saunders",
address = "Philadelphia, PA, USA",
pages = "vii + 258",
year = "1973",
ISBN = "0-7216-8150-6",
ISBN-13 = "978-0-7216-8150-4",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Shampine:1994:NSO,
author = "Lawrence F. Shampine",
title = "Numerical Solution of Ordinary Differential
Equations",
publisher = pub-CH,
address = pub-CH:adr-NY,
pages = "x + 484",
year = "1994",
ISBN = "0-412-05151-6",
ISBN-13 = "978-0-412-05151-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Shapiro:1982:OSM,
author = "Alexander Shapiro",
title = "Optimally Scaled Matrices, Necessary and Sufficient
Conditions",
journal = j-NUM-MATH,
volume = "39",
pages = "239--245",
year = "1982",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Shapiro:1985:OBD,
author = "Alexander Shapiro",
title = "Optimal Block Diagonal {$l_2$}-Scaling of Matrices",
journal = j-SINUM,
volume = "22",
number = "1",
pages = "81--94",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Shapiro:1991:UBN,
author = "Alexander Shapiro",
title = "Upper Bounds for Nearly Optimal Diagonal Scaling of
Matrices",
journal = j-LMA,
volume = "29",
pages = "147--147",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Sharangpani:1994:SAF,
author = "H. P. Sharangpani and M. L. Barton",
title = "Statistical Analysis of Floating Point Flaw in the
{Pentium} Processor (1994)",
institution = "Intel Corporation",
pages = "31",
month = nov,
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Shroff:1992:ACE,
author = "Gautam M. Shroff and Christian H. Bischof",
title = "Adaptive Condition Estimation for Rank-One Updates of
{QR} Factorizations",
journal = j-SIMAX,
volume = "13",
number = "4",
pages = "1264--1278",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Shewchuk:1997:APF,
author = "Jonathan Richard Shewchuk",
title = "Adaptive Precision Floating-Point Arithmetic and Fast
Robust Geometric Predicates",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "18",
number = "3",
pages = "305--363",
year = "1997",
CODEN = "DCGEER",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
}
@Article{Shampine:1997:MOS,
author = "Lawrence F. Shampine and Mark W. Reichelt",
title = "The {MATLAB} {ODE} Suite",
journal = j-SISC,
volume = "18",
number = "1",
pages = "1--22",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Shepherd:1989:MCW,
author = "David Shepherd and Greg Wilson",
title = "Making Chips that Work",
journal = j-NEW-SCIENTIST,
pages = "61--64",
year = "1989",
CODEN = "NWSCAL",
ISSN = "0262-4079, 0028-6664",
ISSN-L = "0262-4079",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "13 May",
fjournal = "New Scientist",
journal-URL = "http://www.sciencedirect.com/science/journal/02624079",
}
@Article{Skeel:1979:SNS,
author = "Robert D. Skeel",
title = "Scaling for Numerical Stability in {Gaussian}
Elimination",
journal = j-ACM,
volume = "26",
number = "3",
pages = "494--526",
year = "1979",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Skeel:1980:IRI,
author = "Robert D. Skeel",
title = "Iterative Refinement Implies Numerical Stability for
{Gaussian} Elimination",
journal = j-MATH-COMP,
volume = "35",
number = "151",
pages = "817--832",
year = "1980",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Skeel:1981:EER,
author = "Robert D. Skeel",
title = "Effect of Equilibration on Residual Size for Partial
Pivoting",
journal = j-SINUM,
volume = "18",
number = "3",
pages = "449--454",
year = "1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Skeel:1989:SNB,
author = "Robert D. Skeel",
title = "Safety in Numbers: {The} Boundless Errors of Numerical
Computation",
type = "Working Document",
number = "89-3",
institution = "Department of Computer Science, University of
Illinois",
address = "Urbana, IL, USA",
pages = "9",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Skeel:1993:ENC,
author = "Robert D. Skeel and Jerry B. Keiper",
title = "Elementary Numerical Computing with {Mathematica}",
publisher = pub-MH,
address = pub-MH:adr,
pages = "xiv + 434",
year = "1993",
ISBN = "0-07-057820-6",
ISBN-13 = "978-0-07-057820-3",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Blackford:1997:SUG,
author = "L. S. Blackford and J. Choi and A. Cleary and E.
D'Azevedo and J. Demmel and I. Dhillon and J. Dongarra
and S. Hammarling and G. Henry and A. Petitet and K.
Stanley and D. Walker and R. C. Whaley",
title = "{ScaLAPACK} Users' Guide",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxvi + 325",
year = "1997",
ISBN = "0-89871-397-8",
ISBN-13 = "978-0-89871-397-8",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Smale:1990:SRF,
author = "Steve Smale",
title = "Some Remarks on the Foundations of Numerical
Analysis",
journal = j-SIREV,
volume = "32",
number = "2",
pages = "211--220",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Smith:1962:ACD,
author = "Robert L. Smith",
title = "Algorithm 116: {Complex} Division",
journal = j-CACM,
volume = "5",
number = "8",
pages = "435",
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Smith:1965:ASO,
author = "Francis J. Smith",
title = "An Algorithm for Summing Orthogonal Polynomial Series
and their Derivatives with Applications to
Curve-Fitting and Interpolation",
journal = j-MATH-COMP,
volume = "19",
pages = "33--36",
year = "1965",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Smith:1975:SAP,
author = "Jon M. Smith",
title = "Scientific Analysis on the Pocket Calculator",
publisher = pub-Wiley,
address = pub-Wiley:adr,
pages = "xii + 380",
year = "1975",
ISBN = "0-471-79997-1",
ISBN-13 = "978-0-471-79997-9",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Smith:1991:AFP,
author = "David M. Smith",
title = "Algorithm 693: {A} {FORTRAN} Package for
Floating-Point Multiple-Precision Arithmetic",
journal = j-TOMS,
volume = "17",
number = "2",
pages = "273--283",
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Smith:1998:AMP,
author = "David M. Smith",
title = "Algorithm 786: {Multiple}-Precision Complex Arithmetic
and Functions",
journal = j-TOMS,
volume = "24",
number = "4",
pages = "359--367",
year = "1998",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Smoktunowicz:1995:NSC,
author = "Alicja Smoktunowicz",
title = "A Note on the Strong Componentwise Stability of
Algorithms for Solving Symmetric Linear Systems",
journal = j-DEMONSTRATIO-MATHEMATICA,
volume = "28",
number = "2",
pages = "443--448",
year = "1995",
CODEN = "DEMADO",
ISSN = "0420-1213",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Demonstratio Mathematica",
}
@Article{Smoktunowicz:1984:BCI,
author = "Alicja Smoktunowicz and Jolanta Sokolnicka",
title = "Binary Cascades Iterative Refinement in
Doubled-Mantissa Arithmetics",
journal = j-BIT,
volume = "24",
pages = "123--127",
year = "1984",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Snyder:1955:ISS,
author = "James N. Snyder",
title = "On the Improvement of the Solutions to a Set of
Simultaneous Linear Equations using the {ILLIAC}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "9",
pages = "177--184",
year = "1955",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Sorensen:1985:APP,
author = "D. C. Sorensen",
title = "Analysis of Pairwise Pivoting in {Gaussian}
Elimination",
journal = j-IEEE-C,
volume = "C-34",
pages = "274--278",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Soderstrom:1974:NPI,
author = "Torsten S{\"o}derstr{\"o}m and G. W. Stewart",
title = "On the Numerical Properties of an Iterative Method for
Computing the {Moore--Penrose} Generalized Inverse",
journal = j-SINUM,
volume = "11",
number = "1",
pages = "61--74",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Spiess:1976:UZD,
author = "J. Spie{\ss}",
title = "Untersuchungen des {Zeitgewinns} durch neue
{Algorithmen} zur {Matrix-Multiplikation}",
journal = j-COMPUTING,
volume = "17",
pages = "23--36",
year = "1976",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Stegun:1956:PC,
author = "Irene A. Stegun and Milton Abramowitz",
title = "Pitfalls in Computation",
journal = j-SIAM,
volume = "4",
number = "4",
pages = "207--219",
year = "1956",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Stoer:1980:INA,
author = "Josef Stoer and R. Bulirsch",
title = "Introduction to Numerical Analysis",
publisher = "Springer-Verlag",
address = "New York",
pages = "ix + 609",
year = "1980",
ISBN = "0-387-90420-4",
ISBN-13 = "978-0-387-90420-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Sterbenz:1974:FPC,
author = "Pat H. Sterbenz",
title = "Floating-Point Computation",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xiv + 316",
year = "1974",
ISBN = "0-13-322495-3",
ISBN-13 = "978-0-13-322495-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stewart:1971:EAA,
author = "G. W. Stewart",
title = "Error Analysis of the Algorithm for Shifting the Zeros
of a Polynomial by Synthetic Division",
journal = j-MATH-COMP,
volume = "25",
number = "113",
pages = "135--139",
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Stewart:1973:IMC,
author = "G. W. Stewart",
title = "Introduction to Matrix Computations",
publisher = pub-AP,
address = pub-AP:adr-NY,
pages = "xiii + 441",
year = "1973",
ISBN = "0-12-670350-7",
ISBN-13 = "978-0-12-670350-4",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stewart:1973:EPB,
author = "G. W. Stewart",
title = "Error and Perturbation Bounds for Subspaces Associated
with Certain Eigenvalue Problems",
journal = j-SIREV,
volume = "15",
number = "4",
pages = "727--764",
year = "1973",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stewart:1974:MPE,
author = "G. W. Stewart",
title = "Modifying Pivot Elements in {Gaussian} Elimination",
journal = j-MATH-COMP,
volume = "28",
number = "126",
pages = "537--542",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stewart:1977:PPI,
author = "G. W. Stewart",
title = "On the Perturbation of Pseudo-Inverses, Projections
and Linear Least Squares Problems",
journal = j-SIREV,
volume = "19",
number = "4",
pages = "634--662",
year = "1977",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stewart:1977:PBF,
author = "G. W. Stewart",
title = "Perturbation Bounds for the {$QR$} Factorization of a
Matrix",
journal = j-SINUM,
volume = "14",
number = "3",
pages = "509--518",
year = "1977",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Stewart:1977:RDL,
author = "G. W. Stewart",
editor = "John R. Rice",
booktitle = "Mathematical Software {III}",
title = "Research, Development, and {LINPACK}",
publisher = pub-AP # ", " # pub-AP:adr-NY,
pages = "1--14",
year = "1977",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stewart:1980:EGR,
author = "G. W. Stewart",
title = "The Efficient Generation of Random Orthogonal Matrices
With an Application to Condition Estimators",
journal = j-SINUM,
volume = "17",
number = "3",
pages = "403--409",
year = "1980",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stewart:1985:NCD,
author = "G. W. Stewart",
title = "A Note on Complex Division",
journal = j-TOMS,
volume = "11",
number = "3",
pages = "238--241",
year = "1985",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Stewart:1990:SPT,
author = "G. W. Stewart",
title = "Stochastic Perturbation Theory",
journal = j-SIREV,
volume = "32",
number = "4",
pages = "579--610",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Stewart:1992:NGS,
author = "G. W. Stewart",
title = "Note on a Generalized {Sylvester} Equation",
type = "IMA Preprint Series",
number = "\#985",
institution = inst-IMA,
address = inst-IMA:adr,
pages = "3",
month = may,
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stewart:1993:PLC,
author = "G. W. Stewart",
title = "On the Perturbation of {LU}, {Cholesky}, and {QR}
Factorizations",
journal = j-SIMAX,
volume = "14",
number = "4",
pages = "1141--1145",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stewart:1993:EHS,
