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@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org|,
URL: \path|http://www.math.utah.edu/~beebe/|"}
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@Article{Olver:1965:EBA,
author = "F. W. J. Olver and F. Stenger",
title = "Error Bounds for Asymptotic Solutions of Second-Order
Differential Equations having an Irregular Singularity
of Arbitrary Rank",
journal = j-SIAM-J-NUM-ANALYSIS-B,
volume = "2",
number = "2",
pages = "244--249",
month = "????",
year = "1965",
CODEN = "????",
DOI = "https://doi.org/10.1137/0702018",
ISSN = "0887-459X (print), 1095-7170 (electronic)",
ISSN-L = "0887-459X",
MRclass = "41.50 (34.00)",
MRnumber = "MR0185351 (32 \#2819)",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/siamjnumeranal.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/SIAMJNUMERANAL/siamjnumeranal.bib;
http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0887-459X(1965)2:2<244:EBFASO>2.0.CO%3B2-N",
ZMnumber = "0173.34001",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Society for Industrial and Applied
Mathematics: Series B, Numerical Analysis",
journal-URL = "http://epubs.siam.org/loi/sjnaam.1",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@TechReport{Stenger:1965:EBAa,
author = "Frank Stenger",
title = "Error bounds for asymptotic solutions of differential
equations. 1, {The} distinct eigenvalue case",
type = "Technical Report",
number = "2",
institution = "Department of Computing Science, University of
Alberta",
address = "Edmonton, AB, Canada",
pages = "34",
year = "1965",
LCCN = "QA 76 A1 A33 no.002",
bibdate = "Wed May 09 10:12:54 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://web.sirsitest.library.ualberta.ca/uhtbin/cgisirsi/QWzmKzdaVV/UAARCHIVES/295120075/9?first_hit=1&last_hit=20&form_type=&VIEW%5E3.x=49&VIEW%5E1.y=10",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@TechReport{Stenger:1965:EBAb,
author = "Frank Stenger",
title = "Error bounds for asymptotic solutions of differential
equations. 2, {The} general case",
type = "Technical Report",
number = "3",
institution = "Department of Computing Science, University of
Alberta",
address = "Edmonton, AB, Canada",
pages = "44",
year = "1965",
LCCN = "QA 76 A1 A33 no.003",
bibdate = "Wed May 09 10:12:54 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://web.sirsitest.library.ualberta.ca/uhtbin/cgisirsi/3DeRFr4iWs/UAARCHIVES/295120075/9?first_hit=1&last_hit=20&form_type=&VIEW%5E4.x=49&VIEW%5E1.y=10",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@TechReport{McNamee:1966:CFS,
author = "J. McNamee and F. Stenger",
title = "Construction of fully symmetric numerical integration
formulas",
type = "Technical Report",
number = "4",
institution = "Department of Computing Science, University of
Alberta",
address = "Edmonton, AB, Canada",
pages = "32",
year = "1966",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/nummath.bib;
http://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1966:BEG,
author = "F. Stenger",
title = "Bounds on the error of {Gauss}-type quadratures",
journal = j-NUM-MATH,
volume = "8",
number = "2",
pages = "150--160",
month = apr,
year = "1966",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02163184",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 19:01:15 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/nummath.bib;
http://www.math.utah.edu/pub/tex/bib/nummath.bib",
ZMnumber = "0149.12002",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1966:EBAa,
author = "Frank Stenger",
title = "Error bounds for asymptotic solutions of differential
equations. {I}: The distinct eigenvalue case",
journal = j-J-RES-NATL-BUR-STAND-B,
volume = "70",
number = "3",
pages = "167--186",
month = jul # "\slash " # sep,
year = "1966",
CODEN = "JNBBAU",
DOI = "https://doi.org/10.6028/jres.070b.017",
ISSN = "0022-4340 (print), 2376-5283 (electronic)",
ISSN-L = "0022-4340",
bibdate = "Thu May 10 16:31:08 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0233.65048",
acknowledgement = ack-nhfb,
classmath = "65L70 (Error bounds (numerical methods for ODE)) 65L15
(Eigenvalue problems for ODE (numerical methods)) 65L10
(Boundary value problems for ODE (numerical methods))",
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",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1966:EBAb,
author = "Frank Stenger",
title = "Error bounds for asymptotic solutions of differential
equations. {II}: The general case",
journal = j-J-RES-NATL-BUR-STAND-B,
volume = "70",
number = "3",
pages = "187--210",
month = may,
year = "1966",
CODEN = "JNBBAU",
DOI = "https://doi.org/10.6028/jres.070b.018",
ISSN = "0022-4340 (print), 2376-5283 (electronic)",
ISSN-L = "0022-4340",
bibdate = "Thu May 10 16:31:06 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0233.65049",
acknowledgement = ack-nhfb,
classmath = "65L70 (Error bounds (numerical methods for ODE)) 65L10
(Boundary value problems for ODE (numerical methods))",
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",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1966:EBE,
author = "F. Stenger",
title = "Error bounds for the evaluation of integrals by
repeated {Gauss}-type formulae",
journal = j-NUM-MATH,
volume = "9",
number = "3",
pages = "200--213",
month = dec,
year = "1966",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02162084",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 20:47:18 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0147.35804",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@PhdThesis{Stenger:1966:EBS,
author = "Frank Stenger",
title = "Error Bounds for Solutions of Differential Equations",
type = "{Ph.D.} Thesis",
school = "Department of Computing Science, University of
Alberta",
address = "Edmonton, AB, Canada",
pages = "148",
year = "1966",
bibdate = "Wed May 09 10:09:05 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{McNamee:1967:CFS,
author = "J. McNamee and F. Stenger",
title = "Construction of fully symmetric numerical integration
formulas",
journal = j-NUM-MATH,
volume = "10",
number = "4",
pages = "327--344",
month = nov,
year = "1967",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02162032",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.61",
MRnumber = "MR0219241 (36 \#2324)",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/nummath.bib;
http://www.math.utah.edu/pub/tex/bib/nummath.bib",
ZMnumber = "0155.21702",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@TechReport{Dolph:1968:SPH,
author = "Charles L. Dolph and Frank Stenger and A.
Wiin-Nielsen",
title = "On the stability problems of the
{Helmholtz--Kelvin--Rayleigh} type",
type = "Technical Report",
number = "08759-3-T",
institution = "Department of Meteorology and Oceanography, University
of Michigan",
address = "Ann Arbor, MI, USA",
pages = "72",
year = "1968",
bibdate = "Thu May 10 10:12:58 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1968:BRB,
author = "Frank Stenger",
title = "Book Review: {{\booktitle{Numerical Integration}}
(Philip J. Davis and Philip Rabinowitz)}",
journal = j-SIAM-REVIEW,
volume = "10",
number = "2",
pages = "239--240",
month = "????",
year = "1968",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1010051",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:56 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/10/2;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "April 1968",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1968:KPE,
author = "Frank Stenger",
title = "{Kronecker} Product Extensions of Linear Operators",
journal = j-SIAM-J-NUMER-ANAL,
volume = "5",
number = "2",
pages = "422--435",
month = jun,
year = "1968",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0705033",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0036-1429(196806)5:2<422:KPEOLO>2.0.CO%3B2-7",
ZMnumber = "0165.17801",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1968:RNI,
author = "Frank Stenger",
title = "Review: {{\em Numerical Integration}}, by {Philip J.
Davis and Philip Rabinowitz}",
journal = j-SIAM-REVIEW,
volume = "10",
number = "2",
pages = "239--240",
month = apr,
year = "1968",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1010051",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu May 10 17:20:18 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://links.jstor.org/sici?sici=0036-1445(196804)10:2<239:NI>2.0.CO%3B2-Y",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1968:TC,
author = "Frank Stenger",
title = "A trap in computations",
journal = j-SIGNUM,
volume = "3",
number = "3",
pages = "2--2",
month = jul,
year = "1968",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1198460.1198462",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Mon Mar 5 17:26:27 MST 2007",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/signum.bib",
note = "See \cite{Moler:1969:MSC}.",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Goodrich:1970:MSQ,
author = "R. F. Goodrich and F. Stenger",
title = "Movable Singularities and Quadrature",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "283--300",
month = apr,
year = "1970",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2004478",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.55",
MRnumber = "MR0275669 (43 \#1422)",
MRreviewer = "H. E. Fettis",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/MATHCOMP/mathcomp1970.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0025-5718(197004)24:110<283:MSAQ>2.0.CO%3B2-S",
ZMnumber = "0209.17803",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1970:AAC,
author = "Frank Stenger",
title = "The Asymptotic Approximation of Certain Integrals",
journal = j-SIAM-J-MATH-ANA,
volume = "1",
number = "3",
pages = "392--404",
month = aug,
year = "1970",
CODEN = "SJMAAH",
DOI = "https://doi.org/10.1137/0501036",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
bibdate = "Sun Nov 28 19:22:00 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/1/3;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0203.37201",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1970:AST,
author = "F. Stenger",
title = "On the asymptotic solution of two first order linear
differential equations with large parameter",
journal = j-FUNKCIAL-EKVAC,
volume = "13",
pages = "1--18",
year = "1970",
CODEN = "FESIAT",
ISSN = "0532-8721",
ISSN-L = "0532-8721",
MRnumber = "MR0264176",
bibdate = "Thu Nov 6 17:29:47 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://fe.math.kobe-u.ac.jp/FE/Free/vol13/fe13-1.pdf",
ZMnumber = "0204.40301",
acknowledgement = ack-nhfb,
fjournal = "Funkcialaj Ekvacioj. Serio Internacia",
journal-URL = "http://www.math.kobe-u.ac.jp/~fe/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{G:1971:RTC,
author = "W. G.",
title = "Review: {{\em Tabulation of Certain Fully Symmetric
Numerical Integration Formulas of Degree 7, 9 and 11}},
by {Frank Stenger}",
journal = j-MATH-COMPUT,
volume = "25",
number = "116",
pages = "935--935",
month = oct,
year = "1971",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-71-99709-2",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Thu May 10 16:53:59 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://www.jstor.org/stable/2004361",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{McNamee:1971:WCF,
author = "J. McNamee and F. Stenger and E. L. Whitney",
title = "{Whittaker}'s Cardinal Function in Retrospect",
journal = j-MATH-COMPUT,
volume = "25",
number = "113",
pages = "141--154",
month = jan,
year = "1971",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1971-0301428-0",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "41A30 (65R05)",
MRnumber = "MR0301428 (46 \#586)",
MRreviewer = "F. J. Schuurmann",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/mathcomp.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0025-5718(197101)25:113<141:WCFIR>2.0.CO%3B2-6;
http://www.ams.org/journals/mcom/1971-25-113/S0025-5718-1971-0301428-0/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1971:BRB,
author = "Frank Stenger",
title = "Book Review: {{\booktitle{Integrals and Sums}} (P. C.
Chakravarti)}",
journal = j-SIAM-REVIEW,
volume = "13",
number = "4",
pages = "582--583",
month = "????",
year = "1971",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1013113",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:06:33 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/13/4;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "October 1971",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1971:CPA,
author = "Frank Stenger",
title = "Constructive proofs for approximation by inner
functions",
journal = j-J-APPROX-THEORY,
volume = "4",
number = "4",
pages = "372--386",
month = dec,
year = "1971",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1016/0021-9045(71)90004-9",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "30E10",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0227.30031",
abstract = "An inner function is a function on the unit circle $T$
whose values almost everywhere have modulus $1$ and are
the radial limits of a bounded holomorphic function on
the open unit disk $U$. Recently, it has been proved
that, given a function $f$ which is Lebesgue measurable
and essentially bounded on $T$ and given $ \epsilon > 0
$, there exist inner functions $ \phi_1, \psi_1,
\phi_2, \psi_2, \ldots {}, \phi_n, \psi_n $ and
constants $ c_1, \ldots {}, c_n $ such that $ |f(e^{i
\theta }) - l i m_{r \rightarrow 1} \sum_{k = 1}^n C_k
\phi_k(r e^{i \theta }) / \psi_k(r e^{i \theta })| <
\epsilon $ a.e. on $T$. The paper gives a constructive
proof of this result.",
acknowledgement = ack-nhfb,
classmath = "30E10 (Approximation in the complex domain)",
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1971:ERT,
author = "Frank Stenger",
title = "Erratum: {The reduction of two dimensional integrals
into a finite number of one-dimensional integrals}",
journal = j-AEQUATIONES-MATHEMATICAE,
volume = "6",
number = "2--3",
pages = "316--317",
month = jun,
year = "1971",
CODEN = "AEMABN",
DOI = "https://doi.org/10.1007/bf01819776",
ISSN = "0001-9054 (print), 1420-8903 (electronic)",
ISSN-L = "0001-9054",
bibdate = "Fri Nov 7 08:39:48 MST 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
note = "See \cite{Stenger:1971:RTD}.",
acknowledgement = ack-nhfb,
fjournal = "Aequationes Mathematicae",
journal-URL = "http://link.springer.com/journal/10",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1971:RIS,
author = "Frank Stenger",
title = "Review: {{\em Integrals and Sums}}, by {P. C.
Chakravarti}",
journal = j-SIAM-REVIEW,
volume = "13",
number = "4",
pages = "582--583",
month = oct,
year = "1971",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1013113",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu May 10 16:58:16 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://links.jstor.org/sici?sici=0036-1445(197110)13:4<582:IAS>2.0.CO%3B2-1",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1971:RTD,
author = "Frank Stenger",
title = "The reduction of two dimensional integrals into a
finite number of one dimensional integrals",
journal = j-AEQUATIONES-MATHEMATICAE,
volume = "6",
number = "2--3",
pages = "278--287",
month = jun,
year = "1971",
CODEN = "AEMABN",
DOI = "https://doi.org/10.1007/bf01819765",
ISSN = "0001-9054 (print), 1420-8903 (electronic)",
ISSN-L = "0001-9054",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
note = "See erratum \cite{Stenger:1971:ERT}.",
ZMnumber = "0235.30044",
acknowledgement = ack-nhfb,
classmath = "30E20 (Integration (one complex variable))",
fjournal = "Aequationes Mathematicae",
journal-URL = "http://link.springer.com/journal/10",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Lipow:1972:HSC,
author = "Peter R. Lipow and Frank Stenger",
title = "How Slowly Can Quadrature Formulas Converge?",
journal = j-MATH-COMPUT,
volume = "26",
number = "120",
pages = "917--922",
month = oct,
year = "1972",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/s0025-5718-1972-0319356-4;
https://doi.org/10.2307/2005875",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/MATHCOMP/mathcomp1970.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0025-5718(197210)26:120<917:HSCQFC>2.0.CO%3B2-R",
ZMnumber = "0261.65017",
acknowledgement = ack-nhfb,
classcodes = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
classmath = "65D30 (Numerical integration)",
corpsource = "Univ. Montreal, Que., Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "convergence of numerical methods; convergence of
quadrature formulae; integration",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
treatment = "T Theoretical or Mathematical",
}
@Article{Stenger:1972:ASW,
author = "Frank Stenger",
title = "The approximate solution of {Wiener--Hopf} integral
equations",
journal = j-J-MATH-ANAL-APPL,
volume = "37",
number = "3",
pages = "687--724",
month = mar,
year = "1972",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/0022-247X(72)90251-X",
ISSN = "0022-247x (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
bibdate = "Thu May 10 10:34:25 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0199.17102",
abstract = "This paper develops an explicit approximate method of
solving the integral equation $ f(x) = \int_0^\infty
h_1 (x - t) f(t) \, d t + g(x) $, $ x > 0 $, where $
g(x) $, $ h_1 (x) \in L^1 (R)L^2 (R) $, $ f(x) = g(x) =
0 $ if $ x < 0 $. The approximate solution depends upon
$2$ parameters, $ h > 0 $ and $ k \in (0, 1) $. It is
shown that if this equation has a unique solution, then
as $ h \rightarrow 0^+ $ and $ k \rightarrow 1^- $, the
approximate solution converges to the unique solution
whenever a unique solution $ f \in L^1 (R) \cap L^2 (R)
$ exists for every given $ g \in L^1 (R) \cap L^2 (R)
$, provided that $ h \sum_i|H(i h + (1 / 2)h)|^2
\rightarrow \int_R |H(x)|^2 \, d x $ as $ h \rightarrow
0^+ $, where $ H(x) $ is the Fourier transform of $ h_1
(t) $. An example is given which illustrates the
application of the method.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1972:BRB,
author = "Frank Stenger",
title = "Book Review: {{\booktitle{Quadrature Formulae}} (A.
Ghizetti and A. Ossicini)}",
journal = j-SIAM-REVIEW,
volume = "14",
number = "4",
pages = "662--662",
month = oct,
year = "1972",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1014118",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:06:44 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/14/4;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "October 1972",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1972:RQF,
author = "Frank Stenger",
title = "Review: {{\em Quadrature Formulae}}, by {A. Ghizetti
and A. Ossicini}",
journal = j-SIAM-REVIEW,
volume = "14",
number = "4",
pages = "662--662",
month = oct,
year = "1972",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1014118",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu May 10 17:28:01 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://links.jstor.org/sici?sici=0036-1445(197210)14:4<662:QF>2.0.CO%3B2-J",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1972:TMO,
author = "Frank Stenger",
title = "Transform methods for obtaining asymptotic expansions
of definite integrals",
journal = j-SIAM-J-MATH-ANA,
volume = "3",
number = "1",
pages = "20--30",
month = feb,
year = "1972",
CODEN = "SJMAAH",
DOI = "https://doi.org/10.1137/0503003",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0237.41007",
abstract = "With the condition $ \int R|d h(t)| < \infty $,
asymptotic approximations are obtained to the integral
$ \int R f(t)d h(\lambda t) $ over the real line $R$ as
$ \lambda \rightarrow \infty $, (a) by approximating $
h(x) = \int_R e^{ixt} \, d h(t) $ in a neighbourhood of
$ x = 0 $ and (b) by using a basis $ \{ \psi k(t)
\}^n_{k = 1} $, where in contrast to the usual case $
\psi k(t) $ need not be equal to $ t^{k - 1} $.",
acknowledgement = ack-nhfb,
classmath = "41A60 (Asymptotic problems in approximation) 42A38
(Fourier type transforms, one variable) 41A55
(Approximate quadratures)",
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1973:AAS,
author = "Frank Stenger",
title = "An algorithm for the approximate solution of
{Wiener--Hopf} integral equations",
journal = j-CACM,
volume = "16",
number = "11",
pages = "708--710",
month = nov,
year = "1973",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355611.362549",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:24:11 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Stenger73;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/cacm.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1970.bib",
ZMnumber = "0269.65063",
abstract = "An explicit approximate solution f\alpha(h) is given
for the equation $ f(t) = \int_0^\infty k(t -
\tau)f(\tau) \, d \tau + g(t) $, $ t > 0 $, where $ k,
g \in L_1 ( - \infty, \infty) \cap L_2 ( - \infty,
\infty) $, and it is assumed that the classical
Wiener--Hopf technique may be applied to yield a
solution $ f \in L_1 (0, \infty) \cap L_2 (0, \infty) $
for every such given $g$.",
acknowledgement = ack-nhfb,
classcodes = "B0290R (Integral equations); C4180 (Integral
equations)",
classmath = "65R20 (Integral equations (numerical methods))",
corpsource = "Univ. Utah, Salt Lake City, UT, USA",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "algorithm; approximate solution; convolution; Hopf;
integral equations; numerical methods; Wiener",
oldlabel = "Stenger73",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Stenger73",
}
@Article{Stenger:1973:ASC,
author = "Frank Stenger",
title = "The approximate solution of convolution-type integral
equations",
journal = j-SIAM-J-MATH-ANA,
volume = "4",
number = "3",
pages = "536--555",
month = may,
year = "1973",
CODEN = "SJMAAH",
DOI = "https://doi.org/10.1137/0504047",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0258.45005; 0232.45019",
acknowledgement = ack-nhfb,
classmath = "65R20 (Integral equations (numerical methods)) 45E10
(Integral equations of the convolution type)",
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1973:BRB,
author = "Frank Stenger",
title = "Book Review: {{\booktitle{Approximate Calculation of
Multiple Integrals}} (A. H. Stroud)}",
journal = j-SIAM-REVIEW,
volume = "15",
number = "1",
pages = "234--235",
month = jan,
year = "1973",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1015023",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:06:46 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/15/1;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1973",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1973:IFB,
author = "Frank Stenger",
title = "Integration formulae based on the trapezoidal
formula",
journal = j-J-INST-MATH-APPL,
volume = "12",
number = "1",
pages = "103--114",
year = "1973",
CODEN = "JMTAA8",
DOI = "https://doi.org/10.1093/imamat/12.1.103",
ISSN = "0020-2932",
ISSN-L = "0020-2932",
MRclass = "65D30",
MRnumber = "52 #2158",
MRreviewer = "G. Blanch",
bibdate = "Fri Apr 5 08:08:39 MST 2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/jinstmathappl.bib;
http://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib",
note = "See remarks \cite{Stenger:1977:RIF,Sack:1978:CSQ}.",
ZMnumber = "0262.65011",
acknowledgement = ack-nhfb,
classmath = "65D30 (Numerical integration)",
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1973:RAC,
author = "Frank Stenger",
title = "Review: {{\em Approximate Calculation of Multiple
Integrals}}, by {A. H. Stroud}",
journal = j-SIAM-REVIEW,
volume = "15",
number = "1",
pages = "234--235",
month = jan,
year = "1973",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1015023",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu May 10 17:21:25 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://links.jstor.org/sici?sici=0036-1445(197301)15:1<234:ACOMI>2.0.CO%3B2-7;
https://epubs.siam.org/doi/abs/10.1137/1015023",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Gearhart:1974:ACE,
author = "W. B. Gearhart and F. Stenger",
title = "An approximate convolution equation of a given
response",
crossref = "Kirby:1974:OCT",
pages = "168--196",
year = "1974",
MRclass = "93C05",
MRnumber = "MR0479523 (57 \#18947)",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0323.65006",
abstract = "This paper presents a number of linear numerical
methods which construct exponential sum approximations
by determining a convolution equation which is
approximately satisfied by the data $ f(t) $.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Rahman:1974:EPP,
author = "Q. I. Rahman and Frank Stenger",
title = "An extremal problem for polynomials with a prescribed
zero",
journal = j-PROC-AM-MATH-SOC,
volume = "43",
number = "1",
pages = "84--90",
month = mar,
year = "1974",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/s0002-9939-1974-0333123-0;
https://doi.org/10.2307/2039331",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://links.jstor.org/sici?sici=0002-9939(197403)43:1<84:AEPFPW>2.0.CO%3B2-2",
ZMnumber = "0288.30005",
acknowledgement = ack-nhfb,
classmath = "30C10 (Polynomials (one complex variable)) 30C15
(Zeros of polynomials, etc. (one complex variable))
30C75 (Extremal problems for (quasi-)conformal
mappings, other methods)",
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1974:CEB,
author = "Frank Stenger",
title = "On the convergence and error of the {Bubnov--Galerkin}
method",
journal = j-LECT-NOTES-MATH,
volume = "362",
pages = "434--450",
year = "1974",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/bfb0066604",
ISBN = "3-540-06602-0 (print), 3-540-37911-8 (e-book)",
ISBN-13 = "978-3-540-06602-6 (print), 978-3-540-37911-9
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
bibdate = "Fri May 9 19:07:48 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/lnm1970.bib",
ZMnumber = "0275.65033",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0066582",
book-URL = "http://www.springerlink.com/content/978-3-540-37911-9",
classmath = "65R20 (Integral equations (numerical methods)) 65N30
(Finite numerical methods (BVP of PDE)) 65J05 (General
theory of numerical methods in abstract spaces) 65L99
(Numerical methods for ODE) 65E05 (Numerical methods in
complex analysis) 65D30 (Numerical integration)",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@TechReport{Stenger:1974:CTD,
author = "Frank Stenger",
title = "Computing the topological degree of a mapping in {$
{\cal R}^n $}",
type = "Report",
institution = "National Oceanic and Atmospheric Administration",
address = "Washington, DC, USA",
year = "1974",
bibdate = "Thu May 10 10:10:06 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Chauvette:1975:ASN,
author = "Jean Chauvette and Frank Stenger",
title = "The approximate solution of the nonlinear equation {$
\Delta u = u - u^3 $}",
journal = j-J-MATH-ANAL-APPL,
volume = "51",
number = "1",
pages = "229--242",
month = jul,
year = "1975",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/0022-247x(75)90155-9",
ISSN = "0022-247x (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0311.65063",
acknowledgement = ack-nhfb,
classmath = "65N30 (Finite numerical methods (BVP of PDE)) 35J60
(Nonlinear elliptic equations) 35A35 (Theoretical
approximation to solutions of PDE)",
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Rosenberg:1975:LBA,
author = "Ivo G. Rosenberg and Frank Stenger",
title = "A Lower Bound on the Angles of Triangles Constructed
by Bisecting the Longest Side",
journal = j-MATH-COMPUT,
volume = "29",
number = "130",
pages = "390--395",
month = apr,
year = "1975",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/s0025-5718-1975-0375068-5;
https://doi.org/10.2307/2005558",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65N30 51M20 51M25 41A63 65H10",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "Graphics/imager/imager.75.bib;
Graphics/siggraph/75.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/mathcomp.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0025-5718(197504)29:130<390:ALBOTA>2.0.CO%3B2-H",
ZMnumber = "0302.65085",
acknowledgement = ack-nhfb,
classcodes = "B0290P (Differential equations); C4170 (Differential
equations)",
corpsource = "Univ. Montreal, Montreal, Que., Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "differential equations; finite element analysis;
infinite sequence; interior angle; lower bound;
numerical methods; partial; side; triangles constructed
by bisecting the longest",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
treatment = "T Theoretical or Mathematical",
}
@Article{Stenger:1975:AFW,
author = "Frank Stenger",
title = "An Analytic Function which is an Approximate
Characteristic Function",
journal = j-SIAM-J-NUMER-ANAL,
volume = "12",
number = "2",
pages = "239--254",
month = apr,
year = "1975",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0712022",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65E05 65D30 30D05 30E10",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/siamjnumeranal.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/SIAMJNUMERANAL/siamjnumeranal.bib;
http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0036-1429(197504)12:2<239:AAFWIA>2.0.CO%3B2-V",
ZMnumber = "0274.65010",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1975:ATD,
author = "Frank Stenger",
title = "An algorithm for the topological degree of a mapping
in $n$-space",
journal = j-BULL-AMS,
volume = "81",
number = "1",
pages = "179--182",
month = jan,
year = "1975",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/s0002-9904-1975-13698-6",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Wed Jun 08 11:51:35 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://projecteuclid.org/euclid.bams/1183536266",
ZMnumber = "0305.65023",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1975:CBC,
author = "Frank Stenger",
title = "Connection between a {Cauchy} system representation of
{Kalaba} and {Fourier} transforms",
journal = j-APPL-MATH-COMP,
volume = "1",
number = "1",
pages = "83--91",
month = jan,
year = "1975",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/0096-3003(75)90032-6",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0338.65063",
acknowledgement = ack-nhfb,
classmath = "65R20 (Integral equations (numerical methods)) 42A38
(Fourier type transforms, one variable)",
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1975:CTD,
author = "Frank Stenger",
title = "Computing the topological degree of a mapping in {$
{\cal R}^n $}",
journal = j-NUM-MATH,
volume = "25",
number = "1",
pages = "23--38",
month = mar,
year = "1975",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/bf01419526",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0316.55007",
abstract = "Let P be connected n-dimensional polyhedron, and let $
b(P) = \sum_{j = 1}^m t_j[Y_1 (j), \ldots {}, Y_n(j)] $
be the oriented boundary of $P$ in terms of oriented $
n - 1 $ simplexes $ t_j[Y_1 (j), \ldots {}, Y_n(j)] $,
where $ Y_i(j) $ is a vertex of a simplex and $ t_j =
\pm 1 $. Let $ F = (f_1, \ldots {}, f_n) $ be a vector
of real continuous functions defined on $P$, and let $
F \neq \theta \equiv (0, \ldots {}, 0) $ on $ b(P) $.