author = "G. W. Stewart",
title = "On the Early History of the Singular Value
Decomposition",
journal = j-SIREV,
volume = "35",
number = "4",
pages = "551--566",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Gauss:1995:TCO,
author = "Carl Friedrich Gauss",
title = "Theory of the Combination of Observations Least
Subject to Errors. {Part} One, Part Two, Supplement",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xi + 241",
year = "1995",
ISBN = "0-89871-347-1",
ISBN-13 = "978-0-89871-347-3",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Translated from the Latin by G. W. Stewart",
}
@Article{Stewart:1995:GSG,
author = "G. W. Stewart",
title = "{Gauss}, Statistics, and {Gaussian} Elimination",
journal = j-COMPUT-GRAPH-STAT,
volume = "4",
number = "1",
pages = "1--11",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stewart:1997:PCF,
author = "G. W. Stewart",
title = "On the Perturbation of {$LU$} and {Cholesky} Factors",
journal = j-IMAJNA,
volume = "17",
number = "1",
pages = "1--6",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stewart:1997:TMG,
author = "G. W. Stewart",
title = "The Triangular Matrices of {Gaussian} Elimination and
Related Decompositions",
journal = j-IMAJNA,
volume = "17",
number = "1",
pages = "7--16",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stewart:1997:MCS,
author = "G. W. Stewart",
title = "On {Markov} Chains with Sluggish Transients",
journal = "Communication in Statistics, Stochastic Models",
volume = "13",
pages = "85--95",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stewart:1998:AM,
author = "G. W. Stewart",
title = "On the Adjugate Matrix",
journal = j-LAA,
volume = "283",
pages = "151--164",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stewart:1997:CFS,
author = "Michael Stewart",
title = "{Cholesky} Factorization of Semidefinite {Toeplitz}
Matrices",
journal = j-LAA,
volume = "254",
pages = "497--525",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Stewart:2001:MAV,
author = "G. W. Stewart",
title = "Matrix Algorithms. {Volume II}: Eigensystems",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xix + 469",
year = "2001",
ISBN = "0-89871-503-2",
ISBN-13 = "978-0-89871-503-3",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Starke:1991:S,
author = "Gerhard Starke and Wilhelm Niethammer",
title = "{SOR} for {$AX-XB=C$}",
journal = j-LAA,
volume = "154--156",
pages = "355--375",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Stoer:1972:ENM,
author = "Josef Stoer",
title = "Einf{\"u}hrung in die Numerische Mathematik {I}",
publisher = pub-Springer,
address = pub-Springer:adr-B,
pages = "ix + 250",
year = "1972",
ISBN = "0-387-05750-1",
ISBN-13 = "978-0-387-05750-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stone:1962:BPR,
author = "Betty Jane Stone",
title = "Best Possible Ratios of Certain Matrix Norms",
journal = j-NUM-MATH,
volume = "4",
pages = "114--116",
year = "1962",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Stoutemyer:1977:AEA,
author = "David R. Stoutemyer",
title = "Automatic Error Analysis Using Computer Algebraic
Manipulation",
journal = j-TOMS,
volume = "3",
number = "1",
pages = "26--43",
year = "1977",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Stoutemyer:1991:CMC,
author = "David R. Stoutemyer",
title = "Crimes and Misdemeanours in the Computer Algebra
Trade",
journal = j-NAMS,
volume = "38",
number = "7",
pages = "778--785",
year = "1991",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
}
@Article{Strassen:1969:GEO,
author = "V. Strassen",
title = "Gaussian Elimination is Not Optimal",
journal = j-NUM-MATH,
volume = "13",
pages = "354--356",
year = "1969",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Strang:1986:PTM,
author = "Gilbert Strang",
title = "A Proposal for {Toeplitz} Matrix Calculations",
journal = j-STUDIES-APPL-MATH,
volume = "74",
pages = "171--176",
year = "1986",
CODEN = "SAPMB6",
ISSN = "0022-2526 (print), 1467-9590 (electronic)",
ISSN-L = "0022-2526",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Studies in Applied Mathematics",
}
@Book{Strang:1993:ILA,
author = "Gilbert Strang",
title = "Introduction to Linear Algebra",
publisher = pub-Wellesley,
address = pub-Wellesley:adr,
pages = "viii + 472",
year = "1993",
ISBN = "0-9614088-5-5",
ISBN-13 = "978-0-9614088-5-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Stewart:1990:MPT,
author = "Gilbert Wright (Gilbert W.) Stewart and {Ji-guang}
Sun",
title = "Matrix Perturbation Theory",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xv + 365",
year = "1990",
ISBN = "0-12-670230-6 (hardcover)",
ISBN-13 = "978-0-12-670230-9 (hardcover)",
LCCN = "QA871 .S775 1990",
bibdate = "Thu May 29 07:15:52 MDT 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/numana1990.bib;
z3950.loc.gov:7090/Voyager",
series = "Computer science and scientific computing",
URL = "http://catalog.hathitrust.org/api/volumes/oclc/21227976.html;
http://www.loc.gov/catdir/description/els032/90033378.htm;
http://www.loc.gov/catdir/description/els032/90033378.html;
http://www.loc.gov/catdir/toc/els031/90033378.htm;
http://www.loc.gov/catdir/toc/els031/90033378.html",
acknowledgement = ack-nhfb,
GWS-number = "B3",
subject = "Perturbation (Mathematics); Matrices",
tableofcontents = "I. Preliminaries \\
1. Notation \\
2. The $QR$ decomposition \\
projections \\
3. Eigenvalues and eigenvectors \\
4. The singular value decomposition \\
II. Norms and metrics \\
1. Vector norms \\
2. Matrix norms \\
3. Unitarily invariant norms \\
4. Metrics on subspaces of C'n' \\
III. Linear systems and least squares problems \\
1. The pseudo-inverse and least squares \\
2. Inverses and linear systems \\
3. The pseudo-inverse \\
4. Projections \\
5. The Linear least squares problem \\
IV. The perturbation of Eigenvalues \\
1. General perturbation theorems \\
2. Gerschgorin theory: differentiability \\
3. Normal and diagonalizable matrices \\
4. Hermitian matrices \\
5. Some further results \\
V. Invariant subspaces \\
1. The theory of simple invariant subspaces \\
2. Perturbation of invariant subspaces \\
3. Hermitian matrices \\
4. The singular value decomposition \\
VI. Generalized Eigenvalue problems \\
1. Background \\
2. Regular matrix pairs \\
3. Definite matrix pairs \\
References \\
Notation \\
Index",
}
@Article{Stummel:1980:REA,
author = "F. Stummel",
title = "Rounding Error Analysis of Elementary Numerical
Algorithms",
journal = j-COMPUTING,
volume = "Suppl. 2",
pages = "169--195",
year = "1980",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Stummel:1981:PTE,
author = "F. Stummel",
title = "Perturbation Theory For Evaluation Algorithms of
Arithmetic Expressions",
journal = j-MATH-COMP,
volume = "37",
number = "156",
pages = "435--473",
year = "1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stummel:1982:OEE,
author = "F. Stummel",
title = "Optimal Error Estimates For {Gaussian} Elimination in
Floating-Point Arithmetic",
journal = j-ZAMM,
volume = "62",
pages = "T355--T357",
year = "1982",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Stummel:1985:FEAa,
author = "Friedrich Stummel",
title = "Forward Error Analysis of {Gaussian} Elimination,
{Part I}: {Error} and Residual Estimates",
journal = j-NUM-MATH,
volume = "46",
pages = "365--395",
year = "1985",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Stummel:1985:FEAb,
author = "Friedrich Stummel",
title = "Forward Error Analysis of {Gaussian} Elimination,
{Part II}: {Stability} Theorems",
journal = j-NUM-MATH,
volume = "46",
pages = "397--415",
year = "1985",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Stummel:1985:SOE,
author = "F. Stummel",
title = "Strict Optimal Error Estimates for {Gaussian}
Elimination",
journal = j-ZAMM,
volume = "65",
pages = "T405--T407",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Steele:1990:HPF,
author = "Guy L. {Steele, Jr.} and Jon L. White",
title = "How to Print Floating-Point Numbers Accurately",
journal = j-SIGPLAN,
volume = "25",
number = "6",
pages = "112--126",
year = "1990",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Stoer:1962:TDM,
author = "Josef Stoer and C. Witzgall",
title = "Transformations by Diagonal Matrices in a Normed
Space",
journal = j-NUM-MATH,
volume = "4",
pages = "158--171",
year = "1962",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Sun:1995:BKR,
author = "Xiaobai Sun and Christian H. Bischof",
title = "A Basis-Kernel Representation of Orthogonal Matrices",
journal = j-SIMAX,
volume = "16",
number = "4",
pages = "1184--1196",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Sun:1991:PBC,
author = "{Ji-guang} Sun",
title = "Perturbation Bounds for the {Cholesky} and {$QR$}
Factorizations",
journal = j-BIT,
volume = "31",
pages = "341--352",
year = "1991",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Sun:1992:REP,
author = "{Ji-guang} Sun",
title = "Rounding-Error and Perturbation Bounds for the
{Cholesky} and {$LDL^T$} Factorizations",
journal = j-LAA,
volume = "173",
pages = "77--97",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Sun:1992:CPB,
author = "{Ji-guang} Sun",
title = "Componentwise Perturbation Bounds for Some Matrix
Decompositions",
journal = j-BIT,
volume = "32",
number = "4",
pages = "702--714",
year = "1992",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Sun:1995:NBP,
author = "{Ji-guang} Sun",
title = "A Note on Backward Perturbations for the {Hermitian}
Eigenvalue Problem",
journal = j-BIT,
volume = "35",
pages = "385--393",
year = "1995",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Sun:1995:PBQ,
author = "{Ji-guang} Sun",
title = "On Perturbation Bounds for the {QR} Factorization",
journal = j-LAA,
volume = "215",
pages = "95--111",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Sun:1996:OBP,
author = "{Ji-guang} Sun",
title = "Optimal Backward Perturbation Bounds for the Linear
Least-Squares Problem with Multiple Right-Hand Sides",
journal = j-IMAJNA,
volume = "16",
number = "1",
pages = "1--11",
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Sun:1997:OBPa,
author = "{Ji-guang} Sun",
title = "On Optimal Backward Perturbation Bounds for the Linear
Least Squares Problem",
journal = j-BIT,
volume = "37",
number = "1",
pages = "179--188",
year = "1997",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Sun:1998:BSB,
author = "{Ji-guang} Sun",
title = "Bounds for the Structured Backward Errors of
{Vandermonde} Systems",
journal = j-SIMAX,
volume = "20",
number = "1",
pages = "45--59",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{sunM92,
key = "Sun",
title = "{SPARCompiler FORTRAN}: {Numerical} Computation
Guide",
publisher = "Sun Microsystems, Inc.",
address = "Mountain View, CA, USA",
month = oct,
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Part No. 800-7097-11, Revision A",
}
@Book{sunM92a,
key = "Sun",
title = "{SPARCompiler FORTRAN} \textup{2.0.1}: {User's}
Guide",
publisher = "Sun Microsystems, Inc.",
address = "Mountain View, CA, USA",
month = oct,
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Part No. 800-6552-11, Revision A",
}
@Article{Sun:1997:OBPb,
author = "{Ji-guang} Sun and Zheng Sun",
title = "Optimal Backward Perturbation Bounds for
Underdetermined Systems",
journal = j-SIMAX,
volume = "18",
number = "2",
pages = "393--402",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Sleijpen:2000:DER,
author = "Gerard L. G. Sleijpen and Henk A. van der Vorst and
Jan Modersitzki",
title = "Differences in the Effects of Rounding Errors in
{Krylov} Solvers for Symmetric Indefinite Linear
Systems",
journal = j-SIMAX,
volume = "22",
number = "3",
pages = "726--751",
year = "2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Swartzlander:1975:SLN,
author = "Earl E. {Swartzlander, Jr.} and Aristides G.
Alexopolous",
title = "The Sign/Logarithm Number System",
journal = j-IEEE-C,
volume = "C-24",
number = "12",
pages = "1238--1242",
year = "1975",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Swann:1972:DSM,
author = "W. H. Swann",
editor = "W. Murray",
booktitle = "Numerical Methods for Unconstrained Optimization",
title = "Direct Search Methods",
publisher = pub-AP # ", " # pub-AP:adr-L,
pages = "13--28",
year = "1972",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Swann:1974:COD,
author = "W. H. Swann",
editor = "P. E. Gill and W. Murray",
booktitle = "Numerical Methods for Constrained Optimization",
title = "Constrained Optimization by Direct Search",
publisher = pub-AP # ", " # pub-AP:adr-L,
pages = "191--217",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Swartzlander:1980:CA,
editor = "Earl E. {Swartzlander, Jr.}",
title = "Computer Arithmetic",
volume = "21",
publisher = "Dowden, Hutchinson and Ross",
address = "Stroudsburg, PA, USA",
year = "1980",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Benchmark Papers in Electrical Engineering and
Computer Science",
}
@Article{Sweeney:1965:AFP,
author = "D. W. Sweeney",
title = "An Analysis of Floating-Point Addition",
journal = j-IBM-SYS-J,
volume = "4",
pages = "31--42",
year = "1965",
CODEN = "IBMSA7",
ISSN = "0018-8670",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted in
\cite[pp.~317--328]{Swartzlander:1980:CA}",
fjournal = "IBM Systems Journal",
}
@Book{sylv04,
key = "Sylvester, James Joseph",
title = "The Collected Mathematical Papers of James Joseph
Sylvester",
volume = "1 (1837--1853)",
publisher = pub-CUP,
pages = "xii + 650",
year = "1904",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Sylvester:1850:AAN,
author = "J. J. Sylvester",
title = "Additions to the Articles, ``{On a New Class of
Theorems},'' and ``{On Pascal's Theorem}''",
journal = j-PHIL-MAGAZINE,
volume = "37",
pages = "363--370",
year = "1850",
CODEN = "PHMAA4",
ISSN = "0031-8086",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted in \cite[pp.~1451--151]{sylv04}",
}
@Article{Sylvester:1851:RBM,
author = "J. J. Sylvester",
title = "On the Relation Between the Minor Determinants of
Linearly Equivalent Quadratic Functions",
journal = j-PHIL-MAGAZINE,
volume = "(Fourth Series) 1",
pages = "295--305",
year = "1851",
CODEN = "PHMAA4",
ISSN = "0031-8086",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted in \cite[pp.~241--250]{sylv04}",
}
@Article{Sylvester:1884:EM,
author = "J. J. Sylvester",
title = "Sur l'Equation en Matrices {$px=xq$}",
journal = j-C-R-ACAD-SCI,
pages = "67--71 and 115--116",
year = "1884",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Comptes Rendus de l'Acad{\'e}mie des Sciences",
}
@Article{Tang:1981:BDV,
author = "W. P. Tang and G. H. Golub",
title = "The Block Decomposition of a {Vandermonde} Matrix and
its Applications",
journal = j-BIT,
volume = "21",
pages = "505--517",
year = "1981",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@InCollection{Taussky:1962:EFM,
author = "Olga Taussky and Marvin Marcus",
editor = "John Todd",
booktitle = "Survey of Numerical Analysis",
title = "Eigenvalues of Finite Matrices",
publisher = pub-MH,
address = pub-MH:adr,
pages = "279--313",
year = "1962",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Tang:1989:TDI,
author = "Ping Tak Peter Tang",
title = "Table-Driven Implementation of the Exponential
Function in {IEEE} Floating-Point Arithmetic",
journal = j-TOMS,
volume = "15",
number = "2",
pages = "144--157",
year = "1989",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Tang:1990:AET,
author = "Ping Tak Peter Tang",
title = "Accurate and Efficient Testing of the Exponential and
Logarithm Functions",
journal = j-TOMS,
volume = "16",
number = "3",
pages = "185--200",
year = "1990",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Tang:1990:TDI,
author = "Ping Tak Peter Tang",
title = "Table-Driven Implementation of the Logarithm Function
in {IEEE} Floating-Point Arithmetic",
journal = j-TOMS,
volume = "16",
number = "3",
pages = "378--400",
year = "1990",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@InProceedings{Tang:1991:TLA,
author = "Ping Tak Peter Tang",
editor = "Peter Kornerup and David W. Matula",
booktitle = "Proc. 10th IEEE Symposium on Computer Arithmetic",
title = "Table-Lookup Algorithms for Elementary Functions and
Their Error Analysis",
publisher = "IEEE Computer Society Press, Los Alamitos, CA, USA",
pages = "232--236",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Tang:1992:TDI,
author = "Ping Tak Peter Tang",
title = "Table-Driven Implementation of the Expm1 Function in
{IEEE} Floating-Point Arithmetic",
journal = j-TOMS,
volume = "18",
number = "2",
pages = "211--222",
year = "1992",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Book{Taub:1963:JNC,
editor = "A. H. Taub",
title = "{John von Neumann} Collected Works",
volume = "V, {Design of Computers, Theory of Automata and
Numerical Analysis}",
publisher = "Pergamon",
address = "Oxford",
pages = "ix + 784",
year = "1963",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Taussky:1949:RCC,
author = "Olga Taussky",
title = "A Remark Concerning the Characteristic Roots of the
Finite Segments of the {Hilbert} Matrix",
journal = j-QUART-J-MATH,
volume = "20",
pages = "80--83",
year = "1949",
CODEN = "QJMAAT",
ISSN = "0033-5606 (print), 1464-3847 (electronic)",
ISSN-L = "0033-5606",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Quarterly Journal of Mathematics",
}
@Article{Taussky:1988:HBT,
author = "Olga Taussky",
title = "How {I} Became a Torchbearer for Matrix Theory",
journal = j-AMM,
volume = "95",
number = "9",
pages = "801--812",
month = nov,
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Tasche:2001:WAC,
author = "Manfred Tasche and Hansmartin Zeuner",
title = "Worst and Average Case Roundoff Error Analysis for
{FFT}",
journal = j-BIT,
volume = "41",
number = "3",
pages = "563--581",
year = "2001",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Book{Barrett:1994:TSL,
author = "Richard Barrett and Michael Berry and Tony F. Chan and
James Demmel and June Donato and Jack Dongarra and
Victor Eijkhout and Roldan Pozo and Charles Romine and
Henk van der Vorst",
title = "Templates for the Solution of Linear Systems:
{Building} Blocks for Iterative Methods",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xiii + 112",
year = "1994",
ISBN = "0-89871-328-5",
ISBN-13 = "978-0-89871-328-2",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Thacher:1961:ACP,
author = "Henry C. {Thacher, Jr.}",
title = "Algorithm 43: {Crout} With Pivoting {II}",
journal = j-CACM,
volume = "4",
number = "4",
pages = "176--177",
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Book{Thisted:1988:ESC,
author = "Ronald A. Thisted",
title = "Elements of Statistical Computing: {Numerical}
Computation",
publisher = "Chapman and Hall",
address = "New York",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Thompson:1942:GFC,
author = "D'Arcy Wentworth Thompson",
title = "On Growth and Form. {The} Complete Revised Edition",
publisher = pub-CUP,
pages = "viii + 1116",
year = "1942",
ISBN = "0-486-67135-6",
ISBN-13 = "978-0-486-67135-2",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted by Dover, New York, 1992",
}
@Article{Tienari:1970:SMR,
author = "Martti Tienari",
title = "A Statistical Model of Roundoff Error for Varying
Length Floating-Point Arithmetic",
journal = j-BIT,
volume = "10",
pages = "355--365",
year = "1970",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Tisseur:2001:QEP,
author = "Fran\c{c}oise Tisseur and Karl Meerbergen",
title = "The Quadratic Eigenvalue Problem",
journal = j-SIREV,
volume = "43",
number = "2",
pages = "235--286",
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Tisseur:2001:NMF,
author = "Fran\c{c}oise Tisseur",
title = "Newton's Method in Floating Point Arithmetic and
Iterative Refinement of Generalized Eigenvalue
Problems",
journal = j-SIMAX,
volume = "22",
number = "4",
pages = "1038--1057",
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InCollection{Todd:1954:CFS,
author = "John Todd",
editor = "Olga Taussky",
booktitle = "Contributions to the Solution of Systems of Linear
Equations and the Determination of Eigenvalues",
title = "The Condition of the Finite Segments of the {Hilbert}
Matrix",
number = "39",
publisher = "National Bureau of Standards, United States Department
of Commerce",
address = "Washington, D. C.",
pages = "109--116",
year = "1954",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Applied Mathematics Series",
}
@Article{Todd:1961:CPC,
author = "John Todd",
title = "Computational Problems Concerning the {Hilbert}
Matrix",
journal = j-J-RES-NATL-BUR-STAND-B,
volume = "65",
number = "1",
pages = "19--22",
year = "1961",
CODEN = "JNBBAU",
ISSN = "0022-4340",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Journal of Research of the National Bureau of Standards. Section B, Mathematics and Mathematical Physics",
journal-URL = "http://www.nist.gov/nvl/jrespastpapers.cfm",
}
@InProceedings{Todd:1968:CN,
author = "J. Todd",
booktitle = "Programmation en Math{\'e}matiques Num{\'e}riques,
Besan{\c{c}}on, 1966",
title = "On Condition Numbers",
volume = "7 (no. 165)",
pages = "141--159",
year = "1968",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "{\'E}ditions Centre Nat. Recherche Sci., Paris",
}
@Book{Todd:1977:BNM,
author = "John Todd",
title = "Basic Numerical Mathematics, Vol.~2: Numerical
Algebra",
publisher = "Birkh{\"a}user, Basel, and Academic Press, New York",
year = "1977",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Toledo:1997:LRL,
author = "Sivan Toledo",
title = "Locality of Reference in {LU} Decomposition with