Assume that for $ 1 < \mu \leq n $, and $ \Phi \mu =
(\psi^1, \ldots {}, \psi^\mu) $ where $ \psi^i = f^{ji}
$, $ j_k \not = j_l $ if $ k \not = l $, the sets $
S(A_\mu) = \{ X \in b(P) : \Phi_\mu (X) / | \Phi_\mu
(X)| = A_\mu \} \cap H_\mu $ and $ b(P) - S(A_\mu) $
consist of a finite number of connected subsets of $
b(P) $, for all vectors $ A_\mu = (\pm 1, 0, \ldots {},
0) $, $ (0, \pm 1, 0, \ldots {}, 0), \ldots {}, (0,
\ldots {}, 0, \pm 1) $ and for all $ \mu - 1 $
dimensional simplexes $ H_\mu $ on $ b(P) $. It is
shown that if $m$ is sufficiently large, and $
\max_{(j; 1 \leq k < l \leq n)} |Y k(j) - Y l(j)| $
sufficiently small, then $ d(F, P, \theta) $, the
topological degree of $F$ at $ \theta $ relative to
$P$, is given by $ d(F, P, \theta) = (1) / (2 n n!)
\sum_{j = 1}^m t_j \Delta (\sgn F(Y_1^{(j)}, \ldots {},
\sgn F(Y_n^{(j)}))) $.",
acknowledgement = ack-nhfb,
classification = "B0250 (Combinatorial mathematics); B0290R (Integral
equations); C1160 (Combinatorial mathematics); C4180
(Integral equations)",
classmath = "55M25 (Degree, etc.)",
corpsource = "Dept. of Math., Univ. of Utah, Salt Lake City, UT,
USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "$n$ dimensional polyhedron; continuous functions;
mapping; simplex; subsets; topological degree;
topology",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
treatment = "T Theoretical or Mathematical",
}
@Article{Stenger:1975:LBA,
author = "F. Stenger and I. Rosenberg",
title = "A lower Bound on the Angles of Triangles Constructed
by Bisecting the Longest Side",
journal = j-MATH-COMPUT,
volume = "29",
number = "130",
pages = "390--395",
year = "1975",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1975-0375068-5",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Graphics/imager/1975.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Graphics/siggraph/1975.bib",
URL = "http://www.ams.org/journals/mcom/1975-29-130/S0025-5718-1975-0375068-5/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Harvey:1976:TDA,
author = "Charles Harvey and Frank Stenger",
title = "A two-dimensional analogue to the method of bisections
for solving nonlinear equations",
journal = j-QUART-APPL-MATH,
volume = "33",
number = "??",
pages = "351--368",
month = "????",
year = "1976",
CODEN = "QAMAAY",
DOI = "https://doi.org/10.1090/qam/455361",
ISSN = "0033-569X (print), 1552-4485 (electronic)",
ISSN-L = "0033-569X",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://www.ams.org/journals/qam/1976-33-04/S0033-569X-1976-0455361-7/",
ZMnumber = "0365.65032",
acknowledgement = ack-nhfb,
classmath = "65H10 (Systems of nonlinear equations (numerical
methods))",
fjournal = "Quarterly of Applied Mathematics",
journal-URL = "http://www.ams.org/journals/qam",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InCollection{Ikebe:1976:NSH,
author = "Y. Ikebe and T. Y. Li and F. Stenger",
booktitle = "Theory of approximation, with applications (Proc.
Conf., Univ. Calgary, Calgary, Alta., 1975; dedicated
to the memory of Eckard Schmidt)",
title = "The numerical solution of the {Hilbert} problem",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "338--358",
year = "1976",
MRclass = "65R05",
MRnumber = "MR0440972 (55 \#13840)",
MRreviewer = "Jacob Steinberg",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@TechReport{Nickel:1976:EBU,
author = "Karl Nickel",
title = "Error Bounds and Uniqueness for the Solutions of
Nonlinear, Strongly Coupled, Parabolic Systems of
Differential Equations",
type = "MRC Technical Summary Report",
number = "1596",
institution = "Mathematics Research Center, US Department of the
Army",
address = "Madison, WI, USA",
pages = "20",
year = "1976",
bibdate = "Wed May 09 10:22:08 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
xxauthor = "Frank Stenger",
xxnote = "Check: conflicting library catalog data??",
}
@Article{Stenger:1976:ACE,
author = "F. Stenger and W. Petrick and Z. Rotsides",
title = "Algorithm for Computing Electromagnetic Scattered
Field from an Axially-Symmetric Body with an Impedance
Boundary Condition",
journal = j-SIAM-REVIEW,
volume = "18",
number = "4",
pages = "828--829",
month = "????",
year = "1976",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1018136",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "https://epubs.siam.org/doi/abs/10.1137/1018136",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1976:AWC,
author = "Frank Stenger",
title = "Approximations via {Whittaker}'s cardinal function",
journal = j-J-APPROX-THEORY,
volume = "17",
number = "3",
pages = "222--240",
month = jul,
year = "1976",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1016/0021-9045(76)90086-1",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "41A30",
MRnumber = "MR0481786 (58 \#1885)",
MRreviewer = "R. S. Dahiya",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0332.41013",
abstract = "Whittaker's cardinal function is used to derive
various types of extremely accurate approximation
procedures, along with error bounds, for interpolating,
integrating, and evaluating the Fourier (over $ ( -
\infty, \infty) $ only) and the Hilbert (over $ ( -
\infty, \infty) $, $ (0, \infty) $, and $ ( - 1, 1) $ )
transforms of functions.",
acknowledgement = ack-nhfb,
classmath = "41A30 (Approximation by other special function
classes) 65D20 (Computation of special functions) 65D15
(Algorithms for functional approximation)",
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Hanson:1977:DSS,
author = "F. Hanson and J. M. Steele and F. Stenger",
title = "Distinct sums over subsets",
journal = j-PROC-AM-MATH-SOC,
volume = "66",
number = "1",
pages = "179--180",
month = sep,
year = "1977",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/S0002-9939-1977-0447167-4",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "10L10",
MRnumber = "MR0447167 (56 \#5482)",
MRreviewer = "S. L. G. Choi",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://links.jstor.org/sici?sici=0002-9939(197709)66:1<179:SNDSOS>2.0.CO%3B2-9;
http://www.ams.org/journals/proc/1977-066-01/S0002-9939-1977-0447167-4/",
ZMnumber = "0367.10046",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1977:RIF,
author = "Frank Stenger",
title = "Remarks on {``Integration formulae based on the
trapezoidal formula'' (J. Inst. Math. Appl. {\bf 12}
(1973), 103--114)}",
journal = j-J-INST-MATH-APPL,
volume = "19",
number = "2",
pages = "145--147",
year = "1977",
CODEN = "JMTAA8",
DOI = "https://doi.org/10.1093/imamat/19.2.145",
ISSN = "0020-2932",
ISSN-L = "0020-2932",
MRclass = "65D30",
MRnumber = "MR0440879 (55 \#13747)",
MRreviewer = "G. Blanch",
bibdate = "Fri Apr 5 07:41:12 MST 2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
note = "See \cite{Stenger:1973:IFB,Sack:1978:CSQ}.",
ZMnumber = "0353.65014",
acknowledgement = ack-nhfb,
classmath = "65D30 (Numerical integration)",
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1978:OCM,
author = "Frank Stenger",
title = "Optimal convergence of minimum norm approximations in
{$ H_p $}",
journal = j-NUM-MATH,
volume = "29",
number = "4",
pages = "345--362",
month = apr,
year = "1978",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/bf01432874",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65D30 (30A78)",
MRnumber = "MR0483329 (58 \#3342)",
MRreviewer = "Hans-Jurgen Albrand",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/nummath.bib;
http://www.math.utah.edu/pub/tex/bib/nummath.bib",
ZMnumber = "0437.41030",
acknowledgement = ack-nhfb,
classification = "A0260 (Numerical approximation and analysis); B0290F
(Interpolation and function approximation); C4130
(Interpolation and function approximation)",
classmath = "41A55 (Approximate quadratures) 65D32 (Quadrature
formulas (numerical methods)) 65D15 (Algorithms for
functional approximation)",
corpsource = "Dept. of Math., Univ. of Utah, Salt Lake City, UT,
USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "convergence of numerical methods; function
approximation; interpolation quadrature; minimum norm
approximation convergence; minimum norm approximations
in $H_p$; optimal convergence",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
treatment = "T Theoretical or Mathematical",
}
@Article{Stenger:1978:ULE,
author = "Frank Stenger",
title = "Upper and lower estimates on the rate of convergence
of approximations in {$ H_p $}",
journal = j-BULL-AMS,
volume = "84",
number = "1",
pages = "145--148",
year = "1978",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/s0002-9904-1978-14446-2",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
MRclass = "65D30 (30A78)",
MRnumber = "MR0474714 (57 \#14348)",
MRreviewer = "V. Kabaila",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://projecteuclid.org/euclid.bams/1183540395",
ZMnumber = "0381.65014",
acknowledgement = ack-nhfb,
classmath = "65D32 (Quadrature formulas (numerical methods)) 41A55
(Approximate quadratures)",
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Lundin:1979:CTA,
author = "L. Lundin and F. Stenger",
title = "Cardinal-type approximations of a function and its
derivatives",
journal = j-SIAM-J-MATH-ANA,
volume = "10",
number = "1",
pages = "139--160",
month = jan,
year = "1979",
CODEN = "SJMAAH",
DOI = "https://doi.org/10.1137/0510016",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "41A30 (30E10)",
MRnumber = "MR516759 (81c:41043)",
MRreviewer = "Hans-Peter Helfrich",
bibdate = "Sat Dec 5 18:14:13 MST 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "https://epubs.siam.org/doi/abs/10.1137/0510016",
ZMnumber = "0399.41018",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1979:SGM,
author = "Frank Stenger",
title = "A ``{Sinc--Galerkin}'' method of solution of boundary
value problems",
journal = j-MATH-COMPUT,
volume = "33",
number = "145",
pages = "85--109",
month = jan,
year = "1979",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/s0025-5718-1979-0514812-4;
https://doi.org/10.2307/2006029",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65L10 (65N30)",
MRnumber = "MR514812 (80b:65112)",
MRreviewer = "Rolf Rannacher",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/MATHCOMP/mathcomp1970.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0025-5718(197901)33:145<85:A%22MOSO>2.0.CO%3B2-S",
ZMnumber = "0402.65053",
abstract = "This paper illustrates the application of a
`Sinc--Galerkin' method to the approximate solution of
linear and nonlinear second order ordinary differential
equations, and to the approximate solution of some
linear elliptic and parabolic partial differential
equations in the plane. The method is based on
approximating functions and their derivatives by use of
the Whittaker cardinal function. The DE is reduced to a
system of algebraic equations via accurate explicit
approximation of the inner products, the evaluation of
which does not require any numerical integration.",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation);
C4170 (Differential equations)",
classmath = "65L10 (Boundary value problems for ODE (numerical
methods)) 65N30 (Finite numerical methods (BVP of PDE))
65N35 (Collocation methods (BVP of PDE)) 33B10
(Elementary functions) 42A10 (Trigonometric
approximation)",
corpsource = "Dept. of Math., Univ. of British Columbia, Vancouver,
BC, Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "approximate solution; approximating functions;
approximation; boundary value problems; boundary-value
problems; cardinal function; Convergence Rate;
differential equations; function; Galerkin Procedure;
nonlinear; Numerical Methods; Optimal; Ordinary
Differential Equations; partial; Second Order Boundary
Value Problem; second order ordinary differential
equations; Sinc Galerkin method; Whittaker; Whittaker
Cardinal Function",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
treatment = "T Theoretical or Mathematical",
}
@Article{Stenger:1979:UTT,
author = "Frank Stenger and Steven A. Johnson",
title = "Ultrasonic transmission tomography based on the
inversion of the {Helmholtz} wave equation for plane
and spherical wave insonification",
journal = j-APPL-MATH-NOTES,
volume = "4",
number = "3--4",
pages = "102--127",
year = "1979",
CODEN = "????",
ISSN = "0700-9224",
ISSN-L = "0700-9224",
MRclass = "76Q05 (45B05 92A07)",
MRnumber = "MR551083 (81d:76083)",
MRreviewer = "V. M. Babich",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0434.73024",
acknowledgement = ack-nhfb,
classmath = "74J10 (Bulk waves) 35J05 (Laplace equation, etc.)",
fjournal = "Applied Mathematics Notes",
keywords = "inversion of Helmholtz wave equation; planar
grey-scale view; ultrasonic transmission tomography",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Ball:1980:EIH,
author = "James Ball and Steven A. Johnson and Frank Stenger",
title = "Explicit Inversion of the {Helmholtz} Equation for
Ultra-Sound Insonification and Spherical Detection",
crossref = "Wang:1980:AIV",
pages = "451--461",
year = "1980",
DOI = "https://doi.org/10.1007/978-1-4684-3755-3_26",
bibdate = "Fri Nov 7 08:39:48 MST 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1980:AES,
author = "F. Stenger and M. Hagmann and J. Schwing",
title = "An algorithm for the electromagnetic scattering due to
an axially symmetric body with an impedance boundary
condition",
journal = j-J-MATH-ANAL-APPL,
volume = "78",
number = "2",
pages = "531--573",
month = dec,
year = "1980",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/0022-247X(80)90165-1",
ISSN = "0022-247x (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "78A45 (65N30)",
MRnumber = "MR601553 (82b:78020)",
MRreviewer = "D. L. Colton",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "https://www.sciencedirect.com/science/article/pii/0022247X80901651",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Stenger:1981:AUT,
author = "Frank Stenger",
title = "An algorithm for ultrasonic tomography based on
inversion of the {Helmholtz} equation",
crossref = "Allgower:1981:NSN",
pages = "371--406",
year = "1981",
DOI = "https://doi.org/10.1007/BFb0090689",
MRclass = "92A07 (65D15 65N99)",
MRnumber = "MR644338 (83c:92020)",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0461.65085",
acknowledgement = ack-nhfb,
classmath = "65Z05 (Applications to physics) 76K05 (Hypersonic
flows) 65N30 (Finite numerical methods (BVP of PDE))
35J05 (Laplace equation, etc.)",
keywords = "chapeau splines; Helmholtz equation; Rytov
approximation; ultrasonic tomography",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1981:NMB,
author = "Frank Stenger",
title = "Numerical methods based on {Whittaker} cardinal, or
sinc functions",
journal = j-SIAM-REVIEW,
volume = "23",
number = "2",
pages = "165--224",
month = apr,
year = "1981",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1023037",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65D30 (41-02 41A30 65-02)",
MRnumber = "MR618638 (83g:65027)",
MRreviewer = "H. E. Fettis",
bibdate = "Mon Jan 20 09:20:15 MST 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://links.jstor.org/sici?sici=0036-1445(198104)23:2<165:NMBOWC>2.0.CO%3B2-S",
ZMnumber = "0461.65007",
abstract = "This paper summarizes the results known to date for
using sinc functions composed with other functions as
bases for approximations in numerical analysis.
Described are methods of interpolation and
approximation of functions and their derivatives,
quadrature, the approximate evaluation of transforms
(Hilbert, Fourier, Laplace, Hankel and Mellin) and the
approximate solution of differential and integral
equations. The methods have many advantages over
classical methods which use polynomials as bases. In
addition, all of the methods converge at an optimal
rate, if singularities on the boundary of approximation
are ignored.",
acknowledgement = ack-nhfb,
classmath = "65Dxx (Numerical approximation) 65R10 (Integral
transforms (numerical methods)) 41-XX (Approximation
theory) 44A10 (Laplace transform) 44A15 (Special
transforms) 42A38 (Fourier type transforms, one
variable) 65T40 (Trigonometric approximation and
interpolation) 65Lxx (Numerical methods for ODE) 65E05
(Numerical methods in complex analysis) 30E10
(Approximation in the complex domain) 30C30 (Numerical
methods in conformal mapping theory)",
fjournal = "SIAM Review. A Publication of the Society for
Industrial and Applied Mathematics",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "Fourier-transform; Hankel-transform; Hilberttransform;
interpolation; Laplace-transform; Mellin-transform;
quadrature; Whittaker cardinal function",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InCollection{Johnson:1982:WEI,
author = "Steven A. Johnson and Frank Stenger and Calvin Wilcox
and James Ball and Michael J. Berggren",
booktitle = "Acoustical imaging, Vol. 11 (Monterey, Calif., 1981)",
title = "Wave equations and inverse solutions for soft tissue",
publisher = "Plenum",
address = "New York",
pages = "409--424",
year = "1982",
DOI = "https://doi.org/10.1007/978-1-4684-1137-9_27",
MRclass = "92A07 (73P10)",
MRnumber = "MR690072 (84e:92008)",
MRreviewer = "G. Eason",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Sikorski:1982:OQA,
author = "K. Sikorski",
title = "Optimal quadrature algorithms in {$ H_p $} spaces",
journal = j-NUM-MATH,
volume = "39",
number = "3",
pages = "405--410",
month = oct,
year = "1982",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01407871",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65D30 (41A55)",
MRnumber = "84c:65045",
MRreviewer = "B. Boyanov",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/nummath.bib;
http://www.math.utah.edu/pub/tex/bib/nummath.bib",
URL = "https://link.springer.com/article/10.1007/BF01407871",
acknowledgement = ack-nhfb,
classification = "B0290F (Interpolation and function approximation);
B0290M (Numerical integration and differentiation);
C4130 (Interpolation and function approximation); C4160
(Numerical integration and differentiation)",
corpsource = "Dept. of Math., Univ. of Utah, Salt Lake City, UT,
USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "approximation; approximation theory; complex plane;
conformal map; F. Stenger; function approximation;
integration; optimal error quadrature; simply connected
domain; unit disc",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
treatment = "T Theoretical or Mathematical",
}
@InCollection{Stenger:1982:AUI,
author = "Frank Stenger",
editor = "John P. Powers",
booktitle = "Acoustical imaging, Vol. 11 (Monterey, Calif., 1981)",
title = "Asymptotic ultrasonic inversion based on using more
than one frequency",
publisher = "Plenum",
address = "New York, NY, USA",
pages = "425--444",
year = "1982",
DOI = "https://doi.org/10.1007/978-1-4684-1137-9_28",
ISBN = "1-4684-1139-X, 1-4684-1137-3 (e-book)",
ISBN-13 = "978-1-4684-1139-3, 978-1-4684-1137-9 (e-book)",
ISSN = "0270-5117 (print), 2215-1869 (electronic)",
ISSN-L = "0270-5117",
LCCN = "QC1-75",
MRclass = "76Q05",
MRnumber = "MR690073 (84h:76036)",
MRreviewer = "E. Pinney",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-1-4684-1137-9",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Stenger:1983:ANT,
author = "Frank Stenger and Michael J. Berggren and Steven A.
Johnson and Y. Li",
title = "An Adaptive, Noise Tolerant, Frequency Extrapolation
Algorithm for Diffraction Corrected Ultrasound
Tomography",
crossref = "McAvoy:1983:IUS",
pages = "726--731",
year = "1983",
DOI = "https://doi.org/10.1109/ULTSYM.1983.198154",
bibdate = "Wed May 09 18:07:17 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://ieeexplore.ieee.org/iel5/10283/32716/01535094.pdf?tp=&arnumber=1535094&isnumber=32716",
abstract = "A procedure was previously developed based on
algorithms for rational function frequency
extrapolation and 1-norm averaging to circumvent both
the effects of noise and the errors due to refracted
curved paths in solving the inverse scattering problem
in ultrasonic imaging. In this paper, the order of the
first two algorithms is reversed, that is the l1
averaging procedure is first applied and then the
rational function procedure is carried out,
extrapolating to infinite frequency. An adaptive method
for choosing the best rational function expansion is
also employed. The underlying ideas of the procedure
are described, and examples of reconstruction in the
presence and absence of Gaussian noise are illustrated.
These results are then compared with results of
previous experiments",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Eiger:1984:BMS,
author = "A. Eiger and K. Sikorski and F. Stenger",
title = "A Bisection Method for Systems of Nonlinear
Equations",
journal = j-TOMS,
volume = "10",
number = "4",
pages = "367--377",
month = dec,
year = "1984",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2701.2705",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65H10",
MRnumber = "MR792001 (86g:65102)",
bibdate = "Sun Sep 04 20:32:29 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
ZMnumber = "0548.65033",
abstract = "This paper describes an algorithm for the solution of
a system of nonlinear equations $ F(X) = \theta $,
where $ t h e t a = (0, \ldots {}, 0) $ is an element
of $ R^n $, and $F$ is a given continuous
transformation of $n$-dimensional simplex $S$ into $
R^n (n \geq 2) $. The program is based on computation
of the topological degree (deg) of a mapping and a
simplex-bisection scheme. The algorithm is primarily
useful for small $n$ ($ n \leq 5 $ ), since the amount
of work needed to compute the topological degree for
large $n$ is significant. The size of the original
simplex is arbitrary, and the algorithm is globally
convergent in a residual sense. The algorithm is
illustrated on several simplified model problems.",
acknowledgement = ack-nhfb,
fjournal = "Association for Computing Machinery. Transactions on
Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Johnson:1984:FIA,
author = "S. A. Johnson and Y. Zhou and M. K. Tracy and M. J.