Partial Pivoting",
journal = j-SIMAX,
volume = "18",
number = "4",
pages = "1065--1081",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@PhdThesis{Torczon:1989:MDS,
author = "Virginia J. Torczon",
title = "Multi-Directional Search: {A} Direct Search Algorithm
for Parallel Machines",
school = "Rice University",
address = "Houston, TX, USA",
pages = "vii + 85",
month = may,
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Torczon:1991:CMS,
author = "Virginia J. Torczon",
title = "On the Convergence of the Multidirectional Search
Algorithm",
journal = j-SIOPT,
volume = "1",
number = "1",
pages = "123--145",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Torczon:1997:CPS,
author = "Virginia J. Torczon",
title = "On the Convergence of Pattern Search Algorithms",
journal = j-SIOPT,
volume = "7",
number = "1",
pages = "1--25",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Tornheim:1965:MTP,
author = "L. Tornheim",
title = "Maximum Third Pivot for {Gaussian} Reduction",
type = "Technical Report",
institution = "Calif. Research Corp.",
address = "Richmond, CA",
year = "1965",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Cited in \cite{Cryer:1968:PSG}",
}
@Article{Toh:1994:PPP,
author = "Kim-Chuan Toh and Lloyd N. Trefethen",
title = "Pseudozeros of Polynomials and Pseudospectra of
Companion Matrices",
journal = j-NUM-MATH,
volume = "68",
number = "3",
pages = "403--425",
year = "1994",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Traub:1966:APU,
author = "J. F. Traub",
title = "Associated Polynomials and Uniform Methods for the
Solution of Linear Problems",
journal = j-SIREV,
volume = "8",
number = "3",
pages = "277--301",
year = "1966",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Trefethen:1997:NLA,
author = "Lloyd N. Trefethen and David {Bau III}",
title = "Numerical Linear Algebra",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xii + 361",
year = "1997",
ISBN = "0-89871-361-7",
ISBN-13 = "978-0-89871-361-9",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Trefethen:1985:TMG,
author = "Lloyd N. Trefethen",
title = "Three Mysteries of {Gaussian} Elimination",
journal = j-SIGNUM,
volume = "20",
pages = "2--5",
year = "1985",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
}
@InProceedings{Trefethen:1990:ATN,
author = "Lloyd N. Trefethen",
editor = "J. C. Mason and M. G. Cox",
booktitle = "Algorithms for Approximation II",
title = "Approximation Theory and Numerical Linear Algebra",
publisher = pub-CH # ", " # pub-CH:adr-L,
pages = "336--360",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Trefethen:1992:PM,
author = "Lloyd N. Trefethen",
editor = "D. F. Griffiths and G. A. Watson",
booktitle = "Numerical Analysis \textup{1991}, Proceedings of the
\textup{14}th Dundee Conference",
title = "Pseudospectra of Matrices",
volume = "260",
publisher = pub-Longman-ST # ", " # pub-Longman-ST:adr,
pages = "234--266",
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Pitman Research Notes in Mathematics",
}
@Article{Trefethen:1992:DNA,
author = "Lloyd N. Trefethen",
title = "The Definition of Numerical Analysis",
journal = j-SIAM-NEWS,
volume = "25",
pages = "6 and 22",
month = nov,
year = "1992",
ISSN = "0036-1437",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@InProceedings{Trefethen:1999:SP,
author = "Lloyd N. Trefethen",
editor = "Mark Ainsworth and Jeremy Levesley and Marco
Marletta",
booktitle = "The Graduate Student's Guide to Numerical Analysis
'98",
title = "Spectra and Pseudospectra",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
pages = "217--250",
year = "1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Tropp:1984:FA,
author = "Henry S. Tropp",
title = "{FORTRAN} Anecdotes",
journal = j-AHC,
volume = "6",
number = "1",
pages = "59--64",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Tropp:1984:OTE,
author = "Henry S. Tropp",
title = "Origin of the Term {\emph{Bit}}",
journal = j-AHC,
volume = "6",
number = "2",
pages = "152--155",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Trefethen:1990:ACS,
author = "Lloyd N. Trefethen and Robert S. Schreiber",
title = "Average-Case Stability of {Gaussian} Elimination",
journal = j-SIMAX,
volume = "11",
number = "3",
pages = "335--360",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Trefethen:1987:IPS,
author = "Lloyd N. Trefethen and Manfred R. Trummer",
title = "An Instability Phenomenon in Spectral Methods",
journal = j-SINUM,
volume = "24",
number = "5",
pages = "1008--1023",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Tsao:1975:NIH,
author = "{Nai-kuan} Tsao",
title = "A Note on Implementing the {Householder}
Transformation",
journal = j-SINUM,
volume = "12",
number = "1",
pages = "53--58",
year = "1975",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Tsao:1983:SAE,
author = "{Nai-kuan} Tsao",
title = "A Simple Approach to the Error Analysis of
Division-Free Numerical Algorithms",
journal = j-IEEE-C,
volume = "C-32",
number = "4",
pages = "343--351",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Turnbull:1932:ITC,
author = "H. W. Turnbull and A. C. Aitken",
title = "An Introduction to the Theory of Canonical Matrices",
publisher = "Blackie, London and Glasgow",
pages = "xiii + 200",
year = "1932",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted with appendix, 1952",
}
@Article{Tucker:2002:ROS,
author = "Warwick Tucker",
title = "A Rigorous {ODE} Solver and {Smale's} 14th Problem",
journal = j-FOCM,
volume = "2",
number = "1",
pages = "53--117",
year = "2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Turing:1936:CNA,
author = "A. M. Turing",
title = "On Computable Numbers, with an Application to the
{Entscheidungsproblem}",
journal = j-PROC-LONDON-MATH-SOC-3,
volume = "42",
pages = "230--265",
year = "1936",
CODEN = "PLMTAL",
ISSN = "0024-6115 (print), 1460-244x (electronic)",
ISSN-L = "0024-6115",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Proceedings of the London Mathematical Society. Third Series",
}
@TechReport{Turing:1945:PDM,
author = "A. M. Turing",
title = "Proposal for Development in the {Mathematics Division}
of an {Automatic Computing Engine} {(ACE)}",
type = "{Report E.882, Executive Committee}",
institution = inst-NPL,
address = inst-NPL:adr,
year = "1945",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted in \cite[pp.~20-105]{Carpenter:1986:MTA} and
\cite[pp.~1--86]{Ince:1992:CWM}",
}
@Article{Turing:1948:REM,
author = "A. M. Turing",
title = "Rounding-Off Errors in Matrix Processes",
journal = j-QJMAM,
volume = "1",
pages = "287--308",
year = "1948",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted in \cite{Britton:1992:CWM} with summary and
notes (including corrections)",
}
@Book{Turnbull:1929:TDM,
author = "H. W. Turnbull",
title = "The Theory of Determinants, Matrices, and Invariants",
publisher = "Blackie",
address = "London and Glasgow",
pages = "xvi + 338",
year = "1929",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Turner:1982:DLS,
author = "Peter R. Turner",
title = "The Distribution of Leading Significant Digits",
journal = j-IMAJNA,
volume = "2",
pages = "407--412",
year = "1982",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Turner:1984:FRD,
author = "Peter R. Turner",
title = "Further Revelations on {L.S.D.}",
journal = j-IMAJNA,
volume = "4",
pages = "225--231",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Turner:1991:WRR,
author = "Peter R. Turner",
title = "Will the ``Real'' Real Arithmetic Please Stand Up?",
journal = j-NAMS,
volume = "38",
number = "4",
pages = "298--304",
year = "1991",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
}
@Article{Tyrtyshnikov:1991:CTM,
author = "Evgenij E. Tyrtyshnikov",
title = "Cauchy-{Toeplitz} Matrices and Some Applications",
journal = j-LAA,
volume = "149",
pages = "1--18",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Urabe:1968:RED,
author = "Minoru Urabe",
title = "Roundoff Error Distribution in Fixed-Point
Multiplication and a Remark About the Rounding Rule",
journal = j-SINUM,
volume = "5",
number = "2",
pages = "202--210",
year = "1968",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Uspensky:1948:TE,
author = "J. V. Uspensky",
title = "Theory of Equations",
publisher = pub-MH,
address = pub-MH:adr,
pages = "vii + 353",
year = "1948",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Vanderbei:1995:SQD,
author = "Robert J. Vanderbei",
title = "Symmetric Quasi-Definite Matrices",
journal = j-SIOPT,
volume = "5",
number = "1",
pages = "100--113",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Loan:1979:NEM,
author = "Charles F. {Van Loan}",
title = "A Note on the Evaluation of Matrix Polynomials",
journal = j-IEEE-AC,
volume = "AC-24",
number = "2",
pages = "320--321",
year = "1979",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Loan:1985:MWE,
author = "Charles F. {Van Loan}",
title = "On the Method of Weighting for Equality-Constrained
Least-Squares Problems",
journal = j-SINUM,
volume = "22",
number = "5",
pages = "851--864",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Loan:1987:ECE,
author = "Charles F. {Van Loan}",
title = "On Estimating the Condition of Eigenvalues and
Eigenvectors",
journal = j-LAA,
volume = "88/89",
pages = "715--732",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Loan:1992:CFF,
author = "Charles F. {Van Loan}",
title = "Computational Frameworks for the {Fast Fourier
Transform}",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xiii + 273",
year = "1992",
DOI = "https://doi.org/10.1137/1.9781611970999",
ISBN = "0-89871-285-8 (paperback), 1-61197-099-7 (e-book)",
ISBN-13 = "978-0-89871-285-8 (paperback), 978-1-61197-099-9
(e-book)",
LCCN = "QA403.5 .V35 1992",
bibdate = "Mon Oct 26 07:31:14 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
http://www.math.utah.edu/pub/tex/bib/matlab.bib",
acknowledgement = ack-nhfb,
series = "Frontiers in applied mathematics",
subject = "Fourier transformations",
tableofcontents = "1: The Radix-2 Frameworks: Matrix Notation and
Algorithms \\
The FFT Idea \\
The Cooley--Tukey Factorization \\
Weight and Butterfly Computations \\
Bit Reversal and Transposition \\
The Cooley--Tukey Framework \\
The Stockham Autosort Frameworks \\
The Pease Framework \\
Decimation in Frequency and Inverse FFTs \\
2: General Radix Frameworks: The General Radix Ideas
\\
Index Reversal and Transposition \\
Mixed-Radix Factorizations \\
Radix-4 and Radix-8 Frameworks \\
The Split-Radix Frameworks \\
3: High Performance Frameworks: The Multiple DFT
Problem \\
Matrix Transposition \\
The Large Single-Vector FFT Problem \\
Multi-Dimensional FFT Problem \\
Distributed Memory FFTs \\
Shared Memory FFTs \\
4: Selected Topics: Prime Factor FFTs \\
Convolution \\
FFTs of Real Data \\
Cosine and Sine Transforms \\
Fast Poisson Solvers \\
Bibliography \\
Index",
}
@Book{Rienen:2001:NMC,
author = "Ursula van Rienen",
title = "Numerical Methods in Computational Electrodynamics:
{Linear} Systems in Practical Applications",
number = "12",
publisher = pub-Springer,
address = pub-Springer:adr-B,
pages = "xiii + 375",
year = "2001",
ISBN = "3-540-67629-5",
ISBN-13 = "978-3-540-67629-4",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Lecture Notes in Computational Science and
Engineering",
}
@Article{Varah:1972:SBT,
author = "J. M. Varah",
title = "On the Solution of Block-Tridiagonal Systems Arising
From Certain Finite-Difference Equations",
journal = j-MATH-COMP,
volume = "26",
number = "120",
pages = "859--868",
year = "1972",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Varah:1975:LBS,
author = "J. M. Varah",
title = "A Lower Bound for the Smallest Singular Value of a
Matrix",
journal = j-LAA,
volume = "11",
pages = "3--5",
year = "1975",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Varah:1979:STM,
author = "J. M. Varah",
title = "On the Separation of Two Matrices",
journal = j-SINUM,
volume = "16",
number = "2",
pages = "216--222",
year = "1979",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Varga:1976:DDA,
author = "Richard S. Varga",
title = "On Diagonal Dominance Arguments for Bounding
{$\|A^{-1}\|_\infty$}",
journal = j-LAA,
volume = "14",
pages = "211--217",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Varga:1990:SCM,
author = "Richard S. Varga",
title = "Scientific Computation on Mathematical Problems and
Conjectures",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "vi + 122",
year = "1990",
ISBN = "0-89871-257-2",
ISBN-13 = "978-0-89871-257-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Vavasis:1989:GEP,
author = "S. A. Vavasis",
title = "Gaussian Elimination with Partial Pivoting is
{P}-Complete",
journal = j-SIAM-J-DISCR-MATH,
volume = "2",
pages = "413--423",
year = "1989",
CODEN = "SJDMEC",
ISSN = "0895-4801 (print), 1095-7146 (electronic)",
ISSN-L = "0895-4801",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "SIAM Journal on Discrete Mathematics",
journal-URL = "http://epubs.siam.org/sidma",
}
@Article{Verdonk:2001:PRIa,
author = "Brigitte Verdonk and Annie Cuyt and Dennis
Verschaeren",
title = "A Precision and Range Independent Tool for Testing
Floating-Point Arithmetic {I}: {Basic} Operations,
Square Root and Remainder",
journal = j-TOMS,
volume = "27",
number = "1",
pages = "92--118",
year = "2001",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Verdonk:2001:PRIb,
author = "Brigitte Verdonk and Annie Cuyt and Dennis
Verschaeren",
title = "A Precision and Range Independent Tool for Testing
Floating-Point Arithmetic {II}: {Conversions}",
journal = j-TOMS,
volume = "27",
number = "1",
pages = "119--140",
year = "2001",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Sluis:1969:CNE,
author = "A. van der Sluis",
title = "Condition Numbers and Equilibration of Matrices",
journal = j-NUM-MATH,
volume = "14",
pages = "14--23",
year = "1969",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Sluis:1970:CEP,
author = "A. van der Sluis",
title = "Condition, Equilibration and Pivoting in Linear
Algebraic Systems",
journal = j-NUM-MATH,
volume = "15",
pages = "74--86",
year = "1970",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Sluis:1975:SSL,
author = "A. van der Sluis",
title = "Stability of the Solutions of Linear Least Squares
Problems",
journal = j-NUM-MATH,
volume = "23",
pages = "241--254",
year = "1975",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{vanVeldhuizen:1977:NPP,
author = "M. {van Veldhuizen}",
title = "A Note on Partial Pivoting and {Gaussian}
Elimination",
journal = j-NUM-MATH,
volume = "29",
pages = "1--10",
year = "1977",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Verzuh:1949:SSL,
author = "Frank M. Verzuh",
title = "The Solution of Simultaneous Linear Equations with the
Aid of the 602 Calculating Punch",
journal = j-MTAC,
volume = "3",
pages = "453--462",
year = "1949",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Vignes:1986:ESM,
author = "J. Vignes and R. Alt",
editor = "Willard L. Miranker and Richard A. Toupin",
booktitle = "Accurate Scientific Computations, Proceedings, 1985",
title = "An Efficient Stochastic Method for Round-Off Error
Analysis",
volume = "235",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
pages = "183--205",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Lecture Notes in Computer Science",
}
@InProceedings{Vitasek:1969:NSS,
author = "Emil Vitasek",
editor = "J. Ll. Morris",
booktitle = "Conference on the Numerical Solution of Differential
Equations",
title = "The Numerical Stability in Solution of Differential
Equations",
volume = "109",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
pages = "87--111",
year = "1969",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Lecture Notes in Mathematics",
}
@Article{Vitenko:1968:OAA,
author = "I. V. Viten'ko",
title = "Optimum Algorithms for Adding and Multiplying on
Computers with a Floating Point",
journal = j-USSR-COMP-MATH-MATH-PHYS,
volume = "8",
number = "5",
pages = "183--195",
year = "1968",
CODEN = "CMMPA9",
ISSN = "0041-5553, 0502-9902",
ISSN-L = "0041-5553",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "U.S.S.R. Computational Mathematics and Mathematical Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00415553",
}
@Article{Viswanath:1998:CNR,
author = "D. Viswanath and L. N. Trefethen",
title = "Condition Numbers of Random Triangular Matrices",
journal = j-SIMAX,
volume = "19",
number = "2",
pages = "564--581",
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Neumann:1947:NIM,
author = "John von Neumann and Herman H. Goldstine",
title = "Numerical Inverting of Matrices of High Order",
journal = j-BAMS,
volume = "53",
pages = "1021--1099",
year = "1947",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted in \cite[pp.~479--557]{Taub:1963:JNC}",
}
@InProceedings{vanderVorst:1990:CBP,
author = "H. A. van der Vorst",
editor = "Owe Axelsson and {Lily Yu.} Kolotilina",
booktitle = "Preconditioned Conjugate Gradient Methods",
title = "The Convergence Behaviour of Preconditioned {CG} and
{CG-S} in the Presence of Rounding Errors",
volume = "1457",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
pages = "126--136",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Lecture Notes in Mathematics",
}
@Article{Wachpress:1988:ISL,
author = "Eugene L. Wachpress",
title = "Iterative Solution of the {Lyapunov} Matrix Equation",
journal = j-APPL-MATH-LETT,
volume = "1",
number = "1",
pages = "87--90",
year = "1988",
CODEN = "AMLEEL",
ISSN = "0893-9659 (print), 1873-5452 (electronic)",
ISSN-L = "0893-9659",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Applied Mathematics Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/08939659",
}
@Book{Wallis:1990:IFP,
editor = "Peter J. L. Wallis",
title = "Improving Floating-Point Programming",
publisher = "Wiley",
address = "London",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Wallis:1993:HM,
author = "W. D. Wallis",
editor = "Richard A. Brualdi and Shmuel Friedland and Victor
Klee",
booktitle = "Combinatorial and Graph-Theoretical Problems in Linear
Algebra",
title = "Hadamard Matrices",
volume = "50",
publisher = pub-Springer # ", " # pub-Springer:adr-NY,
pages = "235--243",
year = "1993",
ISBN = "0-387-94086-3",
ISBN-13 = "978-0-387-94086-1",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "IMA Volumes in Mathematics and Its Applications",
}
@Article{Ward:1976:QAH,
author = "Robert C. Ward",
title = "The {QR} Algorithm and {Hyman's} Method on Vector
Computers",
journal = j-MATH-COMP,
volume = "30",
number = "133",
pages = "132--142",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Wareeditor:1960:SCT,
author = "Willis H. {Ware, editor}",
title = "Soviet Computer Technology---1959",
journal = j-CACM,
volume = "3",
number = "3",
pages = "131--166",
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Watson:1991:AOS,
author = "G. A. Watson",
title = "An Algorithm for Optimal {$\ell_2$} Scaling of
Matrices",
journal = j-IMAJNA,
volume = "11",
pages = "481--492",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Wedderburn:1934:LM,
author = "J. H. M. Wedderburn",
title = "Lectures on Matrices",
volume = "17",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "vii + 205",
year = "1934",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "American Mathematical Society Colloquium
Publications",
}
@Article{Wedin:1973:PTP,
author = "Per-{\AA}ke Wedin",
title = "Perturbation Theory for Pseudo-Inverses",
journal = j-BIT,
volume = "13",
pages = "217--232",