Berggren and F. Stenger",
title = "Fast Iterative Algorithms for Inverse Scattering
Solutions of the {Helmholtz} and {Riccati} Wave
Equations",
crossref = "Kaveh:1984:AIP",
pages = "75--87",
year = "1984",
bibdate = "Wed May 09 19:00:11 2007",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
abstract = "Solving the inverse scattering problem for the
Helmholtz wave equation without employing the Born or
Rytov approximations is a challenging problem, but some
slow iterative methods have been proposed. One such
method suggested and demonstrated by us is based on
solving systems of nonlinear algebraic equations that
are derived by applying the method of moments to a sinc
basis function expansion of the fields and scattering
potential. In the past, we have solved these equations
for a 2-D object of $ n \times n $ pixels in a time
proportional to $ n^5 $. We now describe further
progress in the development of new methods based on FFT
convolution and the concept of backprojection, which
solves these equations in time proportional to $ n^3
\times \log n $.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Johnson:1984:ISS,
author = "S. A. Johnson and Y. Zhou and M. L. Tracey and M. J.
Berggren and F. Stenger",
title = "Inverse scattering solutions by a sinc basis, multiple
source, moment method. {Part III}: {Fast} algorithms",
journal = j-ULTRASONIC-IMAGING,
volume = "6",
number = "1",
pages = "103--116",
month = jan,
year = "1984",
CODEN = "ULIMD4",
DOI = "https://doi.org/10.1016/0161-7346(84)90010-5",
ISSN = "0161-7346 (print), 1096-0910 (electronic)",
ISSN-L = "0161-7346",
bibdate = "Thu May 10 16:30:30 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
fjournal = "Ultrasonic Imaging",
journal-URL = "http://www.sciencedirect.com/science/journal/01617346",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Johnson:1984:RDS,
author = "S. A. Johnson and M. J. Berggren and F. Stenger and C.
H. Wilcox and E. Jensen",
editor = "Anonymous",
booktitle = "Proceedings of the 29th Annual Meeting of the American
Institute of Ultrasound in Medicine, and the 13th
Annual Meeting of the Society of Diagnostic Medical
Sonographers, 16--19 September 1984, Kansas City, MO,
USA",
title = "Recent Developments in Solving the Exact Acoustic
Inverse Scattering Problem",
publisher = "American Institute of Ultrasound in Medicine",
address = "Bethesda, MD, USA",
bookpages = "iii + 231",
pages = "126--??",
year = "1984",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Wed May 09 18:56:24 2007",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
abstract = "Ultrasound has been used in the pulsed echo (i.e.,
B-scan) mode for many decades to produce images of the
human body. In the single scan mode the spatial
resolution is presently limited by the transducer
aperture. In the compound scan mode the resolution is
degraded by lack of registration due to the
inhomogeneous speed of sound in the body. Increasing
the aperture of the transducer, or using synthetic
apertures can improve resolution up to the theoretical
limit of one-half wave length (the effective
wavelength) if corrections for refraction are
incorporated into the imaging process. We have
developed several new algorithms for finding tissue
properties with high quantitative accuracy and high
spatial resolution. A decription is given of these
fast, robust inverse scattering techniques that provide
distortionless, quantitative images with 1/2 wavelength
resolution.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Johnson:1984:UTG,
author = "Steven A. Johnson and Frank Stenger",
title = "Ultrasound Tomography by {Galerkin} or Moment
Methods",
crossref = "Nalcioglu:1984:STI",
pages = "254--276",
year = "1984",
DOI = "https://doi.org/10.1007/978-3-642-93253-3_10",
bibdate = "Fri Nov 7 08:39:43 MST 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Sikorski:1984:AFS,
author = "K. Sikorski and F. Stenger and J. Schwing",
title = "{Algorithm 614}: {A FORTRAN} Subroutine for Numerical
Integration in {$ H_p $}",
journal = j-TOMS,
volume = "10",
number = "2",
pages = "152--160",
month = jun,
year = "1984",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/399.449",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D32 (65-04)",
MRnumber = "MR791983 (87a:65054b)",
MRreviewer = "J. B. Butler, Jr.",
bibdate = "Wed Dec 4 10:59:43 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Compiler/fortran.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Compiler/FORTRAN/fortran2.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Compiler/fortran2.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/toms.bib;
http://www.math.utah.edu/pub/tex/bib/fortran2.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib;
Theory/toms.bib",
abstract = "An algorithm is given implementing a method for
optimal quadrature in $ H_p $ space, presented in an
accompanying paper. The procedure is based on the
computation of the trapezoidal approximation to the
integral, together with transformation of the interval
of integration.",
acknowledgement = ack-nhfb,
fjournal = "Association for Computing Machinery. Transactions on
Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "J. B. Butler, Jr.",
}
@Article{Sikorski:1984:FSI,
author = "K. Sikorski and F. Stenger and J. Schwing",
title = "A {Fortran} Subroutine for Integration in $ {H}_p $
Spaces",
journal = j-TOMS,
volume = "10",
number = "2",
pages = "152--157",
month = jun,
year = "1984",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/399.449",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Compiler/FORTRAN/fortran2.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Compiler/fortran2.bib;
Misc/acm.bib",
URL = "https://dl.acm.org/citation.cfm?doid=399.449",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
xxpages = "140--160",
}
@Article{Sikorski:1984:OQS,
author = "K. Sikorski and F. Stenger",
title = "Optimal Quadratures in {$ H_p $} Spaces",
journal = j-TOMS,
volume = "10",
number = "2",
pages = "140--151",
month = jun,
year = "1984",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/399.448",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D32",
MRnumber = "MR791982 (87a:65054a)",
MRreviewer = "J. B. Butler, Jr.",
bibdate = "Sun Sep 04 20:09:42 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0542.65012",
abstract = "A description is given of a family of optimal
quadrature formulas for approximating the integral $
\int f(z) \, d z $ over $ w^{-1} $, where $f$ belongs
to the Hardy's class $ H_p(D) $, $ 1 < p \leq + \infty
$, $D$ is an open simply connected domain in the
complex plane, and $w$ is a conformal map of $D$ onto
the unit disk $U$. Four different classes of domains $
D_d^i $, $ 0 < d \leq \pi / 2 $, $ i 1, 2, 3, 4 $ are
considered. If the user cannot specify the parameters
$p$ or $d$, a heuristic-termination algorithm is
proposed. The results of numerical tests are
included.",
acknowledgement = ack-nhfb,
fjournal = "Association for Computing Machinery. Transactions on
Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "J. B. Butler, Jr.",
}
@Article{Stenger:1984:PSR,
author = "Frank Stenger",
title = "Polynomial, sinc and rational function methods for
approximating analytic functions",
journal = j-LECT-NOTES-MATH,
volume = "1105",
pages = "49--72",
year = "1984",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0072399",
ISBN = "3-540-13899-4 (print), 3-540-39113-4 (e-book)",
ISBN-13 = "978-3-540-13899-0 (print), 978-3-540-39113-5
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
MRclass = "30E10 (41A20 65E05)",
MRnumber = "MR783261 (87c:30055)",
bibdate = "Fri May 9 19:07:44 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/UIA.bib;
http://www.math.utah.edu/pub/tex/bib/lnm1980.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0072399/",
ZMnumber = "0577.41012",
abstract = "This paper presents practically useful constructive
linear methods of approximation of analytic functions
by polynomials, sinc functions and rational functions.
Spaces of functions of the type frequently encountered
in applications are described for approximation by each
method. Within these spaces, the rate of convergence of
each approximation is nearly optimal.",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0072395",
book-URL = "http://www.springerlink.com/content/978-3-540-39113-5",
classmath = "41A30 (Approximation by other special function
classes) 41A10 (Approximation by polynomials) 41A20
(Approximation by rational functions)",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
keywords = "constructive linear methods of approximation; rate of
convergence",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InCollection{Stenger:1984:RFF,
author = "F. Stenger and M. J. Berggren and S. A. Johnson and C.
H. Wilcox",
booktitle = "Wave phenomena: modern theory and applications
(Toronto, 1983)",
title = "Rational function frequency extrapolation in
ultrasonic tomography",
volume = "97",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "19--34",
year = "1984",
MRclass = "92A07 (76Q05)",
MRnumber = "MR801551 (86j:92006)",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
series = "North-Holland Math. Stud.",
ZMnumber = "0577.65110",
abstract = "The authors describe a procedure for solving the
inverse scattering problem in ultrasonic imaging.
Although the derivation of the method is based on the
Helmholtz equation model $ \del^2 u + k^2 (l + f)u = 0
$ it is applicable to any model for which the spatial
sound pressure $ u = u(r^-, k) $ satisfies an
asymptotic equality of the form $ 0 (k) = 1 / i k.L o g
u(r^-, k)|r^-s r^-d = \int p F(r^-) \, d s + O(k -
\sigma) $, $ k \rightarrow \infty $ where $k$ is
proportional to the frequency, $P$ denotes the ray path
along which pressure wave travels from the source point
$ r^-s $ to the detector point $ r^-d $ and $ \sigma $
is a positive constant. The method is based on
predicting $ \phi (\infty) = \int p F(r^-) \, d s $ via
a rational function procedure, using several values $
\phi (k_1), \phi (k_2), \ldots {}, \phi (k_{2m + l}) $.
A perturbation method for correcting for curved ray
paths is also described. The algorithm can also be
modified to image materials with more complicated
frequency dependent attenuation. Examples of images
reconstructed from computer simulated data with and
without Gaussian additive noise are given. The
beneficial effect of a noise tolerant first norm data
fitting algorithm in improving image quality is
shown.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Stenger:1984:SMA,
author = "Frank Stenger",
title = "{Sinc} methods of approximate solution of partial
differential equations",
crossref = "Miller:1984:CMA",
pages = "40--64",
year = "1984",
MRclass = "65M99 (65N99)",
MRnumber = "MR794700",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0581.65082",
abstract = "This paper is devoted to the approximation of
solutions of boundary value problems based upon some
particular expansion of functions involving the
so-called sinc function.",
acknowledgement = ack-nhfb,
classmath = "65N35 (Collocation methods (BVP of PDE)) 35G15
(Boundary value problems for linear higher-order PDE)",
keywords = "sinc function expansion; Whittaker cardinal function",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "P.-L. Lions",
}
@InProceedings{Kim:1985:ISS,
author = "W. W. Kim and Michael J. Berggren and Steven A.
Johnson and Frank Stenger and Calvin H. Wilcox",
title = "Inverse Scattering Solutions to the Exact {Riccati}
Wave Equations by Iterative {RYTOV} Approximations and
Internal Field Calculations",
crossref = "McAvoy:1985:IUS",
pages = "878--882",
year = "1985",
DOI = "https://doi.org/10.1109/ULTSYM.1985.198638",
bibdate = "Wed May 09 18:02:49 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://ieeexplore.ieee.org/iel5/10285/32718/01535578.pdf?tp=&arnumber=1535578&isnumber=32718",
abstract = "A fixed-point iterative method has been applied to
solve the Riccati equation for ultrasonic waves. An
algorithm is developed to calculate the exact field
when an incident plane wave is scattered by a known
object, whose refractive index and/or size are so large
that the Born or Rytov approximations would not apply.
Another algorithm reconstructs the scattering
potentials from given scattered phases measured by sets
of linear detectors. Simulation results are shown for
circularly symmetric cylindrical objects. Limitations
of the fixed-point algorithm are demonstrated; a Newton
type iterative algorithm without these limitations is
suggested.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Berggren:1986:UIS,
author = "M. J. Berggren and S. A. Johnson and B. L. Carruth and
W. W. Kim and F. Stenger and P. K. Kuhn",
title = "Ultrasound Inverse Scattering Solutions from
Transmission and\slash or Reflection Data",
crossref = "Nalcioglu:1986:IWP",
volume = "671",
pages = "114--121",
year = "1986",
bibdate = "Wed May 09 19:10:14 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
abstract = "Although historically the Born or Rytov linear
approximations have received a great deal of attention,
it is now more apparent that only a full nonlinear
formulation of the inverse scattering problem, such as
those we have developed, provide the accuracy for
quantitative clinical ultrasound imaging. Our inverse
scattering solutions have been developed to reconstruct
quantitative images of speed of sound, density, and
absorption using the exact Helmholtz wave equation
without perturbation approximations. We have developed
fast algorithms which are based upon Galerkin or moment
discretizations and use various iterative solution
techniques such as back propagation and descent
methods. In order to reconstruct images with
reflection-only scanner geometries we have extended our
algorithms to include multiple frequency data. We have
demonstrated a procedure for imaging inhomogeneous
density distributions. We also discuss the significance
and potential applications of these new methods.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Schaffer:1986:MSM,
author = "Steve Schaffer and Frank Stenger",
title = "Multigrid-sinc methods",
journal = j-APPL-MATH-COMP,
volume = "19",
number = "1--4",
pages = "311--319",
month = jul,
year = "1986",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/0096-3003(86)90110-4",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
MRclass = "65M60",
MRnumber = "MR849840",
bibdate = "Thu Feb 27 09:47:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
note = "Second Copper Mountain conference on multigrid methods
(Copper Mountain, Colo., 1985).",
ZMnumber = "0612.65046",
abstract = "A Galerkin method using Whittaker cardinal or ``sinc''
functions as basis functions is described for the
solution of boundary value problems. When the solution
is analytic in the interior of the domain, the error of
approximation using $ 2 N + 1 $ points is $ O(e^{-
\gamma N^{1 / 2}}) $ even if derivatives of the
solution are singular at the boundaries. A multigrid
method with overall complexity $ O(N \log N) $ is used
to solve the discrete equations. This paper contains a
description of the multigrid-sinc algorithm along with
some preliminary numerical results for two-point
boundary value problems.",
acknowledgement = ack-nhfb,
classmath = "65L10 (Boundary value problems for ODE (numerical
methods)) 65L60 (Finite numerical methods for ODE)
34B05 (Linear boundary value problems of ODE)",
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
keywords = "complexity; Galerkin method; multigrid-sinc algorithm;
numerical results; sinc series expansion",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "S. F. McCormick",
}
@Article{Stenger:1986:ENO,
author = "Frank Stenger",
title = "Explicit, nearly optimal, linear rational
approximation with preassigned poles",
journal = j-MATH-COMPUT,
volume = "47",
number = "175",
pages = "225--252",
month = jul,
year = "1986",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/s0025-5718-1986-0842132-0;
https://doi.org/10.2307/2008091",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "41A20 (41A25 65D15)",
MRnumber = "MR842132 (87g:41034)",
MRreviewer = "Peter Borwein",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/MATHCOMP/mathcomp1980.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0025-5718(198607)47:175<225:ENOLRA>2.0.CO%3B2-P",
ZMnumber = "0592.41019",
abstract = "This paper gives explicit rational functions for
interpolating and approximating functions on the
intervals $ [ - 1, + 1] $, $ [0, + \infty] $, and $ [ -
\infty, + \infty] $. The rational functions are linear
in the functions to be approximated, and they have
preassigned poles. The error of approximation of these
rationals is nearly as small as the error of best
rational approximation with numerator and denominator
polynomials of the same degrees. Regions of analyticity
are described, which make it possible to tell a priori
the accuracy which we can expect from this type of
rational approximation.",
acknowledgement = ack-nhfb,
classcodes = "B0290B (Error analysis in numerical methods); B0290F
(Interpolation and function approximation); C4110
(Error analysis in numerical methods); C4130
(Interpolation and function approximation)",
classmath = "41A20 (Approximation by rational functions) 41A25
(Degree of approximation, etc.) 65D15 (Algorithms for
functional approximation) 41A50 (Best approximation)",
corpsource = "Dept. of Math., Utah Univ., Salt Lake City, UT, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "accuracy; analytic; and zeros; approximation errors;
epsilon algorithm; error analysis; explicit
nearly-optimal linear rational approximation; explicit
rational functions; function approximation;
interpolation; low-degree; Pad\'e method; poles;
polynomials; preassigned poles; rational approximation;
regions; Thiele algorithm",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Berggren:1987:PFI,
author = "M. J. Berggren and S. A. Johnson and B. L. Carruth and
W. W. Kim and F. Stenger and P. L. Kuhn",
title = "Performance of Fast Inverse Scattering Solutions for
the Exact {Helmholtz} Equation using Multiple
Frequencies and Limited Views",
crossref = "Jones:1987:AIP",
pages = "193--201",
year = "1987",
bibdate = "Wed May 09 18:53:54 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
abstract = "We have previously reported fast algorithms for
imaging by acoustical inverse scattering using the
exact (not linearized) Helmholtz wave equation. We now
report numerical implementations of these algorithms
which allow the reconstruction of quantitative images
of speed of sound, density, and absorption from either
transmission or reflection data. We also demonstrate
the application of our results to larger grids (up to
64 multiplied by 64 pixels) and compare our results
with analytically derived data, which are known to be
highly accurate, for scattering from right circular
cylindrical objects. We report on the performance of
our algorithms for both transmission and reflection
data and for the simultaneous solution of scattering
components corresponding to speed of sound and
absorption. We have further examined the performance of
our methods with various amounts of random noise added
to the simulated data. We also report on the
performance of one technique we have devised to extract
quantitative density images from our algorithms.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Misc{Kearfott:1987:SFF,
author = "R. B. Kearfott and K. Sikorski and F. Stenger",
title = "A {Sinc} Function Fast {Poisson} Solver",
year = "1987",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Kim:1987:AIS,
author = "W. W. Kim and S. A. Johnson and M. J. Berggren and F.
Stenger and C. H. Wilcox",
title = "Analysis of Inverse Scattering Solutions from Single
Frequency, Combined Transmission and Reflection Data
for the {Helmholtz} and {Riccati} Exact Wave
Equations",
crossref = "Jones:1987:AIP",
pages = "359--369",
year = "1987",
bibdate = "Wed May 09 18:58:14 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
abstract = "Various numerical methods to solve the exact inverse
scattering problem are presented here. These methods
consist of the following steps: first, modeling the
scattering of acoustic waves by an accurate wave
equation; second, discretizing this equation; and
third, numerically solving the discretized equations.
The fixed-point method and the nonlinear
Newton--Raphson method are applied to both the
Helmholtz and Riccati exact wave equations after
discretizations by the moment method or by the discrete
Fourier transform methods. Validity of the proposed
methods is verified by computer simulation, using exact
scattering data from the analytical solution for
scattering from right circular cylindrical objects.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Ang:1988:NTP,
author = "{\Dbar}{\hckudot{a}}ng {\Dbar}i{\~n}h {\'A}ng and
Fritz Keinert and Frank Stenger",
title = "A nonlinear two-phase {Stefan} problem with melting
point gradient: a constructive approach",
journal = j-J-COMPUT-APPL-MATH,
volume = "23",
number = "2",
pages = "245--255",
month = aug,
year = "1988",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(88)90283-X",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "35R35 (65P05)",
MRnumber = "MR959479 (89h:35350)",
bibdate = "Sat Feb 25 12:20:40 MST 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/037704278890283X",
abstract = "This paper considers a one-dimensional two-phase
Stefan problem, modeling a layer of solid material
floating on liquid. The model includes internal heat
sources, variable total mass (resulting e.g., from
sedimentation or erosion), and a pressure-dependent
melting point. The problem is reduced to a set of
nonlinear integral equations which provides the basis
for an existence and uniqueness proof and a new
numerical method. Numerical results are presented.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Bialecki:1988:SNM,
author = "Bernard Bialecki and Frank Stenger",
title = "{Sinc--Nystr{\"o}m} method for numerical solution of
one-dimensional {Cauchy} singular integral equation
given on a smooth arc in the complex plane",
journal = j-MATH-COMPUT,
volume = "51",
number = "183",
pages = "133--165",
month = jul,
year = "1988",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/s0025-5718-1988-0942147-x;
https://doi.org/10.2307/2008583",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65R20",
MRnumber = "MR942147 (89g:65163)",
MRreviewer = "M. S. Abou El-Seoud",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/mathcomp.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0025-5718(198807)51:183<133:SMFNSO>2.0.CO%3B2-7",
ZMnumber = "0662.65120",
abstract = "The authors consider singular integral equations of
the type $ a w + b S w + K_1 w = f_1 $, where $ S w(t)
:= \frac {1}{\pi i}p.v. \int_L \frac {w(\tau)d \tau
}{\tau - t} $, $ K_1 w(t) := \int_L k_1 (t,
\rho)w(\tau)d \tau $. The integrals are taken over a
smooth, open arc $L$ of finite length in the complex
plane, the integral operator $S$ being defined as a
Cauchy principle value integral. $ a, b, f_1 $ and $
k_1 $ are complex functions, given on L. In order to
solve the equation numerically, the approximation
following Nystr{\"o}m's method, based on sinc
quadrature rules, is studied. Sinc quadrature rules are
rules developed by the second author [SIAM Rev. 23,
165-224 (1981; Zbl 0461.65007)] particularly for the
numerical integration of complex functions. After some
transformation, they are applied on the integral
equation. Error estimates for the numerical solution
are derived. The authors report of numerical examples,
but do not give exact figures.",
acknowledgement = ack-nhfb,
classcodes = "B0290R (Integral equations); B0290B (Error analysis in
numerical methods); C4180 (Integral equations); C4110
(Error analysis in numerical methods)",
classmath = "65R20 (Integral equations (numerical methods)) 65R20
(Integral equations (numerical methods)) 45E05
(Integral equations with kernels of Cauchy type)",
corpsource = "Utah Univ., Salt Lake City, UT, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Cauchy singular integral equation; Nystr{\"o}m's
method; sinc quadrature rules; Error estimates;
numerical examples; Cauchy; Cauchy singular integral
equation; complex plane; convergence rate; error; error
analysis; Fredholm integral equation; integral
equations; N-point approximation; numerical methods;
numerical solution; principal value integrals;
regularization procedure; Sinc function; Sinc
quadrature rule; Sinc--Nystr{\"o}m method; smooth arc",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "G. H{\"a}mmerlin",
treatment = "T Theoretical or Mathematical",
}
@Article{Dikshit:1988:RTW,
author = "H. P. Dikshit and A. Sharma and V. Singh and F.
Stenger",
title = "{Rivlin}'s theorem on {Walsh} equiconvergence",
journal = j-J-APPROX-THEORY,
volume = "52",
number = "3",
pages = "339--349",
month = mar,
year = "1988",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1016/0021-9045(88)90047-0",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "30E10 (41A20)",
MRnumber = "MR934798 (89g:30071)",
MRreviewer = "P. Lappan",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0696.30035",
abstract = "The method of T. J. Rivlin (see ibid., vol.36, p.
334--345, 1982) is based on the properties of Chebyshev
polynomials and their zeros. This makes a further
extension of his results difficult. The authors propose
a mixed problem of interpolation and $ \ell_2
$-approximation and extend Rivlin's result in two
directions. As a special case they obtain `help'
functions which give larger regions of
equiconvergence.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1988:BRB,
author = "Frank Stenger",
title = "Book Review: {{\booktitle{Computational Complexity}}
(K. Wagner and G. Wechsung)}",
journal = j-SIAM-REVIEW,
volume = "30",
number = "2",
pages = "353--354",
month = jun,
year = "1988",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1030086",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:54:24 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/30/2;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://links.jstor.org/sici?sici=0036-1445(198806)30:2<353:CC>2.0.CO%3B2-B",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "June 1988",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1988:RCC,
author = "Frank Stenger",
title = "Review: {{\em Computational Complexity}}, by {K.