year = "1973",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Wei:1990:PLS,
author = "Musheng Wei",
title = "Perturbation of the Least Squares Problem",
journal = j-LAA,
volume = "141",
pages = "177--182",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Wendroff:1966:TNA,
author = "Burton Wendroff",
title = "Theoretical Numerical Analysis",
publisher = "Academic Press",
address = "New York",
pages = "xi + 239",
year = "1966",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Werner:1984:PIL,
author = "Wilhelm Werner",
title = "Polynomial Interpolation: {Lagrange} Versus {Newton}",
journal = j-MATH-COMP,
volume = "43",
number = "167",
pages = "205--217",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Westlake:1968:HNM,
author = "Joan R. Westlake",
title = "A Handbook of Numerical Matrix Inversion and Solution
of Linear Equations",
publisher = pub-Wiley,
address = pub-Wiley:adr,
year = "1968",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Wegert:1994:BNP,
author = "Elias Wegert and Lloyd N. Trefethen",
title = "From the {Buffon} Needle Problem to the {Kreiss}
Matrix Theorem",
journal = j-AMM,
volume = "101",
number = "2",
pages = "132--139",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{White:1997:INL,
author = "Michael White",
title = "{Isaac Newton}: {The} Last Sorcerer",
publisher = "Fourth Estate",
address = "London",
pages = "402",
year = "1997",
ISBN = "1-85702-706-X",
ISBN-13 = "978-1-85702-706-8",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Williams:1989:EBC,
editor = "M. R. Williams and Martin Campbell-Kelly",
title = "The Early British Computer Conferences",
volume = "14",
publisher = pub-MIT,
address = pub-MIT:adr,
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Charles Babbage Institute Reprint Series for the
History of Computing",
}
@Article{Wichmann:1989:TFS,
author = "B. A. Wichmann",
title = "Towards a Formal Specification of Floating Point",
journal = j-COMP-J,
volume = "32",
number = "",
pages = "432--436",
year = "1989",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Wichmann:1992:NUF,
author = "B. A. Wichmann",
title = "A Note on the Use of Floating Point in Critical
Systems",
journal = j-COMP-J,
volume = "35",
number = "1",
pages = "41--44",
year = "1992",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Wijngaarden:1966:NAI,
author = "A. van Wijngaarden",
title = "Numerical Analysis as an Independent Science",
journal = j-BIT,
volume = "6",
pages = "66--81",
year = "1966",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Wilkinson:1948:ACE,
author = "J. H. Wilkinson",
title = "The {Automatic Computing Engine} at the {National
Physical Laboratory}",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "195",
pages = "285--286",
year = "1948",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/",
}
@TechReport{Wilkinson:1948:PRA,
author = "J. H. Wilkinson",
title = "Progress Report on the {Automatic Computing Engine}",
type = "Report",
number = "MA/17/1024",
institution = "Mathematics Division, Department of Scientific and
Industrial Research, National Physical Laboratory",
address = inst-NPL:adr,
pages = "127",
month = apr,
year = "1948",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Wilkinson:1954:PA,
author = "J. H. Wilkinson",
booktitle = "Automatic Digital Computation",
title = "The {Pilot ACE}",
publisher = "Her Majesty's Stationery Office, London",
pages = "5--14",
year = "1954",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Wilkinson:1954:LAP,
author = "J. H. Wilkinson",
booktitle = "Automatic Digital Computation",
title = "Linear Algebra on the {Pilot ACE}",
publisher = "Her Majesty's Stationery Office, London",
year = "1954",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Wilkinson:1955:UIM,
author = "J. H. Wilkinson",
title = "The Use of Iterative Methods for Finding the Latent
Roots and Vectors of Matrices",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "9",
pages = "184--191",
year = "1955",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Wilkinson:1960:EAF,
author = "J. H. Wilkinson",
title = "Error Analysis of Floating-Point Computation",
journal = j-NUM-MATH,
volume = "2",
pages = "319--340",
year = "1960",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Wilkinson:1961:EAD,
author = "J. H. Wilkinson",
title = "Error Analysis of Direct Methods of Matrix Inversion",
journal = j-ACM,
volume = "8",
pages = "281--330",
year = "1961",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Wilkinson:1962:EAE,
author = "J. H. Wilkinson",
title = "Error Analysis of Eigenvalue Techniques Based on
Orthogonal Transformations",
journal = j-SIAM,
volume = "10",
number = "1",
pages = "162--195",
year = "1962",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Wilkinson:1963:REA,
author = "J. H. Wilkinson",
title = "Rounding Errors in Algebraic Processes",
publisher = "Notes on Applied Science No. 32, Her Majesty's
Stationery Office",
address = "London",
pages = "vi + 161",
year = "1963",
ISBN = "0-486-67999-3",
ISBN-13 = "978-0-486-67999-0",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Also published by Prentice-Hall, Englewood Cliffs, NJ,
USA. Reprinted by Dover, New York, 1994",
}
@InCollection{Wilkinson:1963:PRF,
author = "J. H. Wilkinson",
booktitle = "Experimental Arithmetic, High Speed Computing and
Mathematics",
title = "Plane-Rotations in Floating-Point Arithmetic",
volume = "15",
publisher = pub-AMS # ", " # pub-AMS:adr,
pages = "185--198",
year = "1963",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Proceedings of Symposia in Applied Mathematics",
}
@Book{Wilkinson:1965:AEP,
author = "J. H. Wilkinson",
title = "The Algebraic Eigenvalue Problem",
publisher = pub-OUP,
pages = "xviii + 662",
year = "1965",
ISBN = "0-19-853403-5 (\hbk), 0-19-853418-3 (\pbk)",
ISBN-13 = "978-0-19-853403-7 (\hbk), 978-0-19-853418-1 (\pbk)",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Wilkinson:1965:EAT,
author = "J. H. Wilkinson",
editor = "Louis B. Rall",
booktitle = "Error in Digital Computation",
title = "Error Analysis of Transformations Based on the Use of
Matrices of the Form {$I-2ww^H$}",
volume = "2",
publisher = pub-Wiley # ", " # pub-Wiley:adr,
pages = "77--101",
year = "1965",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Wilkinson:1967:BZW,
author = "J. H. Wilkinson",
title = "Bledy Zaokragle{\'n} w Procesach Algebraicznych",
publisher = "PWW",
address = "Warszawa",
year = "1967",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Polish translation of \cite{Wilkinson:1963:REA}",
}
@InProceedings{Wilkinson:1968:PEA,
author = "J. H. Wilkinson",
editor = "I. G. Petrovsky",
booktitle = "Proc. International Congress of Mathematicians, Moscow
1966",
title = "A Priori Error Analysis of Algebraic Processes",
publisher = "Mir Publishers, Moscow",
pages = "629--640",
year = "1968",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Wilkinson:1969:R,
author = "J. H. Wilkinson",
title = "Rundungsfehler",
publisher = pub-Springer,
address = pub-Springer:adr-B,
year = "1969",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "German translation of \cite{Wilkinson:1963:REA}",
}
@Book{Wilkinson:1970:AEP,
author = "J. H. Wilkinson",
title = "The Algebraic Eigenvalue Problem",
publisher = "Nauka",
address = "U.S.S.R. Academy of Sciences",
pages = "564",
year = "1970",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Wilkinson:1971:MEA,
author = "J. H. Wilkinson",
title = "Modern Error Analysis",
journal = j-SIREV,
volume = "13",
number = "4",
pages = "548--568",
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Wilkinson:1971:SCN,
author = "J. H. Wilkinson",
title = "Some Comments from a Numerical Analyst",
journal = j-ACM,
volume = "18",
number = "2",
pages = "137--147",
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Wilkinson:1974:NLA,
author = "J. H. Wilkinson",
title = "Numerical Linear Algebra on Digital Computers",
journal = j-IMA-BULL,
volume = "10",
number = "9/10",
pages = "354--356",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "IMA Bulletin",
}
@Article{Wilkinson:1974:CEA,
author = "J. H. Wilkinson",
title = "The Classical Error Analyses for the Solution of
Linear Systems",
journal = j-IMA-BULL,
volume = "10",
number = "5/6",
pages = "175--180",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "IMA Bulletin",
}
@InBook{Evans:1976:IJH,
author = "Christopher Evans",
title = "Interview with {J}. {H}. Wilkinson",
number = "10",
publisher = "Science Museum, London",
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Pioneers of Computing, 60-Minute Recordings of
Interviews",
}
@InCollection{Wilkinson:1980:TWN,
author = "J. H. Wilkinson",
editor = "N. Metropolis and J. Howlett and Gian-Carlo Rota",
booktitle = "A History of Computing in the Twentieth Century: {A}
Collection of Essays",
title = "Turing's Work at the {National Physical Laboratory}
and the Construction of {Pilot ACE}, {DEUCE}, and
{ACE}",
publisher = "Academic Press",
address = "New York",
pages = "101--114",
year = "1980",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InCollection{Wilkinson:1984:PP,
author = "James H. Wilkinson",
editor = "G. H. Golub",
booktitle = "Studies in Numerical Analysis",
title = "The Perfidious Polynomial",
volume = "24",
publisher = pub-MAA,
address = pub-MAA:adr,
pages = "1--28",
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Studies in Mathematics",
}
@InCollection{Wilkinson:1985:SAE,
author = "J. H. Wilkinson",
booktitle = "NAG Newsletter 2/85",
title = "The State of the Art in Error Analysis",
publisher = "Numerical Algorithms Group",
address = "Oxford, UK",
pages = "5--28",
month = nov,
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Wilkinson:1986:EAR,
author = "J. H. Wilkinson",
title = "Error Analysis Revisited",
journal = j-IMA-BULL,
volume = "22",
number = "11/12",
pages = "192--200",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "IMA Bulletin",
}
@Article{Anonymous:1987:JW,
author = "Anonymous",
title = "{James Wilkinson} (1919--1986)",
journal = j-AHC,
volume = "9",
number = "2",
pages = "205--210",
year = "1987",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "From the introduction: ``A series of lightly edited
extracts from messages that were sent over various
computer networks during the period October 5,
1986--February 13, 1987''",
}
@Article{Wilkes:1997:AE,
author = "M. V. Wilkes",
title = "Arithmetic on the {EDSAC}",
journal = j-IEEE-AHC,
volume = "19",
number = "1",
pages = "13--15",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Winograd:1968:NAI,
author = "S. Winograd",
title = "A New Algorithm for Inner Product",
journal = j-IEEE-C,
volume = "C-18",
pages = "693--694",
year = "1968",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Winograd:1971:MM,
author = "S. Winograd",
title = "On Multiplication of {$2 \times 2$} Matrices",
journal = j-LAA,
volume = "4",
pages = "381--388",
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Walden:1995:OBP,
author = "Bertil Wald{\'e}n and Rune Karlson and {Ji-guang}
Sun",
title = "Optimal Backward Perturbation Bounds for the Linear
Least Squares Problem",
journal = j-NLAA,
volume = "2",
number = "3",
pages = "271--286",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Woehr:1997:CWK,
author = "Jack Woehr",
title = "A Conversation with {William Kahan}",
journal = j-DDJ,
volume = "271",
pages = "18--32",
month = nov,
year = "1997",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Wolfe:1964:RTE,
author = "Jack M. Wolfe",
title = "Reducing Truncation Errors by Programming",
journal = j-CACM,
volume = "7",
number = "6",
pages = "355--356",
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Book{Wolfram:1999:MB,
author = "Stephen Wolfram",
title = "The {Mathematica} Book",
publisher = "Wolfram Media, Champaign, IL, USA and " # pub-CUP # ",
" # pub-CUP:adr,
edition = "Fourth",
pages = "xxvi + 1470",
year = "1999",
ISBN = "1-57955-004-5 (Wolfram), 0-521-64314-7 (Cambridge)",
ISBN-13 = "978-1-57955-004-2 (Wolfram), 978-0-521-64314-6
(Cambridge)",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{wood58,
author = "Michael Woodger",
title = "The History and Present Use of Digital Computers at
the {National Physical Laboratory}",
journal = j-PROC-CONTROL-AUTOMATION,
pages = "437--442",
month = nov,
year = "1958",
CODEN = "PCAUA3",
ISSN = "0552-234X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted in \cite[pp.~125-140]{Carpenter:1986:MTA}.",
fjournal = "Process Control and Automation",
}
@Article{Wozniakowski:1977:NSS,
author = "H. Wo{\'z}niakowski",
title = "Numerical Stability for Solving Nonlinear Equations",
journal = j-NUM-MATH,
volume = "27",
pages = "373--390",
year = "1977",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Wozniakowski:1977:NSC,
author = "H. Wo{\'z}niakowski",
title = "Numerical Stability of the {Chebyshev} Method for the
Solution of Large Linear Systems",
journal = j-NUM-MATH,
volume = "28",
pages = "191--209",
year = "1977",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Wozniakowski:1978:REA,
author = "H. Wo{\'z}niakowski",
title = "Roundoff-error analysis of iterations for large linear
systems",
journal = j-NUM-MATH,
volume = "30",
pages = "301--314",
year = "1978",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Wozniakowski:1980:REA,
author = "H. Wo{\'z}niakowski",
title = "Roundoff-Error Analysis of a New Class of
Conjugate-Gradient Algorithms",
journal = j-LAA,
volume = "29",
pages = "507--529",
year = "1980",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Whaley:2001:AEO,
author = "R. Clint Whaley and Antoine Petitet and Jack J.
Dongarra",
title = "Automated Empirical Optimization of Software and the
{ATLAS} Project",
journal = j-PAR-COMP,
volume = "27",
number = "1--2",
pages = "3--25",
year = "2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Wright:1992:IMC,
author = "Margaret H. Wright",
title = "Interior Methods for Constrained Optimization",
journal = j-ACTA-NUMERICA,
volume = "1",
pages = "341--407",
year = "1992",
CODEN = "ANUMFU",
DOI = "https://doi.org/10.1017/S0962492900002300",
ISBN = "0-521-41026-6",
ISBN-13 = "978-0-521-41026-7",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
bibdate = "Sat Sep 24 10:23:30 MDT 2011",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/att.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/SEL-HPC.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
URL = "ftp://netlib.att.com/netlib/att/cs/doc/91/4-10.ps.Z",
acknowledgement = ack-nhfb,
ajournal = "Acta Numer.",
document-size = "187.8 kbytes",
fjournal = "Acta Numerica",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU",
onlinedate = "07 November 2008",
scope = "opt",
}
@Article{Wright:1993:CPW,
author = "Stephen J. Wright",
title = "A Collection of Problems for Which {Gaussian}
Elimination with Partial Pivoting is Unstable",
journal = j-SISSC,
volume = "14",
number = "1",
pages = "231--238",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@InProceedings{Wright:1996:DSM,
author = "Margaret H. Wright",
editor = "D. F. Griffiths and G. A. Watson",
booktitle = "Numerical Analysis \textup{1995}, Proceedings of the
\textup{16}th Dundee Conference",
title = "Direct Search Methods: {Once} Scorned, Now
Respectable",
volume = "344",
publisher = pub-AWLongman # ", " # pub-AWLongman:adr,
pages = "191--208",
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Pitman Research Notes in Mathematics",
}
@Book{Wright:1997:PDI,
author = "Stephen J. Wright",
title = "Primal-Dual Interior-Point Methods",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xx + 289",
year = "1997",
ISBN = "0-89871-382-X",
ISBN-13 = "978-0-89871-382-4",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Wallis:1972:CRS,
author = "W. D. Wallis and Anne Penfold Street and Jennifer
Seberry Wallis",
title = "Combinatorics: {Room} Squares, Sum-Free Sets,
{Hadamard} Matrices",
volume = "292",
publisher = pub-Springer,
address = pub-Springer:adr-B,
pages = "508",
year = "1972",
ISBN = "3-540-06035-9",
ISBN-13 = "978-3-540-06035-2",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
series = "Lecture Notes in Mathematics",
}
@Article{Weiss:1986:ACN,
author = "N. Weiss and G. W. Wasilkowski and H. Wo{\'z}niakowski
and M. Shub",
title = "Average Condition Number for Solving Linear
Equations",
journal = j-LAA,
volume = "83",
pages = "79--102",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Yalamov:2000:ASS,
author = "Plamen Y. Yalamov",
title = "On the Almost Strong Stability of the Circular
Deconvolution Algorithm",
journal = j-SIMAX,
volume = "22",
number = "2",
pages = "358--363",
year = "2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@TechReport{Yalamov:1995:GSA,
author = "P. Y. Yalamov",
title = "Graphs and Stability of Algorithms",
type = "Preprint",
number = "N27",
institution = "University of Rousse",
address = "Bulgaria",
pages = "17",
month = feb,
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Yeung:1997:PAG,
author = "Man-Chung Yeung and Tony. F. Chan",
title = "Probabilistic Analysis of {Gaussian} Elimination
Without Pivoting",
journal = j-SIMAX,
volume = "18",
number = "2",
pages = "499--517",
year = "1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Yip:1986:NSS,
author = "E. L. Yip",
title = "A Note on the Stability of Solving a Rank-{$p$}
Modification of a Linear System by the
{Sherman--Morrison--Woodbury} Formula",
journal = j-SISSC,
volume = "7",
number = "3",
pages = "507--513",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Young:1972:SNM,
author = "David M. Young and Robert T. Gregory",
title = "A Survey of Numerical Mathematics",
volume = "1",
publisher = pub-AW,
address = pub-AW:adr,
pages = "x + 492 + appendices",
year = "1972",
ISBN = "0-486-65691-8",
ISBN-13 = "978-0-486-65691-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted by Dover, New York, 1988",
}
@Article{Yohe:1979:SIA,
author = "J. M. Yohe",
title = "Software for Interval Arithmetic: {A} Reasonably
Portable Package",
journal = j-TOMS,
volume = "5",
number = "1",
pages = "50--63",
year = "1979",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Yohe:1979:INA,
author = "J. M. Yohe",
title = "Implementing Nonstandard Arithmetics",
journal = j-SIREV,
volume = "21",
number = "1",
pages = "34--56",
year = "1979",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Yohe:1980:PSI,
author = "J. M. Yohe",
title = "Portable Software for Interval Arithmetic",
journal = j-COMPUTING,
volume = "Suppl. 2",
pages = "211--229",
year = "1980",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Book{Young:1971:ISL,
author = "David M. Young",
title = "Iterative Solution of Large Linear Systems",
publisher = "Academic Press",
address = "New York",
pages = "xxiv + 570",
year = "1971",
ISBN = "0-12-773050-8",
ISBN-13 = "978-0-12-773050-9",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Young:1989:HOI,
author = "David M. Young",
title = "A Historical Overview of Iterative Methods",
journal = j-COMP-PHYS-COMM,
volume = "53",
number = "1--3",
pages = "1--17",
month = may,
year = "1989",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(89)90145-8",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
MRclass = "65F10 (65-03)",
MRnumber = "90e:65047",
bibdate = "Mon Feb 13 10:28:26 MST 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465589901458",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
reviewer = "H. R. Schwarz",
}
@Article{Ypma:1983:ERE,
author = "Tjalling J. Ypma",
title = "The Effect of Rounding Errors on {Newton}-like