Wagner and G. Wechsung}",
journal = j-SIAM-REVIEW,
volume = "30",
number = "2",
pages = "353--354",
month = jun,
year = "1988",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1030086",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu May 10 17:18:35 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://links.jstor.org/sici?sici=0036-1445(198806)30:2<353:CC>2.0.CO%3B2-B;
https://epubs.siam.org/doi/abs/10.1137/1030086",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Ang:1989:CVR,
author = "{\Dbar}{\hckudot{a}}ng {\Dbar}i{\~n}h {\'A}ng and John
Lund and Frank Stenger",
title = "Complex variable and regularization methods of
inversion of the {Laplace} transform",
journal = j-MATH-COMPUT,
volume = "53",
number = "188",
pages = "589--608",
month = oct,
year = "1989",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/s0025-5718-1989-0983558-7;
https://doi.org/10.2307/2008722",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65R10 (44A10)",
MRnumber = "MR983558 (90e:65180)",
MRreviewer = "A. J. Rodrigues",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/MATHCOMP/mathcomp1980.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0025-5718(198910)53:188<589:CVARMO>2.0.CO%3B2-H",
ZMnumber = "0676.65136",
abstract = "The authors derive three new methods for the numerical
inversion of the Laplace transform, i.e., of obtaining
accurate approximations to a function $ f \in L^2
({\bbfR }^+) $, where $ {\bbfR }^+ := (0, \infty) $,
satisfying the equation $ (*) \quad \int^{\infty }_0
e^{- stf}(t)d t = g(s), $ where $g$ is a given function
in $ L^2 ({\bbfR }^+) $. The first method is based on a
rational approximation of $g$ by a sinc-like function $
(\sin c x := (\sin x) / x). $ The second method is
based on a sinc solution of the integral equation (*)
via standard regularization. The third method is based
on first converting (*) to a convolution integral
equation over $ {\bbfR } $ (using a well known change
of variables) and then finding a sinc approximation to
the solution via the application of a special
regularization procedure to solve the Fourier transform
problem. The authors obtain bounds on the error of
approximation, which depend on both the method of
approximation and the regularization parameter. The
main features and scope (and limitations) of each of
the three methods are clearly delineated. This paper is
an important addition to the vast literature on the
numerical inversion of the Laplace transform in which
proposed methods are backed up by thorough analyses and
tested on specific functions.",
abstract2 = "Three methods are derived for approximating $f$, given
its Laplace transform $g$ on $(0, \infty)$, i.e.,
$\int_0^\infty f(t) exp(-st)\,dt = g(s)$. Assuming that
$g \in L^2(0, \infty)$, the first method is based on a
Sinc-like rational approximation of $g$, the second on
a Sinc solution of the integral equation $\int_0^\infty
f(t) \exp (-st)\, dt = g(s)$ via standard
regularization, and the third method is based on first
converting $\int_0^\infty f(t) \exp (-st)\, dt = g(s)$
to a convolution integral over $R$, and then finding a
Sinc approximation to $f$ via the application of a
special regularization procedure to solve the Fourier
transform problem. The paper also obtains bounds on the
error of approximation, which depends on both the
method of approximation and the regularization
parameter.",
acknowledgement = ack-nhfb,
classcodes = "C1130 (Integral transforms); C4130 (Interpolation and
function approximation); C4180 (Integral equations)",
classmath = "65R10 (Integral transforms (numerical methods)) 65R20
(Integral equations (numerical methods)) 65R20
(Integral equations (numerical methods)) 44A10 (Laplace
transform) 45E10 (Integral equations of the convolution
type)",
corpsource = "Dept. of Math., Ho Chi Minh City Univ., Viet Nam",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "approximation theory; bounds; complex variable
methods; convolution integral; convolution integral
equation; equations; error of approximation; Fourier
transform; Fourier transforms; integral; integral
equation; Laplace; Laplace transform; Laplace
transforms; numerical inversion; problem; rational
approximation; regularization; regularization methods;
sinc approximation; Sinc solution; sinc-like function;
Sinc-like rational approximation; transform",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "M. Z. Nashed",
treatment = "T Theoretical or Mathematical",
}
@Article{Ang:1989:VFD,
author = "{\Dbar}{\hckudot{a}}ng {\Dbar}i{\~n}h {\'A}ng and Tim
Folias and Fritz Keinert and Frank Stenger",
title = "Viscoplastic flow due to penetration: a free boundary
value problem",
journal = j-INT-J-FRACTURE,
volume = "39",
number = "1--3",
pages = "121--127",
year = "1989",
CODEN = "IJFRAP",
DOI = "https://doi.org/10.1007/978-94-009-0927-4_11;
https://doi.org/10.1007/bf00047445",
ISSN = "0376-9429 (print), 1573-2673 (electronic)",
ISSN-L = "0376-9429",
MRclass = "35R35 (35K20 45G05 73F15)",
MRnumber = "MR989695 (90c:35203)",
MRreviewer = "Shuzi Zhou",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Fracture",
journal-URL = "http://link.springer.com/journal/10704",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Kowalski:1989:OCR,
author = "Marek A. Kowalski and Frank Stenger",
title = "Optimal complexity recovery of band- and
energy-limited signals. {II}",
journal = j-J-COMPLEXITY,
volume = "5",
number = "1",
pages = "45--59",
month = mar,
year = "1989",
CODEN = "JOCOEH",
DOI = "https://doi.org/10.1016/0885-064x(89)90012-5",
ISSN = "0885-064X (print), 1090-2708 (electronic)",
ISSN-L = "0885-064X",
MRclass = "41A05 (41A65 94A12)",
MRnumber = "MR990811 (90c:41003)",
MRreviewer = "A. Bultheel",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0672.94001",
abstract = "This paper deals with the recovery of band- and
energy-limited signals in $ L_p(I) $-norm from
Hermitian information gathered on a given finite
interval I. Let $ m_p(\epsilon) $ be the minimal number
of the information pieces required to find an $
\epsilon $-accurate approximation to any such signal.
We shall prove that $$ \lim_{\epsilon \to 0^+} \frac
{m_o(\epsilon) \log \log (1 / \epsilon)}{\log (1 /
\epsilon)} = 1 $$ for any $p$ in $ [1, \infty] $, and
that for sufficiently small $ \epsilon & g t; 0 $,
Hermitian interpolation using $ m_p(\epsilon)(1 + o(1))
$ arbitrary nodes yields an $ \epsilon $-approximation
in $ L_p(I) $-norm with almost minimal cost. [For part
I see ibid. 2, 239-254 (1986; Zbl 0626.94005).]",
acknowledgement = ack-nhfb,
classmath = "94A12 (Signal theory)",
fjournal = "Journal of Complexity",
journal-URL = "http://www.sciencedirect.com/science/journal/0885064X",
keywords = "Hermitian information; Hermitian interpolation;
recovery of band- and energy-limited signals",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Stenger:1989:EAM,
author = "Frank Stenger",
title = "Explicit approximate methods for computational control
theory",
crossref = "Bowers:1989:CCP",
pages = "299--316",
year = "1989",
DOI = "https://doi.org/10.1007/978-1-4612-3704-4_21",
MRclass = "93B40",
MRnumber = "MR1046859",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0704.93021",
abstract = "The author considers a number of approximations for
functions which are suitable for use over an infinite
interval. It is stated that these approximations will
be useful for evaluating Laplace transforms, and their
inverses, and may also be used to approximate to
filter, step and delta functions.",
acknowledgement = ack-nhfb,
classmath = "93B40 (Computational methods in systems theory) 65D30
(Numerical integration) 65R10 (Integral transforms
(numerical methods))",
keywords = "Laplace transforms, and their inverses",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "L. G. Chambers",
}
@InProceedings{Ikebe:1990:RAS,
author = "Yasuhiko Ikebe and Marek Kowalski and Frank Stenger",
title = "Rational approximation of the step, filter, and
impulse functions",
crossref = "Wong:1990:ACA",
pages = "441--454",
year = "1990",
MRclass = "41A20 (30E10)",
MRnumber = "MR1052446 (91c:41041)",
MRreviewer = "A. Bultheel",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0701.41023",
abstract = "The authors give rational approximants $ H_N(\omega) $
(where $N$ is the cut-off index for a doubly infinite
series) to the Heaviside function $ H(\omega) $, to the
filter function $ \chi (\omega) $ (which is nothing
else but the characteristic function for the interval $
( - 1, 1) $, with value $ 1 / 2 $ at $ \pm 1 $ ) using
$ H_N((1 + \omega) / (1 - \omega)) $ and to the Dirac
delta function using $ H_N'(\omega) $. The results
include estimates for the error in the approximation as
a function of the parameter $N$. For the Delta function
the result is of the following form: $$ \int^{\infty
}_{- \infty }H_N(\omega)f(\omega)d \omega = f(0) +
O(\omega (f; \exp ( - (\pi / 2)(N + 1)^{1 / 2})) +
O(N^{-1 / 2})), \quad N \to \infty, $$ for $f$
continuous and bounded on the real axis and absolutely
integrable over $ ( - \infty, \infty) $ and where $
\omega (f; .) $ is the ordinary modulus of continuity.
The proofs are straightforward and lucid.",
acknowledgement = ack-nhfb,
classmath = "41A20 (Approximation by rational functions)",
keywords = "Delta function; filter function",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "M. G. de Bruin",
}
@Article{Stenger:1990:BRB,
author = "Frank Stenger",
title = "Book Review: {{\booktitle{Rational Approximation of
Real Functions}} (P. P. Petrushev and V. I. Popov)}",
journal = j-SIAM-REVIEW,
volume = "32",
number = "1",
pages = "187--188",
month = mar,
year = "1990",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1032034",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:54:41 MDT 2014",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/siamreview.bib;
http://epubs.siam.org/toc/siread/32/1;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://links.jstor.org/sici?sici=0036-1445(199003)32:1<187:RAORF>2.0.CO%3B2-R",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "March 1990",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1990:RRA,
author = "Frank Stenger",
title = "Review: {{\em Rational Approximation of Real
Functions}} by {P. P. Petrushev and V. I. Popov}",
journal = j-SIAM-REVIEW,
volume = "32",
number = "1",
pages = "187--188",
month = mar,
year = "1990",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1032034",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Mon Jan 20 09:29:37 MST 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/siamreview.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://links.jstor.org/sici?sici=0036-1445(199003)32:1<187:RAORF>2.0.CO%3B2-R;
https://epubs.siam.org/doi/abs/10.1137/1032034",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Stenger:1990:SOR,
author = "Frank Stenger",
title = "Some open research problems in sonic and
electromagnetic inversion",
crossref = "Martin:1990:VSL",
pages = "73--89",
year = "1990",
MRclass = "65P05 (35R30)",
MRnumber = "MR1064331",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0758.35089",
acknowledgement = ack-nhfb,
classmath = "35R30 (Inverse problems for PDE) 78A99 (Miscellaneous
topics in optics and electromagnetic theory)",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Gustafson:1991:CAA,
author = "Sven-{\AA}ke Gustafson and Frank Stenger",
title = "Convergence acceleration applied to {Sinc}
approximation with application to approximation of $
|x|^\alpha $",
crossref = "Bowers:1991:CCI",
pages = "161--171",
year = "1991",
DOI = "https://doi.org/10.1007/978-1-4612-0427-5_12",
MRclass = "41A30 (93B40)",
MRnumber = "MR1140021",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0746.41034",
abstract = "The author studies mainly the role of Chebyshev
acceleration of Sinc approximation. Then he considers
various methods of approximating $ \vert x \vert^\alpha
$ and applies Chebyshev acceleration to the various
type of approximants for the case of $ \alpha = 1 $.",
acknowledgement = ack-nhfb,
classmath = "41A65 (Abstract approximation theory)",
keywords = "Chebyshev acceleration",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "Zhang Ganglu (Dongying)",
}
@InProceedings{Stenger:1992:SII,
author = "Frank Stenger and Brian Keyes and Mike O'Reilly and
Ken Parker",
title = "{Sinc} indefinite integration and initial value
problems",
crossref = "Espelid:1992:NIR",
pages = "281--282",
year = "1992",
DOI = "https://doi.org/10.1007/978-94-011-2646-5_21",
MRclass = "65D30",
MRnumber = "MR1198912",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0742.65015",
abstract = "The sinc indefinite integral has been discussed by
several authors: by {\it R. B. Kearfott} [Math. Comput.
41, 559--572 (1983; Zbl 0523.65018)], {\it S. Haber}
[Two formulas for numerical indefinite integration;
ibid. (to appear)], and the first author [SIAM Rev. 23,
165--224 (1981; Zbl 0461.65007)]. The following
presentation summarizes some of the results in the
monograph by the first author [Sinc numerical methods.
Textbook (to appear)], involving both sinc indefinite
integration and the application of this formula to the
solution of initial value problems in ordinary
differential equations.",
acknowledgement = ack-nhfb,
classmath = "65D30 (Numerical integration) 65L05 (Initial value
problems for ODE (numerical methods)) 34A34 (Nonlinear
ODE and systems, general) 41A55 (Approximate
quadratures)",
keywords = "initial value problems; sinc indefinite integration",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1993:BRB,
author = "Frank Stenger",
title = "Book Review: {{\booktitle{Sinc Methods for Quadrature
and Differential Equations}} (J. Lund and K. L.
Bowers)}",
journal = j-SIAM-REVIEW,
volume = "35",
number = "4",
pages = "682--683",
month = dec,
year = "1993",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1035172",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:55:16 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/35/4;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://links.jstor.org/sici?sici=0036-1445(199312)35:4<682:SMFQAD>2.0.CO%3B2-F",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "December 1993",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InCollection{Stenger:1993:DE,
author = "Frank Stenger",
title = "Differential Equations",
crossref = "Stenger:1993:NMB",
chapter = "7",
pages = "441--532",
year = "1993",
DOI = "https://doi.org/10.1007/978-1-4612-2706-9_7",
ISBN = "978-146-127-6-3-7-1",
ISBN-13 = "978-1-4612-7637-1",
bibdate = "Fri Nov 7 06:22:36 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
series = "Springer Series in Computational Mathematics",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InCollection{Stenger:1993:IE,
author = "Frank Stenger",
title = "Integral Equations",
crossref = "Stenger:1993:NMB",
chapter = "6",
pages = "311--440",
year = "1993",
DOI = "https://doi.org/10.1007/978-1-4612-2706-9_6",
ISBN = "978-146-127-6-3-7-1",
ISBN-13 = "978-1-4612-7637-1",
bibdate = "Fri Nov 7 06:22:36 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
series = "Springer Series in Computational Mathematics",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InCollection{Stenger:1993:MP,
author = "Frank Stenger",
title = "Mathematical Preliminaries",
crossref = "Stenger:1993:NMB",
chapter = "1",
pages = "1--103",
year = "1993",
DOI = "https://doi.org/10.1007/978-1-4612-2706-9_1",
ISBN = "978-146-127-6-3-7-1",
ISBN-13 = "978-1-4612-7637-1",
bibdate = "Fri Nov 7 06:22:36 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
series = "Springer Series in Computational Mathematics",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InCollection{Stenger:1993:PA,
author = "Frank Stenger",
title = "Polynomial Approximation",
crossref = "Stenger:1993:NMB",
chapter = "2",
pages = "105--130",
year = "1993",
DOI = "https://doi.org/10.1007/978-1-4612-2706-9_2",
ISBN = "978-146-127-6-3-7-1",
ISBN-13 = "978-1-4612-7637-1",
bibdate = "Fri Nov 7 06:22:36 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
series = "Springer Series in Computational Mathematics",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1993:RSM,
author = "Frank Stenger",
title = "Review: {{\em Sinc Methods for Quadrature and
Differential Equations}}, by {J. Lund and K. L.
Bowers}",
journal = j-SIAM-REVIEW,
volume = "35",
number = "4",
pages = "682--683",
month = dec,
year = "1993",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1035172",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Mon Jan 20 09:29:37 MST 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://links.jstor.org/sici?sici=0036-1445(199312)35:4<682:SMFQAD>2.0.CO%3B2-F;
https://epubs.siam.org/doi/abs/10.1137/1035172",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InCollection{Stenger:1993:SA,
author = "Frank Stenger",
title = "Sinc Approximation on {$ \Gamma $}",
crossref = "Stenger:1993:NMB",
chapter = "4",
pages = "179--242",
year = "1993",
DOI = "https://doi.org/10.1007/978-1-4612-2706-9_4",
ISBN = "978-146-127-6-3-7-1",
ISBN-13 = "978-1-4612-7637-1",
bibdate = "Fri Nov 7 06:22:36 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
series = "Springer Series in Computational Mathematics",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InCollection{Stenger:1993:SAS,
author = "Frank Stenger",
title = "Sinc Approximation in Strip",
crossref = "Stenger:1993:NMB",
chapter = "3",
pages = "131--178",
year = "1993",
DOI = "https://doi.org/10.1007/978-1-4612-2706-9_3",
ISBN = "978-146-127-6-3-7-1",
ISBN-13 = "978-1-4612-7637-1",
bibdate = "Fri Nov 7 06:22:36 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
series = "Springer Series in Computational Mathematics",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InCollection{Stenger:1993:SCA,
author = "F. Stenger and B. Barkey and R. Vakili",
booktitle = "Computation and control, III (Bozeman, MT, 1992)",
title = "{Sinc} convolution approximate solution of {Burgers}'
equation",
volume = "15",
publisher = pub-BIRKHAUSER-BOSTON,
address = pub-BIRKHAUSER-BOSTON:adr,
pages = "341--354",
year = "1993",
MRclass = "65N06",
MRnumber = "MR1247487",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
series = "Progr. Systems Control Theory",
ZMnumber = "0822.65073",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InCollection{Stenger:1993:SRM,
author = "Frank Stenger",
title = "Sinc-Related Methods",
crossref = "Stenger:1993:NMB",
chapter = "5",
pages = "243--310",
year = "1993",
DOI = "https://doi.org/10.1007/978-1-4612-2706-9_5",
ISBN = "978-146-127-6-3-7-1",
ISBN-13 = "978-1-4612-7637-1",
bibdate = "Fri Nov 7 06:22:36 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
series = "Springer Series in Computational Mathematics",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Chan:1994:NPB,
author = "Kwong-Yu Chan and Douglas Henderson and Frank
Stenger",
title = "Nonlinear {Poisson--Boltzmann} equation in a model of
a scanning tunneling microscope",
journal = j-NUMER-METHODS-PARTIAL-DIFFER-EQU,
volume = "10",
number = "6",
pages = "689--702",
year = "1994",
CODEN = "NMPDEB",
DOI = "https://doi.org/10.1002/num.1690100605",
ISSN = "0749-159X (print), 1098-2426 (electronic)",
ISSN-L = "0749-159X",
MRclass = "65N06",
MRnumber = "MR1298117 (95f:65193)",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0812.65125",
abstract = "This paper presents a finite difference application to
model the electrolyte solution interface between the
tip and the substrate in a scanning tunneling
microscope. An essential feature of the problem is
nonlinearity which makes the partial differential
equations that describe the problem take the form of a
Poisson--Boltzmann equation. The problem formulation is
elegant in the sense that it uses mirror imaging
technique to describe the boundary conditions which are
of Dirichlet and Neumann types.\par
The proposed technique is supported by numerical
simulation of several case studies with and without a
centrally adsorbed molecule. Simulation results are
provided and supported by comparison with those
obtained via analytical techniques.",
acknowledgement = ack-nhfb,
classmath = "65Z05 (Applications to physics) 65N06 (Finite
difference methods (BVP of PDE)) 35Q60 (PDE of
electromagnetic theory and optics) 78A55 (Technical
appl. of optics and electromagnetic theory)",
fjournal = "Numerical Methods for Partial Differential Equations.
An International Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1098-2426",
keywords = "electrolyte solution interface; finite difference
method; mirror imaging technique; nonlinear
Poisson-Boltzman equation; numerical examples; scanning
tunneling microscope",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "R. Chedid (Beirut)",
}
@Article{McArthur:1994:RNM,
author = "K. M. McArthur",
title = "Review: {{\em Numerical Methods Based on Sinc and
Analytic Functions}} ({Frank Stenger})",
journal = j-SIAM-REVIEW,
volume = "36",
number = "4",
pages = "673--674",
month = dec,
year = "1994",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1036167",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Tue May 13 16:55:17 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/siamreview.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib;
http://www.siam.org/journals/sirev/sirev364.htm",
URL = "http://links.jstor.org/sici?sici=0036-1445(199412)36:4<673:NMBOSA>2.0.CO%3B2-J;
https://epubs.siam.org/doi/abs/10.1137/1036167",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Schmeisser:1994:RBM,
author = "G. Schmeisser",
title = "Review: {{\booktitle{Numerical Methods Based on Sinc
and Analytic Functions}}, by Frank Stenger}",
journal = j-MATH-COMPUT,
volume = "63",
number = "208",
pages = "817--819",
month = oct,
year = "1994",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2153301",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Thu May 10 17:12:05 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://links.jstor.org/sici?sici=0025-5718(199410)63:208<817:NMBOSA>2.0.CO%3B2-K",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Stenger:1994:NMT,
author = "Frank Stenger",
title = "Numerical methods via transformations",
crossref = "Zahar:1994:ACF",
pages = "543--550",
year = "1994",
DOI = "https://doi.org/10.1007/978-1-4684-7415-2_36",
MRclass = "65D30",
MRnumber = "MR1333642 (96a:65031)",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0829.65022",
abstract = "This paper comprises a chain of numerical quadrature
rules with error estimate. Some are derived from others
by a simple transformation. The initial element is the
trapezoidal rule, applied to a periodic function which
is analytic in a strip $ | \text {Im z}| & l t; \delta
$ in the complex plane. The transformation $ z' = \text
{exp}i z $ leads to a rule for integration round $ |z'|
= 1 $, and applying a symmetry condition, to the
Fej{\'e}r rule.\par
An equally interesting treatment of the doubly infinite
trapezoidal rule is based on error bounds for the sinc
series approximation, and this is related to other
familiar rules.\par
While most readers or lecturers would approach many of
these rules differently, all can enjoy the inter-rule
relationships elegantly presented in this paper.",
acknowledgement = ack-nhfb,
classmath = "65D32 (Quadrature formulas (numerical methods)) 41A55
(Approximate quadratures) 65E05 (Numerical methods in
complex analysis) 41A80 (Remainders in approximation
formulas)",
keywords = "doubly infinite trapezoidal rule; error estimate;
Fej\'er rule; numerical quadrature; periodic function;
sinc series approximation; trapezoidal rule",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "J. N. Lyness (Argonne)",
}
@Book{Kowalski:1995:STA,
author = "Marek A. Kowalski and Krzysztof A. Sikorski and Frank
Stenger",
title = "Selected Topics in Approximation and Computation",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xiv + 349",
year = "1995",
ISBN = "0-19-508059-9",
ISBN-13 = "978-0-19-508059-9",
MRclass = "41-02 (65Dxx 68Q25)",
MRnumber = "MR1418861 (97k:41001)",
MRreviewer = "D. Leviatan",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/complexity.information.bib",
URL = "http://site.ebrary.com/lib/utah/Doc?id=10087215",
ZMnumber = "0839.41001",
abstract = "As is mentioned in the Preface, this book covers basic
results of approximation theory. It contains also new
developments in the theory of moments and Sinc
approximation, $n$-widths, $s$-numbers and relationship
of these to computational algorithms. The volume
consists of 8 chapters. The chapter headings are: (1)
Classical approximation; (2) Splines; (3) Sinc
approximation; (4) Explicit Sinc-like methods; (5)
Moment problems; (6) $n$-widths and $s$-numbers; (7)
Optimal approximation methods; (8)
Applications.\par
Chapter 1 covers basic concepts of classical
approximation. The theory of best approximation is
presented in the setting of normed spaces. The authors
discuss best approximation in unitary spaces, including
several practically important examples. Concepts of
approximation in the uniform norm are presented in
Banach space setting.\par
Chapter 2 provides an introduction to basic classes of
polynomial splines and $B$-splines, which have
variation-diminishing properties when used to
approximate data. It is underlined that splines provide
useful methods of approximation in the important areas
of computer-aided geometric design and for representing
computer graphics displays.\par
In chapter 3 the authors present the Sinc methods as a
new family of self-contained methods of approximation,
which have several advantages over classical methods of
approximation in the case of the presence of end-point
singularities, when we have a semi-infinite or infinite
interval of approximation, or in the case of the
presence of a boundary layer situation. They introduce
methods of approximation and inversion of Laplace and
Hilbert transforms.\par
In chapter 4 is presented a family of simple rational
functions, which make possible the explicit and
arbitrarily accurate rational approximation of the
filter, the step and impulse functions.\par
In Chapter 5 the moment problems are discussed in the
setting of approximation theory, including discrete and
continuous moment problems of Hausdorff, Stieltjes and
Hamburger, as well as the discrete and continuous
trigonometric moment problems.\par
Chapter 6 deals with $n$-widths and $s$-numbers, which
provide conceptional generalizations of the classical
concepts of best approximation.\par
In chapter 7 are discussed optimal methods of
approximation and optimal algorithms for general,
nonlinear approximation problems. The investigation is
made in the general setting of normed
spaces.\par
Chapter 8 contains applications of the approximation
procedures presented in the previous chapters. They
discuss the solution of Burger's equation, the
approximation of band-limited signals and a nonlinear
zero-finding problem. Each section of the book ends
with a set of exercises, annotations, specific comments
and references. This important book can be of great
interest to graduate students and researchers in
approximation, constructive function theory and
numerical methods.",
acknowledgement = ack-nhfb,
classmath = "41-02 (Research monographs (approximations and
expansions)) 41A10 (Approximation by polynomials) 41A15
(Spline approximation) 65D15 (Algorithms for functional
approximation) 65D17 (Computer aided design (modeling
of curves and surfaces)) 65Y20 (Complexity and
performance of numerical algorithms)",
keywords = "moment problems; optimal approximation; splines",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
remark = "In the fall of 1996, the authors were awarded ``First
Prize of the Secretary of National Education in
Poland'', for the research leading to the publication
of this monograph. This is the most prestigious
research award in Poland, and is awarded annually to
only selected groups of researchers.",
reviewer = "D. D. Stancu (Cluj-Napoca)",
shorttableofcontents = "1: Classical Approximation \\
2: Splines \\
3: Sinc Approximation \\
4: Explicit Sinc-Like Methods \\
5: Moment Problems \\
6: $n$-Widths and $s$-Numbers \\
7: Optimal Approximation Methods \\
8: Applications",
tableofcontents = "Classical Approximation / 1 \\
1.1 General results / 1 \\
1.1.1 Exercises / 12 \\
1.2 Approximation in unitary spaces / 13 \\
1.2.1 Computing the best approximation / 17 \\
1.2.2 Completeness of orthogonal systems / 20 \\
1.2.3 Examples of orthogonal systems / 21 \\
1.2.4 Remarks on convergence of Fourier series / 34 \\
1.2.5 Exercises / 36 \\
1.3 Uniform approximation / 39 \\
1.3.1 Chebyshev subspaces / 42 \\
1.3.2 Maximal functional / 47 \\
1.3.3 The Remez algorithm / 56 \\
1.3.4 The Korovkin operators / 58 \\
1.3.5 Quality of polynomial approximations / 63 \\
1.3.6 Converse theorems in polynomial approximation /
66 \\
1.3.7 Projection operators / 72 \\
1.3.8 Exercises / 83 \\
1.4 Annotations / 87 \\
1.5 References / 89 \\
Splines / 93 \\
2.1 Polynomial splines / 93 \\
2.1.1 Exercises / 102 \\
2.2 B-splines / 103 \\
2.2.1 General spline interpolation / 109 \\
2.2.2 Exercises / 110 \\
2.3 General splines / 111 \\
2.3.1 Exercises / 114 \\
2.4 Annotations / 114 \\
2.5 References / 115 \\
3 Sinc Approximation / 117 \\
3.1 Basic definitions / 117 \\
3.1.1 Exercises / 125 \\
3.2 Interpolation and quadrature / 126 \\
3.2.1 Exercises / 132 \\
3.3 Approximation of derivatives on $\Gamma$ / 134 \\
3.3.1 Exercises / 136 \\
3.4 Sinc indefinite integral over $\Gamma$ / 136 \\
3.4.1 Exercises / 139 \\
3.5 Sinc indefinite convolution over $\Gamma$ / 139 \\
3.5.1 Derivation and justification of procedure / 141
\\
3.5.2 Multidimensional indefinite convolutions / 146
\\
3.5.3 Two dimensional convolution / 147 \\
3.5.4 Exercises / 149 \\
3.6 Annotations / 150 \\
3.7 References / 150 \\
4 Explicit Sine-Like Methods / 153 \\
4.1 Positive base approximation / 153 \\
4.1.1 Exercises / 158 \\
4.2 Approximation via elliptic functions / 158 \\
4.2.1 Exercises / 160 \\
4.3 Heaviside, filter, and delta functions / 161 \\
4.3.1 Heaviside function / 162 \\
4.3.2 The filter or characteristic function / 163 \\
4.3.3 The impulse or delta function / 164 \\
4.3.4 Exercises / 166 \\
4.4 Annotations / 166 \\
4.5 References / 166 \\
5 Moment Problems / 169 \\
5.1 Duality with approximation / 170 \\
5.1.1 Exercises / 175 5.2 The moment problem in the
space CQ(D) / 175 \\
5.3 Classical moment problems / 178 \\
5.3.1 Exercises / 185 \\
5.4 Density and determinateness / 189 \\
5.4.1 Exercises / 203 \\
5.5 A Sinc moment problem / 205 \\
5.5.1 Exercises / 206 \\
5.6 Multivariate orthogonal polynomials / 206 \\
5.6.1 Exercises / 218 \\
5.7 Annotations / 219 \\
5.8 References / 220 \\
6 $n$-Widths and $s$-Numbers / 223 \\
6.1 $n$-Widths / 223 \\
6.1.1 Relationships between $n$-widths / 229 \\
6.1.2 Algebraic versions of $a_n$ and $c_n$ / 235 \\
6.1.3 Exercises / 236 \\
6.2 $s$-Numbers / 237 \\
6.2.1 $s$-Numbers and singular values / 240 \\
6.2.2 Relationships between $s$-numbers / 246 \\
6.2.3 Exercises / 255 \\
6.3 Annotations / 255 \\
6.4 References / 256 \\
7 Optimal Approximation Methods / 259 \\
7.1 A general approximation problem / 262 \\
7.1.1 Radius of information optimal algorithms / 264
\\
7.1.2 Exercises / 270 \\
7.2 Linear problems / 270 \\
7.2.1 Optimal information / 276 \\
7.2.2 Relations to $n$-widths / 281 \\
7.2.3 Exercises / 285 \\
7.3 Parallel versus sequential methods / 286 \\
7.3.1 Exercises / 290 \\
7.4 Linear and spline algorithms / 291 \\
7.4.1 Spline algorithms / 295 \\
7.4.2 Relations to linear Kolmogorov $n$-widths / 302
\\
7.4.3 Exercises / 304 \\
7.5 s-Numbers, minimal errors / 304 \\
7.5.1 Exercises / 309 \\
7.6 Optimal methods / 310 \\
7.6.1 Optimal complexity methods for linear problems312
7.6.2 Exercises / 314 \\
7.7 Annotations / 314 \\
7.8 References / 316 \\
8 Applications / 319 \\
8.1 Sinc solution of Burgers' equation / 319 \\
8.2 Signal recovery / 321 \\
8.2.1 Formulation of the problem / 321 \\
8.2.2 Relations to $n$-widths / 322 \\
8.2.3 Algorithms and their errors / 325 \\
8.2.4 Asymptotics of minimal cost / 332 \\
8.2.5 Exercises / 333 \\
8.3 Bisection method / 334 \\
8.3.1 Formulation of the problem / 334 \\
8.3.2 Optimality theorem / 335 \\
8.3.3 Exercises / 340 \\
8.4 Annotations / 340 \\
8.5 References / 340 \\
Index / 343",
}
@InCollection{Morlet:1995:SAS,
author = "Anne C. Morlet and Frank Stenger",
booktitle = "Computation and control, IV (Bozeman, MT, 1994)",
title = "Sinc approximation of solution of heat equation with
discontinuous initial condition",
volume = "20",
publisher = pub-BIRKHAUSER-BOSTON,
address = pub-BIRKHAUSER-BOSTON:adr,
pages = "289--303",
year = "1995",
DOI = "https://doi.org/10.1007/978-1-4612-2574-4_19",
MRclass = "65M60",
MRnumber = "MR1349598",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
series = "Progr. Systems Control Theory",
ZMnumber = "0833.65113",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1995:CC,
author = "Frank Stenger",
title = "Collocating convolutions",
journal = j-MATH-COMPUT,
volume = "64",
number = "209",
pages = "211--235",
month = jan,
year = "1995",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/s0025-5718-1995-1270624-7;
https://doi.org/10.2307/2153330",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D30 (41A35 65N35 65R10)",
MRnumber = "MR1270624 (95c:65038)",
MRreviewer = "Rudolf Gorenflo",
bibdate = "Sat Jan 11 13:29:06 MST 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/mathcomp.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
URL = "http://links.jstor.org/sici?sici=0025-5718(199501)64:209<211:CC>2.0.CO%3B2-M",
ZMnumber = "0828.65017",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Stenger:1995:SCT,
author = "Frank Stenger",
title = "{Sinc} convolution --- a tool for circumventing some
limitations of classical signal processing",
crossref = "Ismail:1995:MAW",
pages = "227--240",
year = "1995",
DOI = "https://doi.org/10.1090/conm/190/02305",
MRclass = "94A12 (44A35)",
MRnumber = "MR1354857 (96i:94006)",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0863.65093",
abstract = "The author reviews some sinc approximation procedures
that are applicable to the approximate solution of
indefinite integral convolutions which arise in signal
processing problems. This sinc method works also in
those cases when the functions have some singularities
or slow decrease for large argument. Several examples
illustrate the limitations of classical methods via
fast Fourier transforms and show the advantage of sinc
approximation to the solution of problems in signal
processing.\par
The complete proofs can be found in Section 4.6 of the
author's book \cite{Stenger:1993:NMB}.",
acknowledgement = ack-nhfb,
classmath = "65T40 (Trigonometric approximation and interpolation)
42A10 (Trigonometric approximation) 94A12 (Signal
theory) 44A35 (Convolution) 42C10 (Fourier series in
special orthogonal functions)",
keywords = "fast Fourier transforms; functions with singularities;
functions with slow decrease; integral convolutions;
signal processing; sinc approximation",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "M. Tasche (Rostock)",
}
@InProceedings{Stenger:1995:SIH,
author = "Frank Stenger",
title = "{Sinc} inversion of the {Helmholtz} equation without
computing the forward solution",
crossref = "Ang:1995:IPA",
pages = "149--157",
year = "1995",
MRclass = "35R30 (35J05)",
MRnumber = "MR1327074",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0841.35127",
abstract = "Given the Helmholtz equation, $ \nabla^2 u + \kappa^2
(1 + f) u = 0 $, on a half space $H$, we sketch a
procedure for inversion of this equation, i.e., for
reconstruction of the function $f$ in $H$, via the
application of point sources located on the boundary of
$H$, without computing the solution $u$ of the forward
problem. Indeed, corresponding to a point $ \overline r
$ in $H$ and a point $ \overline r_0 $ on the exterior
of $H$, it is now possible to select linear combination
of sources such that the resulting solution $u$
measured at $ \overline r_0 $ arbitrarily closely
approximates the function $f$ at $ \overline r $.",
acknowledgement = ack-nhfb,
classmath = "35R30 (Inverse problems for PDE) 35J05 (Laplace
equation, etc.)",
keywords = "Helmholtz equation; plane-wave sources; point
sources",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1996:BRS,
author = "Frank Stenger",
title = "Book Reviews: {{\em Solving Problems in Scientific
Computing Using MAPLE and MATLAB}}, by {Walter Gander}
and {J{\'\i}r{\'\i} Hreb{\'\i}cek}",
journal = j-MATH-COMPUT,
volume = "65",
number = "214",
pages = "880--882",
month = apr,
year = "1996",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/s0025-5718-96-00724-7",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Mon Jul 26 11:57:34 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/MATHCOMP/mathcomp1990.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-96-00700-4&u=/mcom/1996-65-214/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Bojanov:1997:BRS,
author = "Borislav Bojanov",
title = "Book Review: {{\em Selected Topics in Approximation
and Computation}, by Marek A. Kowalski, Krzysztof A.
Sikorski, and Frank Stenger}",
journal = j-SIAM-REVIEW,
volume = "39",
number = "2",
pages = "333--334",
month = jun,
year = "1997",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000039000002000333000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Wed Apr 29 18:11:34 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://links.jstor.org/sici?sici=0036-1445(199706)39:2<333:STIAAC>2.0.CO%3B2-Y;
https://epubs.siam.org/doi/abs/10.1137/SIREAD000039000002000333000001",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Quak:1997:BRS,
author = "Ewald Quak",
title = "Book Reviews: {{\em Selected topics in approximation
and computation}}, by {Marek A. Kowalski, Krzysztof A.
Sikorski and Frank Stenger}",
journal = j-MATH-COMPUT,
volume = "66",
number = "219",
pages = "1374--1374",
month = jul,
year = "1997",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-97-00877-6",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Fri Jul 16 10:38:45 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/mathcomp.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
URL = "http://links.jstor.org/sici?sici=0025-5718(199707)66:219<1374:STIAAC>2.0.CO%3B2-L;
http://www.ams.org/journals/mcom/1997-66-219/S0025-5718-97-00877-6/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1997:MSM,
author = "Frank Stenger",
title = "Matrices of {Sinc} methods",
journal = j-J-COMPUT-APPL-MATH,
volume = "86",
number = "1",
pages = "297--310",
day = "28",
month = nov,
year = "1997",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/s0377-0427(97)00163-5",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65D15 (65F30)",
MRnumber = "MR1491441 (99b:65014)",
MRreviewer = "W. Govaerts",
bibdate = "Sat Feb 25 12:36:04 MST 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
note = "Special issue dedicated to William B. Gragg (Monterey,
CA, 1996)",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042797001635",
ZMnumber = "0898.65066",
abstract = "The paper gives a brief review of Sinc methods, with
emphasis on the matrices of Sinc methods. A novel
procedure is presented, based on Sinc convolution, for
solving a Poisson problem over a rectangular region.
Although some of the work of Gragg (1982) may already
be applied to the solution of Sinc-matrix problems,
this paper also points to new directions of matrix
research.",
acknowledgement = ack-nhfb,
classmath = "65N30 (Finite numerical methods (BVP of PDE)) 35J05
(Laplace equation, etc.) 65T50 (Discrete and fast
Fourier transforms)",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "Poisson problem; Sinc convolution; Sinc methods",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "M. Z.Nashed (Newark/Delaware)",
}
@Article{Stenger:1997:RDT,
author = "Frank Stenger",
title = "Reviews and Descriptions of Tables and Books: 22.
{{\booktitle{Integral equations: Theory and numerical
treatment}}, by Wolfgang Hackbusch}",
journal = j-MATH-COMPUT,
volume = "66",
number = "220",
pages = "1756--1758",
month = oct,
year = "1997",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/s0025-5718-97-00910-1",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Mon Jul 26 11:26:13 1999",
bibsource = "http://www.ams.org/mcom/1997-66-220;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/MATHCOMP/mathcomp1990.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00843-0&u=/mcom/1997-66-220/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1997:RIE,
author = "Frank Stenger",
title = "Review: {{\booktitle{Integral Equations: Theory and
Numerical Treatment}}, by Wolfgang Hackbusch}",
journal = j-MATH-COMPUT,
volume = "66",
number = "220",
pages = "1756--1758",
month = oct,
year = "1997",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-97-00910-1",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Thu May 10 17:14:42 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://links.jstor.org/sici?sici=0025-5718(199710)66:220<1756:IETANT>2.0.CO%3B2-V;
http://www.ams.org/journals/mcom/1997-66-220/S0025-5718-97-00910-1/;
https://www.jstor.org/stable/2153702",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Chen:1998:HSS,
author = "Susheela Narasimhan Kuan Chen and Frank Stenger",
title = "A Harmonic-Sinc Solution of the {Laplace} Equation for
Problems with Singularities and Semi-Infinite Domains",
journal = j-NUMER-HEAT-TRANSFER-B,
volume = "33",
number = "4",
pages = "433--450",
month = jun,
year = "1998",
CODEN = "NUHTD6",
DOI = "https://doi.org/10.1080/10407799808915042",
ISSN = "1040-7790 (print), 1521-0626 (electronic)",
ISSN-L = "1040-7790",
bibdate = "Fri Nov 7 08:39:54 MST 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Heat Transfer, Part B (Fundamentals)",
journal-URL = "http://www.tandfonline.com/loi/unhb20",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Kress:1998:SQM,
author = "Rainer Kress and Ian H. Sloan and Frank Stenger",
title = "A sinc quadrature method for the double-layer integral
equation in planar domains with corners",
journal = j-J-INTEGRAL-EQU-APPL,
volume = "10",
number = "3",
pages = "291--317",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1216/jiea/1181074232",
ISSN = "0897-3962 (print), 1938-2626 (electronic)",
ISSN-L = "0897-3962",
MRclass = "45L05 (45B05 65R20)",
MRnumber = "MR1656534 (2000b:45011)",
MRreviewer = "Jean M.-S. Lubuma",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://projecteuclid.org/euclid.jiea/1181074232",
ZMnumber = "0916.65135",
abstract = "Let $$ D_d = \{ z = x + i y; x \in R, | y| & l t; d \}
\subset \bbfC . $$ For $ d \le \pi / 2 $, the function
$$ w(z) = {1 \over 1 + e^{-z}}, \quad z \in \bbfC, $$
maps the strip $ D_d $ bijectively onto an eye-shaped
domain $ E_d = \{ w(z) : z \in D_d \} $ centered around
the interval $ (0, 1) $. Let $ S_{\alpha, d} $ be the
space of all functions $g$, which are holomorphic in $
E_d $, real-valued on $ (0, 1) $, and which satisfy $ |
t(1 - t)|^{1 - \alpha }| g(t)| \le \alpha $, for $ t
\in E_d $. The first part of the paper is devoted to
sinc quadrature rules for the calculation of the
integral $ \int^1_0 g(t)d t $, where $ g \in S_{\alpha,
d} $. A quadrature rule with error $ | E_{n, h}(g)| \le
C e^{- \mu n^{1 / 2}} \| g \|_{S_{\alpha, d}} $, for
some positive constants $C$ and $ \mu $ depending on
$d$ and $ \alpha $ is constructed.\par
In the second part of the paper the application of the
sinc quadrature method to the approximate solution of a
Mellin type integral equation $$ \varphi (t) - \int^1_0
K(t, \tau)[\varphi (\tau) - \varphi (0)]d \tau + \gamma
(t) \varphi (0) = f(t) \tag 1 $$ is investigated. The
kernel $K$ is assumed to have period one with respect
to $t$ and be continuous for $ 0 \le t $, $ \tau \le 1
$ with the exception of the four corners of the square
$ [0, 1] \times [0, 1] $. In these corners $K$ has
Mellin type singularities. Let $ K(t, \tau) = L(t,
\tau) + M(t, \tau) $, where $$ | L(t, \tau)| \le {1
\over \tau } k \Biggl ({t \over \tau } \Biggr), \quad
(t, \tau) \in Q, \quad t \le 1 / 2, $$ $$ | L(t, \tau)|
\le {1 \over 1 - \tau } k \Biggl ({1 - t \over 1 - \tau
} \Biggr), \quad (t, \tau) \in Q, \quad t \ge 1 / 2, $$
$$ Q = \{ (t, \tau) \in [0, 1] \times [0, 1] : 0 & l t;
t + \tau & l t; 2 \}, $$ $$ k(0) = 0, \quad
\int_0^\infty {k(s) \over s} d s & l t; 1. $$ For
equation (1) conditions of existence and uniqueness are
received. The quadrature method is used for an
approximate solution of equation (1). In this method,
the integral in (1) is approximated by the sinc
quadrature rule. Conditions of solvability of the
quadrature method and an error estimation are
obtained.\par
In the third part of the paper the Dirichlet problem
for the Laplace equation $$ \Delta u = 0 $$ is reduced
to a Mellin type integral equation.",
acknowledgement = ack-nhfb,
classmath = "65R20 (Integral equations (numerical methods)) 45E10
(Integral equations of the convolution type) 35J05
(Laplace equation, etc.) 35C15 (Integral
representations of solutions of PDE) 65D32 (Quadrature
formulas (numerical methods)) 41A55 (Approximate
quadratures) 65N38 (Boundary element methods (BVP of
PDE))",
fjournal = "Journal of Integral Equations and Applications",
journal-URL = "http://projecteuclid.org/euclid.jiea",
keywords = "Dirichlet problem; double-layer integral equation;
error estimation; Laplace equation; Mellin type
integral equation; sinc quadrature method; sinc
quadrature rules",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "I. V. Boikov (Penza)",
}
@Article{Narasimhan:1998:HSS,
author = "S. Narasimhan and Kuan Chen and Frank Stenger",
title = "A harmonic-sinc solution of the {Laplace} equation for
problems with singularities and semi-infinite domains",
journal = j-NUMER-HEAT-TRANSFER-B,
volume = "33",
number = "4",
pages = "433--450",
month = jun,
year = "1998",
CODEN = "NUHTD6",
DOI = "https://doi.org/10.1080/10407799808915042",
ISSN = "1040-7790 (print), 1521-0626 (electronic)",
ISSN-L = "1040-7790",
bibdate = "Thu May 10 10:26:37 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "https://www.tandfonline.com/doi/abs/10.1080/10407799808915042",
abstract = "In this article, a recently derived harmonic sinc
approximation method is used to obtain approximate
solutions to two-dimensional steady-state heat
conduction problems with singularities and
semi-infinite domains and Dirichlet boundary
conditions. The first problem is conduction in a square
geometry, and the second one involves a semi-infinite
medium with a rectangular cavity. In the case of square
geometry, results show that the harmonic sinc
approximation method performs better than the
finite-difference and multigrid methods everywhere
within the computational domain, especially at points
close to the singularity at the upper left and right
corners of the square. The results from the harmonic
sinc approximation method for the semi-infinite domain
problem with a very shallow rectangular cavity agree
well with the analytical solution for a semi-infinite
domain without the cavity. The results obtained from
the harmonic sinc approximation also agree well with
the results from the finite-element package ANSYS for
the semi-infinite medium conduction problem with a
rectangular cavity of aspect ratio 1.",
acknowledgement = ack-nhfb,
fjournal = "Numerical Heat Transfer, Part B (Fundamentals)",
journal-URL = "http://www.tandfonline.com/loi/unhb20",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1998:CSM,
author = "Frank Stenger and Michael J. O'Reilly",
title = "Computing solutions to medical problems via {Sinc}
convolution",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "43",
number = "6",
pages = "843--848",
month = jun,
year = "1998",
CODEN = "IETAA9",
DOI = "https://doi.org/10.1109/9.679023",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Wed May 09 17:59:42 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
abstract = "In this paper we illustrate some novel procedures of
using Sinc methods to compute solutions to three types
of medical problems. The first of these is a novel way
to solve optimal control problems, the second is an
original way to reconstruct images for X-ray
tomography, and the third is a novel way to do
ultrasonic tomography inversion. Each of these
procedures uses Sinc convolution, which is a novel
computational procedure for obtaining accurate
approximations to indefinite convolutions.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:1999:BRB,
author = "Frank Stenger",
title = "Book Reviews: {{\booktitle{Boundary element method,
fundamentals and applications}}, by Frederico Paris and
Jose Canas}",
journal = j-MATH-COMPUT,
volume = "68",
number = "225",
pages = "457--459",
month = jan,
year = "1999",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/s0025-5718-99-01069-8",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Mon Jul 26 12:37:20 1999",
bibsource = "http://www.ams.org/mcom/1999-68-225;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/mathcomp.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
URL = "http://links.jstor.org/sici?sici=0025-5718(199901)68:225<457:BEMFAA>2.0.CO%3B2-K;
http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-99-00992-8&u=/mcom/1999-68-225/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Stenger:1999:CMS,
author = "Frank Stenger and Ross Schmidtlein",
title = "Conformal maps via {Sinc} methods",
crossref = "Papamichael:1999:CMF",
pages = "505--549",
year = "1999",
MRclass = "30C30 (41A30 65E05)",
MRnumber = "MR1700373 (2000i:30013)",
MRreviewer = "Nikos S. Stylianopoulos",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "0948.30014",
abstract = "Let $B$ be a simply connected domain in the complex
plane with $ 0 \in B $. The conformal mapping $ f : B
\to U $ from $B$ to the unit disc $U$ normalized by $
f(0) = 0 $ can be written as $ f(z) = z \exp ({\cal
G}(z)) $ with an analytic function $ {\cal G} $ in $B$.
This function can be represented by a Cauchy integral
with a real density function $u$. This real function
$u$ then satisfies a second kind integral equation with
Neumann kernel. The main contribution of the paper
under review consists in the solution of this integral
equation via Sinc methods. The best reference for Sinc
methods is the first author's book [Numerical methods
based on Sinc and analytic functions (1993; Zbl
0803.65141)]. The basic definitions and notions about
Sinc spaces, necessary for this paper, are added to the
paper as an appendix. The numerical algorithm is
described in great detail. A Fortran code may be
obtained from the first author. The procedure for
evaluating $f$ in the interior of $B$ is described as
well as the construction of the inverse mapping $ F : U
\to B $. The method is applicable for regions with
piecewise analytic boundary curves. The convergence of
the numerical approximation to the solution is proven
and the accuracy is investigated. The complexity, i.e.,
the work needed to achieve an approximation to $f$ with
error at most $ \varepsilon $, is of the order $ O(|
\log (\varepsilon)|^6) $. The complexity grows with the
number $n$ of analytic arcs of $ \partial B $ as the
power $ O(n^3) $. The performance of the method is
demonstrated at two examples, namely a semidisc and a
pac-man, and compared with Hough's method, which is
based on Symm's integral equation of the first kind.
The comparison ends with a draw: Each method has its
advantages and may be more efficient in specific
cases.",
acknowledgement = ack-nhfb,
classmath = "30C30 (Numerical methods in conformal mapping theory)
65R20 (Integral equations (numerical methods)) 41A20
(Approximation by rational functions)",
keywords = "integral equations; numerical conformal mapping; sinc
methods",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "R. Wegmann (Garching)",
}
@Article{Stenger:1999:OIP,
author = "F. Stenger and S.-{\AA}. Gustafson and B. Keyes and M.
O'Reilly and K. Parker",
title = "{ODE-IVP-PACK} via {Sinc} indefinite integration and
{Newton}'s method",
journal = j-NUMER-ALGORITHMS,
volume = "20",
number = "2--3",
pages = "241--268",
month = jun,
year = "1999",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1023/A:1019108002140",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65L05 (65Y15)",
MRnumber = "MR1709542 (2000e:65071)",
bibdate = "Mon Sep 29 08:36:57 MDT 2003",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/18/7/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/5058/18/7/fulltext.pdf;
https://link.springer.com/article/10.1023/A%3A1019108002140",
ZMnumber = "0934.65071",
abstract = "This paper describes a package of computer programs
for the unified treatment of initial value problems for
systems of ordinary differential equations. The
programs implement a numerical method which is
efficient for a general class of differential
equations. The user may determine the solutions over
finite or infinite intervals. The solutions may have
singularities at the end-points of the interval for
which the solution is sought. Besides giving the
initial values and the analytical expression for the
differential equations to be solved the user needs to
specify the nature of the singularities and give some
other analytical information as described in the paper
in order to take advantage of the speed and accuracy of
the package described.",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Narasimhan:2000:SIN,
author = "S. Narasimhan and Kuan Chen and F. Stenger",
title = "The solution of incompressible {Navier--Stokes}
equations using the sine collocation method",
crossref = "Kromann:2000:ISI",
pages = "199--214",
year = "2000",
DOI = "https://doi.org/10.1109/ITHERM.2000.866827",
bibdate = "Wed May 09 18:10:20 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
abstract = "Different kind of numerical approaches have been used
in the past to solve the complete set of Navier--Stokes
equations. The traditional methods that have been used
in the past are the finite-difference method,
finite-element method and the boundary element method.
Multigrid methods have been used recently for solving
these complete set of Navier--Stokes equations and they
help in obtaining a faster rate of convergence of the
residual for the solution of these equations. Some of
the problems that are faced in the world of numerical
methods today are the capacity to handle singularities
that occur within or at the boundaries of a
computational domain and also the capacity to handle
semi-infinite and infinite domains. Sine numerical
method has the advantage of handling singularities and
semi-infinite domains very effectively. It also
provides an exponential convergence rate. This study
involves a first step in applying the sine numerical
method to the flow within a driven cavity, which
requires the solution of the complete two-dimensional
Navier--Stokes equations. The sine collocation method
was applied to the driven cavity problem. The
Navier--Stokes equations were solved by means of two
dimensional sine collocation using the primitive
variables method. Simulations were also carried out
with the finite-difference method for the same problem
and the results were matched with the sine collocation
method. Simulations were also carried out by using the
commercial CFD code FLUENT. It was seen that the
profiles compared well between the different methods",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Resch:2000:FER,
author = "Ron Resch and Frank Stenger and J{\"o}rg Waldvogel",
title = "Functional equations related to the iteration of
functions",
journal = j-AEQUATIONES-MATHEMATICAE,
volume = "60",
number = "1--2",
pages = "25--37",
month = aug,
year = "2000",
CODEN = "AEMABN",
DOI = "https://doi.org/10.1007/s000100050133",
ISSN = "0001-9054 (print), 1420-8903 (electronic)",
ISSN-L = "0001-9054",
MRclass = "39B12 (26A18 30D05 37E05)",
MRnumber = "MR1777890 (2002j:39016)",
MRreviewer = "Francisco Balibrea",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "https://link.springer.com/article/10.1007/s000100050133",
ZMnumber = "0974.39011",
abstract = "Motivated by geometrical considerations the authors
deal with some functional equations in one variable
(Schr{\"o}der's equation, Babagge's equation, \dots).
Their special interest lies in finding situations and
conditions where there are unique solutions in certain
classes of functions. The methods and ideas presented
might, in the authors' opinion, be useful in
investigations connected with discrete dynamical
systems.",
acknowledgement = ack-nhfb,
classmath = "39B12 (Iterative functional equations) 30D05
(Functional equations in the complex domain) 26A18
(Iteration of functions of one real variable)",
fjournal = "Aequationes Mathematicae",
journal-URL = "http://link.springer.com/journal/10",
keywords = "iteration of functions; Schr{\"o}der's equation;
functional equations; Babagge's equation; dynamical
systems",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "J. Schwaiger (Graz)",
}
@Article{Stenger:2000:NSS,
author = "F. Stenger and R. Chaudhuri and J. Chiu",
title = "Novel sinc solution of the boundary integral form for
two-dimensional bi-material elasticity problems",
journal = j-COMPOS-SCI-TECH,
volume = "60",
number = "12--13",
pages = "2197--2211",
month = sep,
year = "2000",
CODEN = "CSTCEH",
DOI = "https://doi.org/10.1016/S0266-3538(00)00015-4",
ISSN = "0266-3538 (print), 1879-1050 (electronic)",
ISSN-L = "0266-3538",
bibdate = "Wed May 09 18:49:49 2007",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
abstract = "In this paper we illustrate a procedure for obtaining
an approximate solution of the integral equation form
of the two-dimensional Lame equation for a two-layer
problem, based on collocation via use of Sinc
approximation. The Sinc approach automatically
concentrates points near corners of the boundary where
the solution has singularities and yields exponential
convergence. A model two-layer bi-material elasticity
problem is numerically investigated here as an
illustration of this novel approach.",
acknowledgement = ack-nhfb,
fjournal = "Composites Science and Technology",
journal-URL = "http://www.sciencedirect.com/science/journal/02663538",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:2000:SAC,
author = "Frank Stenger",
title = "{Sinc} approximation of {Cauchy}-type integrals over
arcs",
journal = j-ANZIAM-J,
volume = "42",
number = "1",
pages = "87--97",
month = jul,
year = "2000",
CODEN = "AJNOA2",
DOI = "https://doi.org/10.1017/S1446181100011627",
ISSN = "1446-1811 (print), 1446-8735 (electronic)",
ISSN-L = "1446-1811",
MRclass = "30E20",
MRnumber = "MR1783372 (2001h:30034)",
MRreviewer = "D. Mitrovi{\'c}",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/anziamj.bib",
note = "Papers in honour of David Elliott on the occasion of
his sixty-fifth birthday.",
URL = "https://www.cambridge.org/core/journals/anziam-journal/article/sinc-approximation-of-cauchytype-integrals-over-arcs/F3E8E58B66C08F142BB6C63D61317703",
ZMnumber = "0974.65026",
abstract = "The author reviews the results of {\it D. Elliott} and
{\it F. Strenger} [Sinc method of solution of singular
integral equations, in IMACS Conference on CSIE,
Philadelphia, PA, 155-166 (1984)] in interpolation,
definite integration and the approximation of Hilbert
transforms via the Sinc method and obtains new formulas
for the approximation of Cauchy-type integrals over
analytic arcs $$ \frac {1}{\pi i} \int \frac {\varphi
(\tau)}{\tau - z} d \tau $$ via the Sinc method.",
acknowledgement = ack-nhfb,
ajournal = "ANZIAM J.",
classmath = "65D32 (Quadrature formulas (numerical methods)) 41A55
(Approximate quadratures)",
fjournal = "The ANZIAM Journal. The Australian \& New Zealand
Industrial and Applied Mathematics Journal",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
keywords = "Cauchy-type integrals; quadrature rules; Sinc method",
onlinedate = "17 February 2009",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "I. V. Boikov (Penza)",
}
@Article{Stenger:2000:SSN,
author = "Frank Stenger",
title = "Summary of {Sinc} numerical methods",
journal = j-J-COMPUT-APPL-MATH,
volume = "121",
number = "1--2",
pages = "379--420",
day = "1",
month = sep,
year = "2000",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/s0377-0427(00)00348-4;
https://doi.org/10.1137/0712022",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65D15 (65-02)",
MRnumber = "MR1780056 (2001d:65018)",
bibdate = "Sat Feb 25 12:43:36 MST 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
note = "Numerical analysis in the 20th century, Vol.\ I,
Approximation theory",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700003484",
ZMnumber = "0964.65010",
abstract = "This article attempts to summarize the existing
numerical methods based on Sinc approximation. Starting
with a comparison of polynomial and Sinc approximation,
basic formulas for the latter in the one-dimensional
case are given. The author also covers the
following:\par (i) Explicit spaces of analytic
functions for one dimensional Sinc approximation,\par
(ii) applications of Sinc indefinite integration and
collocation to the solution of ordinary differential
equation initial and boundary value problems,\par (iii)
results obtained for solution of partial differential
equations, via Sinc approximation of the
derivatives,\par (iv) some results obtained on the
solutions of integral equations,\par (v) use of Sinc
convolution, a technique for evaluating one and
multi-dimensional convolution-type integrals.\par A
list of some existing computer algorithms based on Sinc
methods is also given.",
abstract2 = "Sinc approximation methods excel for problems whose
solutions may have singularities, or infinite domains,
or boundary layers. This article summarizes results
obtained to date, on Sinc numerical methods of
computation. Sinc methods provide procedures for
function approximation over bounded or unbounded
regions, encompassing interpolation, approximation of
derivatives, approximate definite and indefinite
integration, solving initial value ordinary
differential equation problems, approximation and
inversion of Fourier and Laplace transforms,
approximation of Hilbert transforms, and approximation
of indefinite convolutions, the approximate solution of
partial differential equations, and the approximate
solution of integral equations, methods for
constructing conformal maps, and methods for analytic
continuation. Indeed, Sinc are ubiquitous for
approximating every operation of calculus.",
acknowledgement = ack-nhfb,
classmath = "65D15 (Algorithms for functional approximation) 65-02
(Research monographs (numerical analysis)) 65L60
(Finite numerical methods for ODE) 65M70 (Spectral,
collocation and related methods (IVP of PDE)) 65N35
(Collocation methods (BVP of PDE)) 65R20 (Integral
equations (numerical methods)) 65T40 (Trigonometric
approximation and interpolation)",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "algorithms; analytic functions; collocation;
convolution-type integrals; integral equations; Sinc
indefinite integration; Sinc methods; survey article",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "H. P. Dikshit (Bhopal)",
}
@TechReport{Stenger:2000:TDH,
author = "Frank Stenger",
title = "Three Dimensional Hybrid {BEM--Sinc} Analysis of
Bonded\slash Bolted Composite Joints with Discrete
Cracks",
type = "Technical Report",
number = "AD-a376 152, SIN-0005",
institution = "Sinc. Inc.",
address = "Salt Lake City, UT, USA",
pages = "53",
year = "2000",
bibdate = "Wed May 09 10:36:19 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
abstract = "In this report we first illustrate a procedure for
obtaining an approximate solution of the boundary
integral equation form to the two-dimensional Lame'
equation for a two-layer problem, based on collocation
via use of Sinc approximation. The Sinc approach
automatically concentrates points near corners of the
boundary where the solution has singularities and
yields exponential convergence. A model two-layer
bi-material elasticity problem is numerically
investigated here as an illustration of this novel
approach. This is followed by altering our method of
solving the two dimensional problem to a ``triangular
form'' which has resulted in decoupling of the boundary
integral equation system into a sequence of subsystem
equations, one over each layer. Additionally, a new
method is derived for accurately approximating the
``Laplace transform'' of the convolution kernel for the
case of extension of the above two dimensional solution
method to its three dimensional counterpart. It may be
noted that non-uniqueness of solution is a frequent
occurrence in layered elastic composite problems, and
this phenomenon is also captured by the boundary
integral equation system, demanding further
modification of the method of solution of the resulting
system of algebraic equations.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@TechReport{Stenger:2000:UAA,
author = "Frank Stenger",
title = "A unified approach to the approximate solution of
{PDE}",
type = "{Berichte aus der Technomathematik}",
number = "00-17",
institution = "{Zentrum f{\"u}r Technomathematik}",
address = "Bremen, Germany",
pages = "47",
year = "2000",
bibdate = "Wed May 09 10:34:27 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Narasimhan:2002:FSA,
author = "S. Narasimhan and Kuan Chen and Frank Stenger",
title = "A first step in applying the {Sinc} collocation method
to the nonlinear {Navier--Stokes} equations",
journal = j-NUMER-HEAT-TRANSFER-B,
volume = "41",
number = "5",
pages = "447--462",
day = "1",
month = may,
year = "2002",
CODEN = "NUHTD6",
DOI = "https://doi.org/10.1080/104077902753725902",
ISSN = "1040-7790 (print), 1521-0626 (electronic)",
ISSN-L = "1040-7790",
bibdate = "Thu May 10 10:19:44 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
abstract = "Different numerical approaches have been proposed in
the past to solve the Navier--Stokes equations.
Conventional methods have often relied on
finite-difference, finite-element, and boundary-element
techniques. Multigrid methods have been recently
introduced because they help to obtain a faster
convergence rate of the error residual. A difficulty
plaguing numerical methods today is the inability to
treat singularities at or near boundaries. Such
difficulties become even more pronounced when coupled
with the need to handle semi-infinite and infinite
domains. Sinc-based numerical algorithms have the
advantage of handling singularities, boundary layers,
and semi-infinite domains very effectively. In
addition, they typically require fewer nodal points and
are proven to provide an exponential convergence rate
in solving linear differential equations. This study
involves a first step in applying the Sinc-based
algorithm to solve a nonlinear set of partial
differential equations. The example we consider arises
in the context of a driven-cavity flow in two space
dimensions. As such, the steady and incompressible
Navier--Stokes equations are solved by means of
two-dimensional Sinc collocation in conjunction with
the primitive variable method and a pressure correction
algorithm based on artificial compressibility.
Simulations are also carried out using forward
differences, central differences, and a commercial
code. Results are compared with one another and with
the Sinc-collocation approximation. It is found that
the error in the Sinc-collocation approximation
outperforms other solutions, especially near the
singular corners of the cavity.",
acknowledgement = ack-nhfb,
fjournal = "Numerical Heat Transfer, Part B (Fundamentals)",
journal-URL = "http://www.tandfonline.com/loi/unhb20",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:2002:RFM,
author = "Frank Stenger and Elaine Cohen and Richard
Riesenfeld",
title = "Radial function methods of approximation based on
using harmonic {Green}'s functions",
journal = j-COMM-APPL-ANAL,
volume = "6",
number = "1",
pages = "1--15",
year = "2002",
CODEN = "????",
ISSN = "1083-2564",
ISSN-L = "1083-2564",
MRclass = "41A30 (41A63)",
MRnumber = "MR1879367 (2003e:41032)",
MRreviewer = "Valdir A. Menegatto",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "1085.41509",
abstract = "In this paper we present an explicit method of radial
basis function approximation over $ \Bbb R^n $, using
the Green's function for Laplace's equation. We prove
convergence of the scheme for all functions that are
continuous and of compact support. Interesting variants
of formulae result, in cases when lower dimensional
formulae are used to construct higher dimensional ones,
and in cases of periodic functions. Various explicit
operations are possible on the derived formulae, such
as obtaining Fourier and Hilbert transforms.",
acknowledgement = ack-nhfb,
classmath = "41A30 (Approximation by other special function
classes) 41A63 (Multidimensional approximation
problems)",
fjournal = "Communications in Applied Analysis. An International
Journal for Theory and Applications",
journal-URL = "http://www.dynamicpublishers.com/CAA/caacontent.htm",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Stenger:2002:SMA,
author = "Frank Stenger and Ahmad Reza Naghsh-Nilchi and Jenny
Niebsch and Ronny Ramlau",
title = "Sampling methods for approximate solution of {PDE}",
crossref = "Nashed:2002:IPI",
pages = "199--249",
year = "2002",
DOI = "https://doi.org/10.1090/conm/313/05377",
MRclass = "35A35 (44A35 65M70 65N35 65R20)",
MRnumber = "MR1940998 (2003m:35013)",
MRreviewer = "Stefka N. Dimova",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "1026.35006",
abstract = "The author proposed a novel procedure that combines
indefinite convolution and sine approximation, for
solving PDE. The PDE is first transformed to an
equivalent integral equation, this ``sine convolution''
procedure then enables solve the problem via method of
separation of variables. The method is flexible to
parallel computation. The time complexity of
computation to solve a $d$-dimensional problem on a
sequential machine is of the order $ (\log
(\varepsilon))^{2d + 2} $. Examples of solution are
illustrated for every type of equation.",
acknowledgement = ack-nhfb,
classmath = "35A35 (Theoretical approximation to solutions of PDE)
65M70 (Spectral, collocation and related methods (IVP
of PDE)) 65N35 (Collocation methods (BVP of PDE)) 65R20
(Integral equations (numerical methods))",
keywords = "Green's function; indefinite convolution; integral
equation; Laplace transformation; parallel computation;
separation of variables; sine approximation",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "Qin Mengzhao (Beijing)",
}
@Article{Chambers:2003:ERB,
author = "Janice J. Chambers and Shaheed Almudhafar and Frank
Stenger",
title = "Effect of Reduced Beam Section Frame Elements on
Stiffness of Moment Frames",
journal = j-J-STRUCT-ENG,
volume = "129",
number = "3",
pages = "383--393",
month = mar,
year = "2003",
CODEN = "JSENEI",
DOI = "https://doi.org/10.1061/(ASCE)0733-9445(2003)129:3(383)",
ISSN = "0970-0137",
ISSN-L = "0970-0137",
bibdate = "Fri Nov 7 08:39:50 MST 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of structural engineering",
journal-URL = "http://ascelibrary.org/journal/jsendh",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@TechReport{Stenger:2004:SCS,
author = "Frank Stenger",
title = "Sinc Convolution Solution of Laminated and Anisotropic
Composite Joints With Discrete Cracks",
type = "Technical Report",
number = "AD-b302 193",
institution = "Sinc. Inc.",
address = "Salt Lake City, UT, USA",
pages = "473",
year = "2004",
bibdate = "Wed May 09 10:38:58 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:2004:SSB,
author = "Frank Stenger and Thomas Cook and Robert M. Kirby",
title = "{Sinc} solution of biharmonic problems",
journal = j-CAN-APPL-MATH-Q,
volume = "12",
number = "3",
pages = "391--414",
month = "Fall",
year = "2004",
CODEN = "????",
ISSN = "1073-1849 (print), 1938-2634 (electronic)",
ISSN-L = "1073-1849",
MRclass = "65N99",
MRnumber = "MR2178866 (2006h:65210)",
MRreviewer = "Nicolae Pop",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://www.math.ualberta.ca/ami/CAMQ/table_of_content/vol_12/12_3h.htm",
ZMnumber = "1096.65117",
abstract = "We solve two biharmonic problems over a square, $ B =
( - 1, 1) \times ( - 1, 1) $. (1) The problem $
\nabla^4 U = f $, for which we determine a particular
solution, $U$, given $f$, via use of Sinc convolution;
and (2) The boundary value problem $ \nabla^4 V = 0 $
for which we determine $V$ given $ V = g $ and normal
derivative $ V_n = h $ on $ \partial B $, the boundary
of $B$. The solution to this problem is carried out
based on the identity $$ V = \Re \bigl \{ \overline {(z
- c)}{\cal E} + {\cal F} \bigr \} = (x - a)u + (y - b)v
+ \varphi, $$ where $ {\cal E} = u + i v $ and $ {\cal
F} = \varphi + i \psi $ are functions analytic in $B$,
and where $ c = a + i b $ is an arbitrary constant. We
thus determine approximations to the harmonic functions
$ u, v $ and $ \varphi $ on $ \partial B $, via use of
Sinc quadrature, and Sinc approximation of derivatives.
We then use a special, explicit Sinc-based analytic
continuation procedure to extend the functions $ u, v $
and $ \varphi $ to the interior of $B$. These
procedures enable us to determine functions $W$ which
solve a boundary problem at the form $ \nabla^4 W = f $
in $B$, given $f$ in $B$ and given $W$ and its normal
derivative, $ W_n $ on the boundary of $B$.\par
Given any $ \varepsilon & g t; 0 $, the time complexity
of sequential computation of an approximation of $
W_\varepsilon $ to $W$ to within a uniform error of $
\varepsilon $ in $B$, i.e., such that $ \sup_{(x, y)
\in B}|W(x, y) - W_\varepsilon (x, y)| & l t;
\varepsilon $, is $ O((\log (\varepsilon))^6) $.",
acknowledgement = ack-nhfb,
classmath = "65N35 (Collocation methods (BVP of PDE)) 35J40 (Higher
order elliptic equations, boundary value problems)
65N15 (Error bounds (BVP of PDE)) 65N12 (Stability and
convergence of numerical methods (BVP of PDE))",
fjournal = "The Canadian Applied Mathematics Quarterly",
journal-URL = "http://www.math.ualberta.ca/ami/camq.html",
keywords = "biharmonic problems; collocation; convergence; error
bounds; numerical examples; Sinc convolution; Sinc
quadrature",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Schmeisser:2007:SAG,
author = "Gerhard Schmeisser and Frank Stenger",
title = "Sinc approximation with a {Gaussian} multiplier",
journal = j-SAMPL-THEORY-SIGNAL-IMAGE-PROCESS,
volume = "6",
number = "2",
pages = "199--221",
year = "2007",
ISSN = "1530-6429",
ISSN-L = "1530-6429",
MRclass = "94A20 (30E10 41A25 41A30 41A80 65B10)",
MRnumber = "2343406 (2008e:94017)",
bibdate = "Tue Aug 24 23:09:55 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://stsip.org/pdf_campaign/vol06/no2/vol06no2pp199-221.pdf",
ZMnumber = "1156.94326",
abstract = "Recently, it was shown with the help of Fourier
analysis that by incorporating a Gaussian multiplier
into the truncated classical sampling series, one can
approximate bandlimited signals of finite energy with
an error that decays exponentially as a function of the
number of involved samples. Based on complex analysis,
we show for a slightly modified operator that this
approximation method applies not only to bandlimited
signals of finite energy, but also to bandlimited
signals of infinite energy, to classes of
non-bandlimited signals, to all entire functions of
exponential type (including those whose samples
increase exponentially), and to functions analytic in a
strip and not necessarily bounded. Moreover, the method
extends to non-real argument. In each of these cases,
the use of $ 2 N + 1 $ samples results in an error
bound of the form $ M{\text {e}}^{- \alpha N} $, where
$M$ and $ \alpha $ are positive numbers that do not
depend on $N$. The power of the method is illustrated
by several examples.",
acknowledgement = ack-nhfb,
classmath = "94A20 (Sampling theory); 30E10 (Approximation in the
complex domain); 65B10 (Summation of series (numerical
analysis))",
fjournal = "Sampling Theory in Signal and Image Processing",
journal-URL = "http://stsip.org/",
keywords = "error bounds, entire functions of exponential type;
functions analytic in a strip; Gaussian convergence
factor; sampling series; sinc approximation",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:2007:SVS,
author = "Frank Stenger",
title = "Separation of variables solution of {PDE} via Sinc
methods",
journal = j-INT-J-APPL-MATH-STAT,
volume = "10",
number = "SO7",
pages = "98--115",
year = "2007",
ISSN = "0973-1377 (print), 0973-7545 (electronic)",
ISSN-L = "0973-1377",
MRclass = "65N35",
MRnumber = "2337105 (2008f:65236)",
bibdate = "Tue Aug 24 23:09:55 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://www.ceser.in/ceserp/index.php/ijamas/article/view/305",
ZMnumber = "1139.65081",
abstract = "In their 1953 text {\it P. M. Morse} and {\it H.
Feshbach} [Methods of theoretical physics. Vol. I. II.
(1953; Zbl 0051.40603)] list 13 regions of when the
three dimensional Laplace and Helmholtz partial
differential equation (PDE), can be solved via use of
separation of variables, i.e., via use of
one-dimensional methods. They describe explicit
transformations which make such solutions possible. In
this paper we state precise assumptions on the PDE, its
piecewise smooth curvilinear spatial boundary and the
boundary conditions, i.e., assumptions of analyticity
in each variable, which are satisfied, in essence,
whenever calculus is used to model the PDE. Under these
assumptions we are able to prove that the approximate
solution of the PDE has similar analyticity properties.
By combining this analyticity assumption with novel
sinc convolution methods, we are able to solve the PDE
to arbitrary uniform accuracy via use of a relatively
small sequence of one dimensional matrix
operations.
The proofs of the above claims are lengthy, and we
therefore present such proofs only for PDE in two
dimensions. Proofs for the case of three dimensional
will be published elsewhere.",
acknowledgement = ack-nhfb,
classmath = "65N38 (Boundary element methods (BVP of PDE)) 35J05
(Laplacian operator, reduced wave equation (Helmholtz
equation), Poisson equation)",
fjournal = "International Journal of Applied Mathematics \&
Statistics",
journal-URL = "http://www.ceser.in/ijamas.html",
keywords = "Dirichlet problem; Laplace equation; Neumann problem;
Poisson equation; separation of variables; sinc
convolution; sinc methods",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:2008:FSZ,
author = "Frank Stenger",
title = "{Fourier} series for zeta function via {Sinc}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "429",
number = "10",
pages = "2636--2639",
day = "1",
month = nov,
year = "2008",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2008.01.037",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "11M06 (42A16)",
MRnumber = "2456801 (2009j:11135)",
bibdate = "Wed Aug 25 16:13:38 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.sciencedirect.com/science/journal/00243795",
ZMnumber = "1149.42002",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:2008:PAB,
author = "Frank Stenger and Brandon Baker and Carl Brewer and
Geoffrey Hunter and Sasha Kaputerko and Jason
Shepherd",
title = "Periodic approximations based on sinc",
journal = j-INT-J-PURE-APPL-MATH,
volume = "49",
number = "1",
pages = "63--72",
year = "2008",
ISSN = "1311-8080 (print), 1314-3395 (electronic)",
ISSN-L = "1314-3395",
MRclass = "41A05",
MRnumber = "2477267",
bibdate = "Tue Aug 24 23:09:55 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://ijpam.eu/contents/2008-49-1/8/index.html",
ZMnumber = "1169.41300",
abstract = "We derive some novel formulas for interpolating
functions that are periodic with period $T$ on $ \Bbb R
= \{ x : - \infty < x < \infty \} $. These formulas are
all based on the Whittaker Cardinal series expansion.
We give some comparative examples of approximations of
smooth periodic functions and discontinuous functions
via both our periodic basis as well as with
corresponding polynomial approximations.",
acknowledgement = ack-nhfb,
classmath = "41A05 (Interpolation (approximations and
expansions))",
fjournal = "International Journal of Pure and Applied
Mathematics",
journal-URL = "http://ijpam.eu/",
keywords = "cardinal expansions; Fourier polynomials;
interpolating functions, algebraic polynomials",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:2009:PFD,
author = "Frank Stenger",
title = "Polynomial function and derivative approximation of
{Sinc} data",
journal = j-J-COMPLEXITY,
volume = "25",
number = "3",
pages = "292--302",
year = "2009",
CODEN = "JOCOEH",
DOI = "https://doi.org/10.1016/j.jco.2009.02.010",
ISSN = "0885-064X (print), 1090-2708 (electronic)",
ISSN-L = "0885-064X",
MRclass = "65D25 (41A30)",
MRnumber = "2524548 (2010d:65050)",
bibdate = "Tue Aug 24 23:09:55 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "1180.65028",
abstract = "Sinc methods consist of a family of one-dimensional
approximation procedures for approximating the
operations of calculus. These procedures are obtained
by operating on the sinc interpolation formulae, which
are based on the function values in the sinc points.
Usually, these operations yield high accuracy. However,
when differentiating a sinc approximation formula that
approximates over an interval with a finite endpoint,
then the accuracy is poor in the neighborhood of the
endpoint.\par
In the present paper the author derives a new way to
obtain an approximation of the derivative of a function
that is known in the sinc points. This method is proved
to be uniformly accurate over the whole interval. A
very simple example (the function $ \sin (x) $ and its
derivative over the interval $ [0, 1] $ ) is studied
numerically to confirm the claimed accuracy.",
acknowledgement = ack-nhfb,
classmath = "65D25 (Numerical differentiation) 65D10 (Smoothing,
curve fitting)",
fjournal = "Journal of complexity",
journal-URL = "http://www.sciencedirect.com/science/journal/0885064X",
keywords = "numerical differentiation; sinc interpolation; sinc
methods",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "Willy Govaerts (Gent)",
}
@Article{Baumann:2011:FCS,
author = "Gerd Baumann and Frank Stenger",
title = "Fractional calculus and {Sinc} methods",
journal = "Fractional Calculus and Applied Analysis",
volume = "14",
number = "4",
pages = "568--622",
year = "2011",
DOI = "https://doi.org/10.2478/s13540-011-0035-3",
ISSN = "1311-0454 (print), 1314-2444 (electronic)",
ISSN-L = "1314-2224",
MRclass = "65D15 (26A33 45J05 65L60)",
MRnumber = "2846377",
MRreviewer = "Roberto Garrappa",
bibdate = "Mon Apr 21 17:26:23 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "1273.65103",
acknowledgement = ack-nhfb,
ajournal = "Fract. Calc. Appl. Anal.",
fjournal = "Fractional Calculus and Applied Analysis. An
International Journal for Theory and Applications",
journal-URL = "http://www.math.bas.bg/~fcaa/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Book{Stenger:2011:HSN,
author = "Frank Stenger",
title = "Handbook of Sinc Numerical Methods",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xx + 463",
year = "2011",
DOI = "https://doi.org/10.1201/b10375",
ISBN = "1-4398-2158-5 (hardback), 1-4398-2159-3 (e-book)",
ISBN-13 = "978-1-4398-2158-9 (hardback), 978-1-4398-2159-6
(e-book)",
LCCN = "QA372 .S8195 2010",
MRclass = "65-02 (65L60 65M70 65N35)",
MRnumber = "2722054",
MRreviewer = "Gregory E. Fasshauer",
bibdate = "Mon Apr 21 17:35:42 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
z3950.loc.gov:7090/Voyager",
series = "Chapman and Hall/CRC numerical analysis and scientific
computation series",
URL = "http://www.crcpress.com/product/isbn/9781439821589",
ZMnumber = "1208.65143",
abstract = "This handbook is essential for solving numerical
problems in mathematics, computer science, and
engineering. The methods presented are similar to
finite elements but more adept at solving analytic
problems with singularities over irregularly shaped yet
analytically described regions. The author makes sinc
methods accessible to potential users by limiting
details as to how or why these methods work. From
calculus to partial differential and integral
equations, the book can be used to approximate almost
every type of operation. It includes more than 470
MATLAB programs, along with a CD-ROM containing these
programs for ease of use",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
subject = "Galerkin methods; Differential equations; Numerical
solutions; mathematics / applied; mathematics /
differential equations; mathematics / number systems",
tableofcontents = "One-Dimensional Sinc Theory \\
Introduction and Summary \\
Sampling over the Real Line \\
More General Sinc Approximation on $R$ \\
Sinc, Wavelets, Trigonometric and Algebraic Polynomials
and Quadratures \\
Sinc Methods on $\Gamma$ \\
Rational Approximation at Sinc Points \\
Polynomial Methods at Sinc Points \\
\\
Sinc Convolution-BIE Methods for PDE and IE \\
Introduction and Summary \\
Some Properties of Green's Functions \\
Free-Space Green's Functions for PDE \\
Laplace Transforms of Green's Functions \\
Multi-Dimensional Convolution Based on Sinc \\
Theory of Separation of Variables \\
\\
Explicit 1-d Program Solutions via Sinc-Pack \\
Introduction and Summary \\
Sinc Interpolation \\
Approximation of Derivatives \\
Sinc Quadrature \\
Sinc Indefinite Integration \\
Sinc Indefinite Convolution \\
Laplace Transform Inversion \\
Hilbert and Cauchy Transforms \\
Sinc Solution of ODE \\
Wavelet Examples \\
\\
Explicit Program Solutions of PDE via Sinc-Pack \\
Introduction and Summary \\
Elliptic PDE \\
Hyperbolic PDE \\
Parabolic PDE \\
Performance Comparisons \\
\\
Directory of Programs \\
Wavelet Formulas \\
One Dimensional Sinc Programs \\
Multi-Dimensional Laplace Transform Programs \\
\\
Bibliography \\
\\
Index",
}
@Article{Baumann:2013:FAD,
author = "Gerd Baumann and Frank Stenger",
title = "Fractional adsorption diffusion",
journal = "Fractional Calculus and Applied Analysis",
volume = "16",
number = "3",
pages = "737--764",
year = "2013",
DOI = "https://doi.org/10.2478/s13540-013-0046-3",
ISSN = "1311-0454 (print), 1314-2444 (electronic)",
ISSN-L = "1314-2224",
MRclass = "65R20 (26A33 35R11 45G05) 65D15 45E10",
MRnumber = "3071211",
bibdate = "Mon Apr 21 17:27:35 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "1312.65215",
acknowledgement = ack-nhfb,
ajournal = "Fract. Calc. Appl. Anal.",
fjournal = "Fractional Calculus and Applied Analysis. An
International Journal for Theory and Applications",
journal-URL = "http://www.math.bas.bg/~fcaa/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Hagmann:2013:LHM,
author = "Mark J. Hagmann and Frank S. Stenger and Dmitry A.
Yarotski",
title = "Linewidth of the harmonics in a microwave frequency
comb generated by focusing a mode-locked ultrafast
laser on a tunneling junction",
journal = j-J-APPL-PHYS,
volume = "114",
number = "22",
pages = "223107",
year = "2013",
CODEN = "JAPIAU",
DOI = "https://doi.org/10.1063/1.4831952",
ISSN = "0021-8979 (print), 1089-7550 (electronic), 1520-8850",
ISSN-L = "0021-8979",
bibdate = "Fri Nov 7 06:05:49 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://scitation.aip.org/content/aip/journal/jap/114/22/10.1063/1.4831952",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Physics",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4915369",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InCollection{Stenger:2013:IAU,
author = "Frank Stenger and Maha Youssef and Jenny Niebsch",
title = "Improved Approximation via Use of Transformations",
crossref = "Shen:2013:MSA",
chapter = "2",
pages = "25--49",
year = "2013",
DOI = "https://doi.org/10.1007/978-1-4614-4145-8_2",
MRclass = "65T40 (42A10) 41A05 41A10 65D10 42C40",
MRnumber = "3024463",
bibdate = "Fri Nov 07 06:46:49 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "1316.41004",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:2013:SMC,
author = "Frank Stenger and Richard B. Hall",
title = "Sinc methods for computing solutions to viscoelastic
and related problems",
journal = j-CAN-APPL-MATH-Q,
volume = "21",
number = "1",
pages = "95--120",
year = "2013",
ISSN = "1073-1849 (print), 1938-2634 (electronic)",
ISSN-L = "1073-1849",
MRclass = "65L60 (74D10)",
MRnumber = "3244323",
bibdate = "Thu Oct 13 11:12:56 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "1334.65211",
acknowledgement = ack-nhfb,
fjournal = "Canadian Applied Mathematics Quarterly",
journal-URL = "http://www.math.ualberta.ca/ami/camq.html",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InProceedings{Stenger:2014:LCS,
author = "Frank Stenger and Hany A. M. El-Sharkawy and Gerd
Baumann",
title = "The {Lebesgue} Constant for Sinc Approximations",
crossref = "Zayed:2014:NPA",
pages = "319--335",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-319-08801-3_13",
MRclass = "42A10 42A15 41A05 41A55 41A20",
MRnumber = "3363036",
MRreviewer = "Tibor K. Pog{\'a}ny",
bibdate = "Fri Nov 7 08:39:52 MST 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "1314.42002",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Baumann:2015:SAF,
author = "Gerd Baumann and Frank Stenger",
title = "Sinc-approximations of fractional operators: a
computing approach",
journal = "Mathematics",
volume = "3",
number = "2",
pages = "444--480",
year = "2015",
DOI = "https://doi.org/10.3390/math3020444",
ISSN = "2227-7390",
ISSN-L = "2227-7390",
MRnumber = "65D05 65D30 44A35 81-04",
bibdate = "Wed Aug 16 06:28:17 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "1328.65051",
acknowledgement = ack-nhfb,
fjournal = "Mathematics",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@TechReport{Stenger:2015:CMCa,
author = "Frank Stenger and Gerd Baumann and Vasilios G.
Koures",
title = "Computational Methods for Chemistry and Physics, and
Schr{\"o}dinger in $ 3 + 1 $",
type = "Preprint",
institution = "University of Utah; German University in Cairo; IISAM
L3C",
address = "Salt Lake City, UT, USA; New Cairo City, Egypt;
Oklahoma City, OK, USA",
pages = "44",
day = "24",
month = feb,
year = "2015",
bibdate = "Thu Feb 26 07:59:05 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
note = "To be published in the proceedings of a conference of
December 2014 honoring the 85th birthday of Frank E.
Harris.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:2015:CMCb,
author = "Frank Stenger and Gerd Baumann and Vasilios G.
Koures",
title = "Computational Methods for Chemistry and Physics, and
{Schr{\"o}dinger} in $ 3 + 1^1 $",
chapter = "11",
journal = j-ADV-QUANTUM-CHEM,
volume = "71",
pages = "265--298",
year = "2015",
CODEN = "AQCHA9",
DOI = "https://doi.org/10.1016/bs.aiq.2015.02.005",
ISSN = "0065-3276 (print), 2162-8815 (electronic)",
ISSN-L = "0065-3276",
bibdate = "Fri Aug 28 07:16:44 MDT 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/advquantumchem.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0065327615000064",
acknowledgement = ack-nhfb,
ajournal = "Adv. Quantum Chem.",
fjournal = "Advances in Quantum Chemistry",
journal-URL = "http://www.sciencedirect.com/science/bookseries/00653276/",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Book{Stenger:2016:NSE,
author = "Frank Stenger and Don Tucker and Gerd Baumann",
title = "{Navier--Stokes} Equations on {$ R^3 \times [0, T]
$}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xi + 219",
year = "2016",
DOI = "https://doi.org/10.1007/978-3-319-27526-0",
ISBN = "3-319-27524-0 (hardcover), 3-319-27526-7 (e-book)",
ISBN-13 = "978-3-319-27524-6 (hardcover), 978-3-319-27526-0
(e-book)",
LCCN = "QA374 .S834 2016",
MRclass = "35-02 35Q30 76D05 65R20 65-04",
MRnumber = "3558942",
MRreviewer = "Michael J. Carley",
bibdate = "Mon May 02 11:20:53 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib",
URL = "http://www.springer.com/us/book/9783319275246",
ZMnumber = "06520143",
ZMnumber = "1368.35001",
abstract = "In this monograph, leading researchers in the world of
numerical analysis, partial differential equations, and
hard computational problems study the properties of
solutions of the Navier--Stokes partial differential
equations on (x, y, z, t) R3 [0, T]. Initially
converting the PDE to a system of integral equations,
the authors then describe spaces A of analytic
functions that house solutions of this equation, and
show that these spaces of analytic functions are dense
in the spaces S of rapidly decreasing and infinitely
differentiable functions. This method benefits from the
following advantages: The functions of S are nearly
always conceptual rather than explicit Initial and
boundary conditions of solutions of PDE are usually
drawn from the applied sciences, and as such, they are
nearly always piece-wise analytic, and in this case,
the solutions have the same properties When methods of
approximation are applied to functions of A they
converge at an exponential rate, whereas methods of
approximation applied to the functions of S converge
only at a polynomial rate Enables sharper bounds on the
solution enabling easier existence proofs, and a more
accurate and more efficient method of solution,
including accurate error bounds Following the proofs of
denseness, the authors prove the existence of a
solution of the integral equations in the space of
functions A R3 [0, T], and provide an explicit novel
algorithm based on Sinc approximation and Picard-like
iteration for computing the solution. Additionally, the
authors include appendices that provide a custom
Mathematica program for computing solutions based on
the explicit algorithmic approximation procedure, and
which supply explicit illustrations of these computed
solutions.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
tableofcontents = "Preface \\
Introduction, PDE, and IE Formulations \\
Spaces of Analytic Functions \\
Spaces of Solution of the N--S Equations \\
Proof of Convergence of Iteration 1.6.3 \\
Numerical Methods for Solving N--S Equations \\
Sinc Convolution Examples \\
Implementation Notes \\
Result Notes",
xxpages = "x + 226",
}
@Article{Baumann:2017:FFP,
author = "Gerd Baumann and Frank Stenger",
title = "Fractional {Fokker--Planck} equation",
journal = "Mathematics",
volume = "5",
number = "1",
pages = "19",
year = "2017",
DOI = "https://doi.org/10.3390/math5010012",
ISSN = "2227-7390",
ISSN-L = "2227-7390",
MRnumber = "65D05 65D30 44A35 81-04 35Q84 35R11",
bibdate = "Wed Aug 16 06:23:51 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
ZMnumber = "1365.65028",
acknowledgement = ack-nhfb,
fjournal = "Mathematics",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@InCollection{Stenger:2017:ARZ,
author = "Frank Stenger",
title = "Approximating the {Riemann} zeta and related
functions",
crossref = "Govil:2017:PAT",
pages = "363--373",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-49242-1_17",
MRclass = "11Y35 (11M06 41A60 42A10)",
MRnumber = "3644752",
bibdate = "Sat Feb 10 18:46:45 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
series = "Springer Optimization and Its Applications",
URL = "https://link.springer.com/chapter/10.1007/978-3-319-49242-1_17",
ZMnumber = "1371.42002",
abstract = "In this chapter we study the well-known function $G$,
as well as some other functions that have the same
zeros as the Riemann zeta function $ \zeta (z)$ in the
critical strip. To this end, we first derive a Fourier
series expansion of $G$. Next, we use asymptotic
methods to derive another function which also has the
same zeros in the critical strip as $ \zeta (z)$, but
which lacks the extreme oscillatory behavior and
extreme amplitude values that $ \zeta (z)$ possesses,
and which is therefore more suitable for computational
purposes.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
series-URL = "https://link.springer.com/bookseries/7393",
}
@Misc{Stenger:2018:ASN,
author = "Frank Stenger",
title = "Approximate Solution of Numerical Problems via
Approximate indefinite Integration",
howpublished = "Talk dedicated to Walter Gautschi on the occasion of
his 90th birthday.",
day = "4",
month = apr,
year = "2018",
bibdate = "Thu Apr 05 19:01:33 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
note = "PDF file not yet released.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:2018:IIO,
author = "Frank Stenger",
title = "Indefinite Integration Operators Identities and their
Approximations",
journal = "arXiv.org",
volume = "",
number = "",
pages = "1--36",
day = "17",
month = oct,
year = "2018",
bibdate = "Thu Oct 03 06:03:22 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "https://arxiv.org/abs/1809.05607",
abstract = "The integration operators (*) $ ({\cal J}^+ g)(x) =
\int_a^x g(t) \, dt $ and (**) $ ({\cal J}^g)(x) =
\int_x^b g(t) \, dt $ defined on an interval $ (a, b)
\subseteq \mathbf {R} $ yield new identities for
indefinite convolutions, control theory, Laplace and
Fourier transform inversion, solution of differential
equations, and solution of the classical Wiener--Hopf
integral equations. These identities are are expressed
in terms of $ {\cal J}^\pm $, and they are thus
esoteric. However the integrals (*) and (**) can be
approximated in many ways, yielding novel and very
accurate methods of approximating all of the above
listed relations. Several examples are presented,
mainly using Legendre polynomial as approximations, and
references are given for approximation of some of the
operations using Sinc methods. These examples
illustrate for a class of sampled statistical models,
the possibility of reconstructing models much more
efficiently than by the usual slow Monte--Carlo ($
O(N^{ -1 / 2}) $ rate. Our examples illustrate that we
need only sample at 5 points to get a representation of
a model that is uniformly accurate to nearly 3
significant figure accuracy.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
}
@Article{Stenger:2018:PRH,
author = "Frank Stenger",
title = "A Proof of the {Riemann} Hypothesis",
journal = "arXiv.org",
volume = "",
number = "",
pages = "1--26",
day = "8",
month = feb,
year = "2018",
bibdate = "Thu Oct 03 05:39:01 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "https://arxiv.org/abs/1708.01209v4",
abstract = "The function $ G(z) = \int_0^\infty \zeta^{z - 1} (1 +
\exp (\zeta))^{ 1} \, d \zeta $ is analytic and has the
same zeros as the Riemann zeta function in the critical
strip $ D = \{ z \in C \colon 0 < \Re z < 1 \} $. This
paper combines some novel methods about indefinite
integration, indefinite convolutions and inversions of
Fourier transforms with numerical ranges of operators
to prove the Riemann hypothesis.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
remark = "[v1] Thu, 3 Aug 2017 16:52:53 UTC (14 KB); [v2] Mon,
14 Aug 2017 16:56:04 UTC (15 KB); [v3] Thu, 4 Jan 2018
19:45:23 UTC (19 KB); [v4] Thu, 8 Feb 2018 20:59:12 UTC
(18 KB)",
}
@InCollection{Stenger:2021:IIO,
author = "Frank Stenger",
title = "Indefinite Integration Operators Identities, and Their
Approximations",
crossref = "Baumann:2021:NSM",
chapter = "9",
pages = "227--254",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-49716-3_9",
bibdate = "Mon May 03 06:55:48 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Stenger:2022:EPR,
author = "Frank Stenger",
title = "An Elementary Proof of the {Riemann Hypothesis}",
type = "Report",
institution = "School of Computing, University of Utah",
address = "Salt Lake City, UT 84112, USA",
pages = "13",
day = "6",
month = apr,
year = "2022",
bibdate = "Thu Apr 07 07:43:04 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "https://arxiv.org/abs/1708.01209",
acknowledgement = ack-nhfb,
}
@Article{Moler:1969:MSC,
author = "C. B. Moler",
title = "More on the sphere in the corner",
journal = j-SIGNUM,
volume = "4",
number = "1",
pages = "7--7",
month = jan,
year = "1969",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1198450.1198451",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Mon Mar 5 17:26:28 MST 2007",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/signum.bib",
note = "See \cite{Stenger:1968:TC}.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
}
@Article{Sack:1978:CSQ,
author = "R. A. Sack",
title = "Comments on some quadrature formulas by {F. Stenger}",
journal = j-J-INST-MATH-APPL,
volume = "21",
number = "3",
pages = "359--361",
month = apr,
year = "1978",
CODEN = "JMTAA8",
DOI = "https://doi.org/10.1093/imamat/21.3.359",
ISSN = "0020-2932",
ISSN-L = "0020-2932",
MRclass = "65D30",
MRnumber = "0494861",
MRreviewer = "David K. Kahaner",
bibdate = "Fri Apr 5 07:55:06 MST 2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/jinstmathappl.bib;
http://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib",
note = "See \cite{Stenger:1973:IFB,Stenger:1977:RIF}.",
URL = "https://academic.oup.com/imamat/article/21/3/359/690581",
ZMnumber = "0374.65011",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
}
@Article{Stynes:1979:SST,
author = "Martin Stynes",
title = "A simplification of {Stenger}'s topological degree
formula",
journal = j-NUM-MATH,
volume = "33",
number = "2",
pages = "147--155",
month = jun,
year = "1979",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01399550",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "55M25 (65H10)",
MRnumber = "80m:55002 (549445)",
MRreviewer = "T. Y. Li",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
note = "See \cite{Stenger:1975:CTD}.",
URL = "https://link.springer.com/article/10.1007/BF01399550",
acknowledgement = ack-nhfb,
classification = "C4140 (Linear algebra)",
corpsource = "Dept. of Math., Univ. Coll., Cork, Ireland",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "matrix algebra; numerical methods; polyhedron;
topological degree formula",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Beighton:1982:EES,
author = "S. Beighton and B. Noble",
title = "An error estimate for {Stenger}'s quadrature formula",
journal = j-MATH-COMPUT,
volume = "38",
number = "158",
pages = "539--545",
month = apr,
year = "1982",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1982-0645669-9;
https://doi.org/10.2307/2007288",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D30",
MRnumber = "83a:65021 (645669)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/mathcomp.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
note = "See \cite{Stenger:1973:IFB}.",
URL = "http://www.ams.org/journals/mcom/1982-38-158/S0025-5718-1982-0645669-9/",
ZMnumber = "0483.65015",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Stynes:1982:RST,
author = "M. Stynes",
title = "A remark on {Stenger}'s topological degree algorithm",
journal = j-PROC-R-IR-ACAD-SECT-A,
volume = "82",
number = "2",
pages = "163--166",
year = "1982",
ISSN = "0035-8975",
ISSN-L = "0035-8975",
MRclass = "55M20",
MRnumber = "701375",
MRreviewer = "Christian Fenske",
bibdate = "Tue Mar 19 05:32:42 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "https://www.jstor.org/stable/20489150",
acknowledgement = ack-nhfb,
ajournal = "Proc. Roy. Irish Acad. Sect. A",
fjournal = "Proceedings of the Royal Irish Academy. Section A",
journal-URL = "https://www.jstor.org/journal/procriasectiona",
}
@Article{McArthur:1994:BRB,
author = "Kelly M. McArthur",
title = "Book Review: {{\booktitle{Numerical Methods Based on
Sine and Analytic Functions}}, by Frank Stenger}",
journal = j-SIAM-REVIEW,
volume = "36",
number = "4",
pages = "673--674",
month = dec,
year = "1994",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1036167",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Nov 7 08:39:45 MST 2014",
bibsource = "http://epubs.siam.org/toc/siread/36/4;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
note = "See \cite{Stenger:1993:NMB}.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "December 1994",
}
@Misc{Davis:2004:IFS,
author = "Philip Davis",
title = "An Interview with {Frank Stenger}",
howpublished = "Interview conducted by the Society for Industrial and
Applied Mathematics, as part of grant \#
DE-FG02-01ER25547 awarded by the US Department of
Energy",
pages = "20",
day = "24",
month = jun,
year = "2004",
bibdate = "Sat Feb 10 18:38:06 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://history.siam.org/oralhistories/stenger.htm",
acknowledgement = ack-nhfb,
}
@Article{Bialecki:2009:GEP,
author = "Bernard Bialecki and Baker R. Kearfott and Krzysztof
A. Sikorski and Masaki Sugihara",
title = "{Guest Editors}' preface: Issue dedicated to
{Professor Frank Stenger}",
journal = j-J-COMPLEXITY,
volume = "25",
number = "3",
pages = "233--236",
month = jun,
year = "2009",
CODEN = "JOCOEH",
DOI = "https://doi.org/10.1016/j.jco.2009.02.002",
ISSN = "0885-064X (print), 1090-2708 (electronic)",
ISSN-L = "0885-064X",
bibdate = "Fri Nov 7 08:39:52 MST 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0885064X09000053",
abstract = "This issue of the Journal of Complexity is dedicated
to Professor Frank Stenger on the occasion of his 65th
birthday, which was celebrated during the conference:
Optimal Algorithms and Computational Complexity for
Numerical Problems, in Salt Lake City, in May 2007.",
acknowledgement = ack-nhfb,
fjournal = "Journal of complexity",
journal-URL = "http://www.sciencedirect.com/science/journal/0885064X",
}
@Article{Han:2014:PSC,
author = "Lixing Han and Jianhong Xu",
title = "Proof of {Stenger}'s conjecture on matrix {$ I^{( -
1)} $} of {Sinc} methods",
journal = j-J-COMPUT-APPL-MATH,
volume = "255",
number = "??",
pages = "805--811",
day = "1",
month = jan,
year = "2014",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/j.cam.2013.07.001",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "15A42 (65F15); 15A18; 15A42; 15B05; 15B57; 41A30;
65F15; 65T40",
MRnumber = "3093462",
MRreviewer = "Egor A. Maksimenko",
bibdate = "Sat Feb 25 13:28:17 MST 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
note = "See \cite{Stenger:1997:MSM}.",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042713003452",
ZMnumber = "1291.15023",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Gautschi:2019:CST,
author = "Walter Gautschi and Ernst Hairer",
title = "On conjectures of {Stenger} in the theory of
orthogonal polynomials",
journal = j-J-INEQUAL-APPL,
pages = "27",
year = "2019",
DOI = "https://doi.org/10.1186/s13660-019-2107-6",
ISSN = "1025-5834",
ISSN-L = "1025-5834",
MRclass = "33C45",
MRnumber = "3959312",
bibdate = "Thu Oct 3 05:45:54 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
note = "Paper no. 159.",
URL = "https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-019-2107-6",
acknowledgement = ack-nhfb,
fjournal = "Journal of Inequalities and Applications",
journal-URL = "http://journalofinequalitiesandapplications.springeropen.com/",
}
@InCollection{Annaby:2021:OCE,
author = "M. H. Annaby and R. M. Asharabi and M. M. Tharwat",
title = "An Overview of the Computation of the Eigenvalues
Using Sinc-Methods",
crossref = "Baumann:2021:NSM",
chapter = "10",
pages = "255--298",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-49716-3_10",
bibdate = "Mon May 03 06:55:48 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Annaby:2021:SGA,
author = "M. H. Annaby and R. M. Asharabi",
title = "Sinc-{Gaussian} Approach for Solving the Inverse Heat
Conduction Problem",
crossref = "Baumann:2021:NSM",
chapter = "1",
pages = "3--21",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-49716-3_1",
bibdate = "Mon May 03 06:55:48 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Attili:2021:NSF,
author = "Basem Attili",
title = "Numerical Solution of the {Falkner--Skan} Equation
Arising in Boundary Layer Theory Using the
Sinc-Collocation Method",
crossref = "Baumann:2021:NSM",
chapter = "7",
pages = "147--162",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-49716-3_7",
bibdate = "Mon May 03 06:55:48 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Baumann:2021:LSE,
author = "Gerd Baumann",
title = "{L{\'e}vy--Schr{\"o}dinger} Equation: Their
Eigenvalues and Eigenfunctions Using Sinc Methods",
crossref = "Baumann:2021:NSM",
chapter = "4",
pages = "55--98",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-49716-3_4",
bibdate = "Mon May 03 06:55:48 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Beebe:2021:PAF,
author = "Nelson H. F. Beebe",
title = "Publications by, and About, {Frank Stenger}",
crossref = "Baumann:2021:NSM",
pages = "385--399",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-49716-3_9",
bibdate = "Mon May 03 06:55:48 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Berrut:2021:IJS,
author = "Jean-Paul Berrut",
title = "The Influence of Jumps on the Sinc Interpolant, and
Ways to Overcome It",
crossref = "Baumann:2021:NSM",
chapter = "12",
pages = "323--339",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-49716-3_12",
bibdate = "Mon May 03 06:55:48 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Dopp:2021:EIA,
author = "Kathy Dopp",
title = "Election Integrity Audits to Ensure Election Outcome
Accuracy",
crossref = "Baumann:2021:NSM",
chapter = "6",
pages = "123--145",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-49716-3_6",
bibdate = "Mon May 03 06:55:48 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Ismail:2021:CMF,
author = "Mourad E. H. Ismail and Ruiming Zhang",
title = "Completely Monotonic {Fredholm} Determinants",
crossref = "Baumann:2021:NSM",
chapter = "11",
pages = "299--321",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-49716-3_11",
bibdate = "Mon May 03 06:55:48 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Nedaiasl:2021:SPS,
author = "Khadijeh Nedaiasl",
title = "Sinc Projection Solutions of {Fredholm} Integral
Equations",
crossref = "Baumann:2021:NSM",
chapter = "3",
pages = "35--53",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-49716-3_3",
bibdate = "Mon May 03 06:55:48 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Rashidinia:2021:ASM,
author = "J. Rashidinia and A. Parsa and R. Salehi",
title = "Application of Sinc on the Multi-Order Fractional
Differential Equations",
crossref = "Baumann:2021:NSM",
chapter = "5",
pages = "99--122",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-49716-3_5",
bibdate = "Mon May 03 06:55:48 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Stromberg:2021:FM,
author = "Marc Stromberg",
title = "{$ L U $} Factorization of Any Matrix",
crossref = "Baumann:2021:NSM",
chapter = "14",
pages = "369--382",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-49716-3_14",
bibdate = "Mon May 03 06:55:48 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Stromberg:2021:SMP,
author = "Marc Stromberg",
title = "Sinc Methods on Polyhedra",
crossref = "Baumann:2021:NSM",
chapter = "8",
pages = "163--224",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-49716-3_8",
bibdate = "Mon May 03 06:55:48 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Tanaka:2021:CAF,
author = "Ken'ichiro Tanaka and Masaaki Sugihara",
title = "Construction of Approximation Formulas for Analytic
Functions by Mathematical Optimization",
crossref = "Baumann:2021:NSM",
chapter = "13",
pages = "341--368",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-49716-3_13",
bibdate = "Mon May 03 06:55:48 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Youssef:2021:PSC,
author = "Maha Youssef",
title = "Poly-Sinc Collocation Method for Solving Coupled
{Burgers} Equations with a Large {Reynolds} Number",
crossref = "Baumann:2021:NSM",
chapter = "2",
pages = "23--34",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-49716-3_2",
bibdate = "Mon May 03 06:55:48 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
}
@Book{Nalcioglu:1984:STI,
editor = "Orhan Nalcio{\u{g}}lu and Zang-Hee Cho",
title = "Selected Topics in Image Science",
volume = "23",
publisher = pub-SV,
address = pub-SV:adr,
pages = "????",
year = "1984",
DOI = "https://doi.org/10.1007/978-3-642-93253-3",
ISBN = "3-642-93255-X, 3-642-93253-3 (e-book)",
ISBN-13 = "978-3-642-93255-7, 978-3-642-93253-3,
978-3-642-93255-7 (e-book)",
ISSN = "0172-7788",
LCCN = "R858-859.7",
bibdate = "Fri Nov 7 09:32:23 MST 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
series = "Lecture Notes in Medical Informatics",
acknowledgement = ack-nhfb,
subject = "Medicine; Medical records; Data processing; Computer
vision; Biology",
}
@Proceedings{Bettis:1974:PCN,
editor = "Dale G. Bettis",
booktitle = "{Proceedings of the Conference on the Numerical
Solution of Ordinary Differential Equations: 19,20
October 1972, The University of Texas at Austin}",
title = "{Proceedings of the Conference on the Numerical
Solution of Ordinary Differential Equations: 19,20
October 1972, The University of Texas at Austin}",
volume = "362",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 490",
year = "1974",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0066582",
ISBN = "0-387-06602-0, 3-540-06602-0 (print), 3-540-37911-8
(e-book)",
ISBN-13 = "978-0-387-06602-8, 978-3-540-06602-6 (print),
978-3-540-37911-9 (e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
LCCN = "QA3 .L35; QA3 .L28 no. 362; QA372; QA3 .L28; QA1
.L471; QA3 .L4; QA372 .C765p 1972",
bibdate = "Tue May 6 14:52:09 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/lnm1970.bib;
melvyl.cdlib.org:210/CDL90",
series = ser-LECT-NOTES-MATH,
URL = "http://link.springer.com/book/10.1007/BFb0066582;
http://www.springerlink.com/content/978-3-540-37911-9",
acknowledgement = ack-nhfb,
meetingname = "Conference on the Numerical Solution of Ordinary
Differential Equations (1972: University of Texas at
Austin)",
remark = "Sponsored jointly by the Society for Industrial and
Applied Mathematics and the Division of Dynamical
Astronomy of the American Astronomical Society.",
series-URL = "http://link.springer.com/bookseries/304",
subject = "Differential equations; Numerical solutions;
Congresses; Many-body problem",
}
@Proceedings{Kirby:1974:OCT,
editor = "Bruce J. Kirby",
booktitle = "{Optimal control theory and its applications:
proceedings of the 14th biennial seminar of the
Canadian Mathematical Congress, University of Western
Ontario, Aug. 12--25, 1973}",
title = "{Optimal control theory and its applications:
proceedings of the 14th biennial seminar of the
Canadian Mathematical Congress, University of Western
Ontario, Aug. 12--25, 1973}",
volume = "106",
publisher = pub-SV,
address = pub-SV:adr,
pages = "403",
year = "1974",
ISBN = "3-540-07026-5",
ISBN-13 = "978-3-540-07026-9",
ISSN = "0075-8442 (print), 2196-9957 (electronic)",
ISSN-L = "0075-8442",
LCCN = "QA402.3 C33 1974",
bibdate = "Wed May 9 10:30:57 MDT 2007",
bibsource = "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
sirsi.library.utoronto.ca:2200/UNICORN",
series = "Lecture notes in economics and mathematical systems",
acknowledgement = ack-nhfb,
}
@Book{Wang:1980:AIV,
editor = "Keith Y. Wang",
booktitle = "Acoustical Imaging: Visualization and
Characterization",
title = "Acoustical Imaging: Visualization and
Characterization",
volume = "9",
publisher = pub-SV,
address = pub-SV:adr,
pages = "????",
year = "1980",
DOI = "https://doi.org/10.1007/978-1-4684-3755-3",
ISBN = "1-4684-3757-7, 1-4684-3755-0 (e-book)",
ISBN-13 = "978-1-4684-3757-7, 978-1-4684-3755-3 (e-book)",
ISSN = "0270-5117 (print), 2215-1869 (electronic)",
ISSN-L = "0270-5117",
LCCN = "QC1-75",
bibdate = "Fri Nov 7 09:17:17 MST 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
series = "Acoustical Imaging",
URL = "http://www.springerlink.com/content/978-1-4684-3755-3",
acknowledgement = ack-nhfb,
subject = "Physics; Physics.",
tableofcontents = "Methods \\
\\
Alternative Scanning Geometries for High-Speed Imaging
With Linear Ultrasonic Arrays / B. P. Hildebrand and S.
R. Doctor / 1 \\
\\
Acoustical Imaging by Means of Multi-Frequency Hologram
Matrix / J. Nakayama and H. Ogura / 23 \\
\\
Focused Line Source Linear Array Holography Using a
Three Dimensional Computer Reconstruction System / H.
Dale Collins, Tom E. Hall, and Richard L. Wilson / 39
\\
\\
Electronic Analog Devices for Sector Scan Imaging / F.
Raine, R. Torquet, C. Bruneel, E. Bridoux, G. Thomin,
and B. Delanney / 57 \\
\\
New Arrangements for Fresnel Focusing / Bruno Richard,
Mathias Fink, and Pierre Alais / 65 \\
\\
Ultrasonic Imaging Using Trapped Energy Mode Fresnel
Lens Transducers / P. Das, S. Talley, R. Craft, H. F.
Tiersten, and J. F. McDonald / 75 \\
\\
Nonlinear Effects in Acoustic Imaging / T. G. Muir / 93
\\
\\
Low Frequency Imaging Technique for Acoustic and
Elastic Waves / Bill D. Cook / 111 \\
\\
Transducers \\
\\
Acoustic Switching Ratios of Piezoelectric and
Electrostrictive OAT's. / Khalid Azim and Keith Wang /
121 \\
\\
Spatial Frequency Characteristics of Optoacoustic
Transducers / Behzad Noorbehesht and Glen Wade / 139
\\
\\
Two-Dimensional Measurement of Ultrasound Beam Patterns
As a Function of Frequency / Paul P. K. Lee, and Robert
C. Waag / 155 \\
\\
Processing and Display \\
\\
An Integrated Circuit Image Reconstruction Processor /
David E. Boyce / 167 \\
\\
Adaptive Array Processing for Acoustic Imaging /
Gregory L. Duckworth / 177 \\
\\
Computer Holographic Reconstruction System Implementing
Integrated Three Dimensional Multi-Image Technique /
Tom E. Hall, Richard L. Wilson, and H. Dale Collins /
205 \\
\\
Ultrafast Analogical Image Reconstruction Device With
Slow Motion Capability / B. Delannoy, C. Bruneel, R.
Torquet, and E. Bridoux / 219 \\
\\
Display of 3-D Ultrasonic Images / Lowell D. Harris,
Titus C. Evans, and James F. Greenleaf / 227 \\
\\
Phased Array Considerations \\
\\
Tolerance Analysis for Phased Arrays / Kenneth N. Bates
/ 239 \\
\\
Quadrature Sampling for Phased Array Application /
Jeffry E. Powers, David J. Phillips, Marco A.
Brandestini, R. Ferraro, and Donald W. Baker / 263 \\
\\
Acoustic Microscopy/Non-Destructive Evaluation \\
\\
Acoustic Microscopy --- A Tutorial Review / Lawrence W.
Kessler and Donald E. Yuhas / 275 \\
\\
Defect Characterization by Means of the Scanning Laser
Acoustic Microscope (SLAM) / D. E. Yuhas and L. W.
Kessler / 301 \\
\\
Imaging in NDE / Bernhard R. Tittmann / 315 \\
\\
A Real-Time Synthetic-Aperture Imaging System / P. D.
Corl, and G. S. Kino / 341 \\
\\
Transmission Imaging: Forward Scattering and Scatter
Reconstruction / C. H. Chou, B. T. Khuri-Yakub, and G.
S. Kino / 357 \\
\\
Reconstructive Tomography and Inversion Techniques \\
\\
Ultrasonic Imaging by Reconstructive Tomography / Glen
Wade / 379 \\
\\
Experimental Results in Ultrasonic Diffraction
Tomography / M. Kaveh, R. K. Mueller, R. Rylander, T.
R. Coulter, and M. Soumekh / 433 \\
\\
Explicit Inversion of the Helmholtz Equation for
Ultrasound Insonification and Spherical Detection /
James S. Ball, Steven A. Johnson, and Frank Stenger /
451 \\
\\
Approximate Propagation Speed Reconstruction Over A
Prescribed Background Slab / S. Raz / 463 \\
\\
Tissue Characterization and Impediography \\
\\
Theory and Measurements of Ultrasonic Scattering for
Tissue Characterization / Robert C. Waag / 477 \\
\\
A Computerized Data Analysis System for Ultrasonic
Tissue Characterization / Joie Pierce Jones and Roger
Kovack / 503 \\
\\
Impediography Revisited / S. Leeman / 513 \\
\\
Tissue Characterization by Ultrasonic Impediography /
C. Q. Lee / 521 \\
\\
Medical Applications \\
\\
Combined Two-Dimensional Tissue/Flow Imaging / E. Aaron
Howard, Marco Brandestini, Jeff Powers, Saeed Taheri,
Mark K. Eyer, David J. Phillips, and Edward B. Weiler /
533 \\
\\
An Ultrasound Imager for Fetal Respiratory Research /
A. J. Cousin / 545 \\
\\
Intraesophageal Ultrasonic Imaging of the Canine Heart
/ Balasubramanian Rajagopalan, Eugene P. DiMagno, James
F. Greenleaf, Patrick T. Regan, James Buxton, Philip S.
Green, and J. William Whitaker / 555 \\
\\
Comparison of Ultrasonography With X-Ray Computer
Tomography and Radionuclide Scan in Terms of Medical
Diagnostic Value / Mahfuz Ahmed and Michael Grossman /
569 \\
\\
Ultrasound and Pathology / Hewlett E. Melton, Jr. and
Elsa B. Cohen / 577 \\
\\
In Vivo Quantitation of Induced Ultrasonic Contrast
Effects in the Mouse / Thomas D. Tyler, Allan H.
Gobuty, Jeff Shewmaker, and Nabil F. Maklad / 587 \\
\\
Underwater Applications \\
\\
A Tutorial on Underwater Imaging / Jerry L. Sutton /
599 \\
\\
Digital Reconstruction of Acoustic Holograms in the
Space Domain with a Vector Space Approximation / Hua
Lee, Carl Schueler, Glen Wade, and Jorge Fontana / 631
\\
\\
Data Acquisition Systems for Computer Aided Coherent
Acoustic Imaging / John P. Powers, Major Reid Carlock,
and Lt. Rod Colton / 643 \\
\\
Seismic Applications \\
\\
Seismic Imaging / Fred J. Hilterman / 653 \\
\\
A Frequency/Dip Formulation of Wave Theoretic Migration
in Stratified Media / Stewart Levin / 681 \\
\\
Limitations in the Reconstruction of Three-Dimensional
Subsurface Images / T. Smith, K. Owusu, and F.
Hilterman / 699 \\
\\
Comparison of Some Seismic Imaging Techniques / Thomas
Hu, Keith Wang, and Fred J. Hilterman / 737 \\
\\
Seismic Imaging with Lenseless Fourier Transform
Holography. / T. Morgan, G. Fitzpatrick, F. Hilterman,
and K. Wang / 761 \\
\\
Phase Contrast Enhancement Techniques Using Generalized
Holographic Interferograms for Seismic Applications /
G. Fitzpatrick, T. Morgan, F. Hilterman, K. Wang, and
A. Haider / 795 \\
\\
Tutorial Papers \\
\\
Acoustic Microscopy --- A Tutorial Review / Lawrence W.
Kessler, and Donald E. Yuhas / 275 \\
\\
Imaging in NDE / Bernhard R. Tittmann / 315 \\
\\
Ultrasonic Imaging by Reconstructive Tomography / Glen
Wade / 379 \\
\\
Theory and Measurements of Ultrasonic Scattering For
Tissue Characterization / Robert C. Waag / 477 \\
\\
A Tutorial on Underwater Acoustic Imaging . / Jerry L.
Sutton / 599 \\
\\
Seismic Imaging / Fred J. Hilterman / 653 \\
\\
List of Participants 817 \\
\\
Index 825",
}
@Proceedings{Allgower:1981:NSN,
editor = "Eugene L. Allgower and Klaus Glashoff and Heinz-Otto
Peitgen",
booktitle = "{Numerical Solution of Nonlinear Equations:
Proceedings, Bremen 1980}",
title = "{Numerical Solution of Nonlinear Equations:
Proceedings, Bremen 1980}",
volume = "878",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiv + 440",
year = "1981",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0090674",
ISBN = "0-387-10871-8, 3-540-10871-8 (print), 3-540-38781-1
(e-book)",
ISBN-13 = "978-0-387-10871-1, 978-3-540-10871-9 (print),
978-3-540-38781-7 (e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
LCCN = "QA3 .L471 no.878; QA3.L471",
bibdate = "Tue May 6 14:53:31 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/lnm1980.bib;
library.mit.edu:9909/mit01",
series = ser-LECT-NOTES-MATH,
URL = "http://link.springer.com/book/10.1007/BFb0090674;
http://www.springerlink.com/content/978-3-540-38781-7",
acknowledgement = ack-nhfb,
remark = "Symposium held July 21-25, 1980, under the sponsorship
of the Forschungsschwerpunkt ``Dynamische Systeme'',
Universit{\"a}t Bremen, and the W. Blaschke
Gesellschaft, Hamburg.",
series-URL = "http://link.springer.com/bookseries/304",
subject = "Differential equations, Nonlinear; Numerical
solutions; Congresses",
}
@Proceedings{McAvoy:1983:IUS,
editor = "B. R. McAvoy",
booktitle = "{IEEE 1983 Ultrasonics Symposium: October 31, November
1-2, 1983, Atlanta Marriott Hotel, Atlanta, Georgia}",
title = "{IEEE 1983 Ultrasonics Symposium: October 31, November
1-2, 1983, Atlanta Marriott Hotel, Atlanta, Georgia}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1180",
year = "1983",
CODEN = "ULSPDT",
ISBN = "????",
ISBN-13 = "????",
ISSN = "0090-5607",
LCCN = "????",
bibdate = "Wed May 09 18:26:26 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
note = "Two volumes. IEEE catalog number 83CH1947-1.",
acknowledgement = ack-nhfb,
}
@Proceedings{Graves-Morris:1984:RAI,
editor = "Peter Russell Graves-Morris and Edward B. Saff and
Richard S. Varga",
booktitle = "{Rational Approximation and Interpolation: Proceedings
of the United Kingdom --- United States Conference held
at Tampa, Florida, December 12--16, 1983}",
title = "{Rational Approximation and Interpolation: Proceedings
of the United Kingdom --- United States Conference held
at Tampa, Florida, December 12--16, 1983}",
volume = "1105",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xii + 528",
year = "1984",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0072395",
ISBN = "3-540-13899-4 (print), 3-540-39113-4 (e-book)",
ISBN-13 = "978-3-540-13899-0 (print), 978-3-540-39113-5
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
LCCN = "QA3 .L471 no.1105; QA3.L471",
bibdate = "Tue May 6 14:54:00 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/lnm1980.bib;
library.mit.edu:9909/mit01",
series = ser-LECT-NOTES-MATH,
URL = "http://link.springer.com/book/10.1007/BFb0072395;
http://www.springerlink.com/content/978-3-540-39113-5",
acknowledgement = ack-nhfb,
remark = "Conference on Rational Approximation and
Interpolation, held 12/12--16/83 in Tampa, Fla., and
sponsored by the US National Science Foundation and the
UK Science and Engineering Research Council.",
series-URL = "http://link.springer.com/bookseries/304",
subject = "Approximation theory; Congresses; Interpolation",
}
@Proceedings{Kaveh:1984:AIP,
editor = "M. Kaveh and R. K. Mueller and J. F. Greenleaf",
booktitle = "{Acoustical imaging: Proceedings of the thirteenth
International Symposium on Acoustical Imaging, held
October 26--28, 1983, in Minneapolis, MN}",
title = "{Acoustical imaging: Proceedings of the thirteenth
International Symposium on Acoustical Imaging, held
October 26--28, 1983, in Minneapolis, MN}",
volume = "13",
publisher = pub-PLENUM,
address = pub-PLENUM:adr,
pages = "xii + 605",
year = "1984",
CODEN = "ACIGD9",
ISBN = "0-306-41717-0",
ISBN-13 = "978-0-306-41717-7",
ISSN = "0270-5117 (print), 2215-1869 (electronic)",
ISSN-L = "0270-5117",
LCCN = "????",
bibdate = "Wed May 9 19:29:39 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
z3950.bibsys.no:2100/BIBSYS",
series = "Acoustical imaging",
acknowledgement = ack-nhfb,
}
@Proceedings{Miller:1984:CMA,
editor = "Anthony Miller",
booktitle = "{Contributions of mathematical analysis to the
numerical solution of partial differential equations}",
title = "{Contributions of mathematical analysis to the
numerical solution of partial differential equations}",
volume = "7",
publisher = "Centre for Mathematical Analysis, Australian National
University",
address = "Canberra, Australia",
pages = "v + 213",
year = "1984",
ISBN = "0-86784-508-2",
ISBN-13 = "978-0-86784-508-2",
LCCN = "QA374 .C661 1984",
bibdate = "Wed May 9 08:52:55 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
melvyl.cdlib.org:210/CDL90",
series = "Proceedings of the Centre for Mathematical Analysis,
Australian National University",
acknowledgement = ack-nhfb,
subject = "Differential equations, Partial; Numerical solutions;
Congresses",
}
@Proceedings{McAvoy:1985:IUS,
editor = "B. R. McAvoy",
booktitle = "{IEEE 1985 Ultrasonics Symposium: October 16--18,
1985, Cathedral Hill Hotel, San Francisco,
California}",
title = "{IEEE 1985 Ultrasonics Symposium: October 16--18,
1985, Cathedral Hill Hotel, San Francisco,
California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1146",
year = "1985",
CODEN = "ULSPDT",
ISBN = "????",
ISBN-13 = "????",
ISSN = "0090-5607",
LCCN = "TA367 U47 1985 v. 1-2",
bibdate = "Wed May 09 18:26:26 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
note = "Two volumes. IEEE catalog number 85CH2209-5.",
acknowledgement = ack-nhfb,
}
@Proceedings{Nalcioglu:1986:IWP,
editor = "O. (Orhan) Nalcioglu and Z.-H. (Zang-