Methods",
journal = j-IMAJNA,
volume = "3",
pages = "109--118",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Ypma:1983:FMZ,
author = "Tjalling J. Ypma",
title = "Finding a Multiple Zero by Transformations and
{Newton}-like Methods",
journal = j-SIREV,
volume = "25",
number = "3",
pages = "365--378",
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Ypma:1995:HDN,
author = "Tjalling J. Ypma",
title = "Historical Development of the {Newton--Raphson}
Method",
journal = j-SIREV,
volume = "37",
number = "4",
pages = "531--551",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Yuval:1978:SPS,
author = "Gideon Yuval",
title = "A Simple Proof of {Strassen's} Result",
journal = j-INFPL,
volume = "7",
number = "6",
pages = "285--286",
year = "1978",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Zawilski:1991:NSC,
author = "Adam T. Zawilski",
title = "Numerical Stability of the Cyclic {Richardson}
Iteration",
journal = j-NUM-MATH,
volume = "60",
pages = "251--290",
year = "1991",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Zha:1993:CPA,
author = "Hongyuan Zha",
title = "A Componentwise Perturbation Analysis of the {$QR$}
Decomposition",
journal = j-SIMAX,
volume = "14",
number = "4",
pages = "1124--1131",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Zha:1993:P,
author = "Hongyuan Zha",
title = "Problem 10312",
journal = j-AMM,
volume = "100",
number = "5",
pages = "499",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Zha:1995:NCS,
author = "Hongyuan Zha and Zhenyue Zhang",
title = "A Note on Constructing a Symmetric Matrix with
Specified Diagonal Entries and Eigenvalues",
journal = j-BIT,
volume = "35",
pages = "448--452",
year = "1995",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Zielke:1986:RTM,
author = "G. Zielke",
title = "Report on Test Matrices for Generalized Inverses",
journal = j-COMPUTING,
volume = "36",
pages = "105--162",
year = "1986",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Zielke:1988:SRM,
author = "Gerhard Zielke",
title = "Some Remarks on Matrix Norms, Condition Numbers, and
Error Estimates for Linear Equations",
journal = j-LAA,
volume = "110",
pages = "29--41",
year = "1988",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Zietak:1985:PCI,
author = "K. Zi{\c{e}}tak",
title = "On a Particular Case of the Inconsistent Linear Matrix
Equation {$AX+YB=C$}",
journal = j-LAA,
volume = "66",
pages = "249--258",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Ziv:1982:RDE,
author = "Abraham Ziv",
title = "Relative Distance---{An} Error Measure in Round-Off
Error Analysis",
journal = j-MATH-COMP,
volume = "39",
number = "160",
pages = "563--569",
year = "1982",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Ziv:1991:FEE,
author = "Abraham Ziv",
title = "Fast Evaluation of Elementary Mathematical Functions
with Correctly Rounded Last Bit",
journal = j-TOMS,
volume = "17",
number = "3",
pages = "410--423",
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Ziv:1995:CAE,
author = "Abraham Ziv",
title = "Converting Approximate Error Bounds into Exact Ones",
journal = j-MATH-COMP,
volume = "64",
number = "209",
pages = "265--277",
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Article{Zlatev:1986:CNE,
author = "Zahari Zlatev and Jerzy Wasniewski and Kjeld
Schaumburg",
title = "Condition Number Estimators in a Sparse Matrix
Software",
journal = j-SISSC,
volume = "7",
number = "4",
pages = "1175--1189",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Cox:1990:RNC,
editor = "M. G. Cox and S. J. Hammarling",
title = "Reliable Numerical Computation",
publisher = pub-OUP,
pages = "xvi + 339",
year = "1990",
ISBN = "0-19-853564-3",
ISBN-13 = "978-0-19-853564-5",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Proceedings{harv46,
key = "Harvard",
title = "A Manual of Operation for the Automatic Sequence
Controlled Calculator",
publisher = pub-Harvard,
address = pub-Harvard:adr,
year = "1946",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted, with new foreword and introduction, Volume
8 in the Charles Babbage Institute Reprint Series for
the History of Computing, MIT Press, Cambridge, MA,
USA, 1985",
}
@Proceedings{harv48,
key = "Harvard",
title = "Proceedings of a Symposium on Large-Scale Digital
Calculating Machinery",
volume = "16",
publisher = pub-Harvard,
address = pub-Harvard:adr,
year = "1948",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
note = "Reprinted, with a new introduction by William Aspray,
Volume 7 in the Charles Babbage Institute Reprint
Series for the History of Computing, MIT Press,
Cambridge, MA, USA, 1985",
series = "The Annals of the Computation Laboratory of Harvard
University",
}
@Proceedings{Kulisch:1983:NAS,
editor = "Ulrich W. Kulisch and Willard L. Miranker",
title = "A New Approach to Scientific Computation",
publisher = pub-AP # ", " # pub-AP:adr-NY,
pages = "xv + 384",
year = "1983",
ISBN = "0-12-428660-7",
ISBN-13 = "978-0-12-428660-3",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
}
@Book{Wilkinson:1971:LA,
editor = "James H. Wilkinson and Christian Reinsch",
booktitle = "Linear Algebra",
title = "Linear Algebra",
volume = "II",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 439",
year = "1971",
ISBN = "0-387-05414-6, 3-540-05414-6",
ISBN-13 = "978-0-387-05414-8, 978-3-540-05414-6",
LCCN = "QA251 .W67",
bibdate = "Wed Dec 15 18:44:50 1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib;
http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/gnu.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
http://www.math.utah.edu/pub/tex/bib/nummath.bib",
series = "Handbook for Automatic Computation, Editors: {F. L.
Bauer, A. S. Householder, F. W. J. Olver, H.
Rutishauser, K. Samelson and E. Stiefel}",
acknowledgement = ack-nhfb,
tableofcontents = "Part I: Linear systems, least squares and linear
programming \\
J. H. Wilkinson / Introduction to Part I / 1--8 \\
1. Introduction \\
2. List of procedures \\
3. Positive definite symmetric matrices \\
4. Non-positive definite symmetric matrices \\
5. Non-Hermitian matrices \\
6. Least squares and related problems \\
7. The linear programming problem \\
R. S. Martin, G. Peters and J. H. Wilkinson / Symmetric
decomposition of a positive definite matrix / 9--30 \\
Martin, Peters and Wilkinson / Iterative refinement of
the solution of a positive definite system of equations
/ 31--44 \\
F. L. Bauer and C. Reinsch / Inversion of positive
definite matrices by the Gauss-Jordan method / 45--49
\\
Martin and Wilkinson / Symmetric decomposition of
positive definite band matrices / 50--56 \\
T. Ginsburg / The conjugate gradient method / 57--69
\\
Martin and Wilkinson / Solution of symmetric and
unsymmetric band equations and the calculation of
eigenvectors of band matrices / 70--92 \\
H. J. Bowdler, Martin, Peters and Wilkinson / Solution
of real and complex systems of linear equations /
93--110 \\
P. Businger and G. H. Golub / Linear least squares
solutions by Householder transformations / 111--118 \\
Bauer / Elimination with weighted row combinations for
solving linear equations and least squares problems /
119--133 \\
Golub and Reinsch / Singular value decomposition and
least squares solutions / 134--151 \\
R. H. Bartels, J. Stoer and Ch. Zenger / A realization
of the simplex method based on triangular
decompositions / 152--190 \\
Part II: The algebraic eigenvalue problem \\
Wilkinson / Introduction to Part II / 191--201 \\
1. Introduction \\
2. List of procedures \\
3. Real, dense, symmetric matrices \\
4. Symmetric band matrices \\
5. Simultaneous determination of dominant eigenvalues
and eigenvectors of a symmetric sparse matrix \\
6. The generalized symmetric eigenvalue problems $A x =
\lambda B x$ and $A B x = \lambda x$ \\
7. Hermitian matrices \\
8. Real dense unsymmetric matrices \\
9. Unsymmetric band matrices \\
10. Dense unsymmetric matrices with complex elements,
H. Rutishauser / The Jacobi method for real symmetric
matrices / 202--211 \\
Martin, Reinsch and Wilkinson / Householder's
tridiagonalization of a symmetric matrix / 212--226 \\
H. Bowdler, Martin, Reinsch and Wilkinson / The $QR$
and $QL$ algorithms for symmetric matrices / 227--240
\\
A. Dubrulle, Martin and Wilkinson / The implicit $QL$
algorithm / 241--248 \\
W. Barth, Martin, and Wilkinson / Calculation of the
eigenvalues of a symmetric tridiagonal matrix by the
method of bisection / 249--256 \\
Reinsch and Bauer / Rational $QR$ transformation with
Newton shift for symmetric tridiagonal matrices /
257--265 \\
Martin, Reinsch and Wilkinson / The $QR$ algorithm for
band symmetric matrices / 266--272 \\
H. R. Schwarz / Tridiagonalization of a symmetric band
matrix / 273--283 \\
Rutishauser / Simultaneous iteration method for
symmetric matrices / 284--302 \\
Martin and Wilkinson / Reduction of the symmetric
eigenproblem $A x = \lambda B x$ and related problems
to standard form / 303--314 \\
B. N. Parlett and Reinsch / Balancing a matrix for
calculation of eigenvalues and eigenvectors / 315--326
\\
P. J. Eberlein and J. Boothroyd / Solution to the
eigenproblem by a norm reducing Jacobi type method /
327--338 \\
Martin and Wilkinson / Similarity reduction of a
general matrix to Hessenberg form / 339--358 \\
Martin, Peters and Wilkinson / The $QR$ algorithm for
real Hessenberg matrices / 359--371 \\
Peters and Wilkinson / Eigenvectors of real and complex
matrices by $LR$ and $QR$ triangularizations / 372--395
\\
Martin and Wilkinson / The modified $LR$ algorithm for
complex Hessenberg matrices / 396--403 \\
Eberlein / Solution to the complex eigenproblem by a
norm reducing Jacobi type method / 404--417 \\
Peters and Wilkinson / The calculation of specified
eigenvectors by inverse iteration / 418--439",
}
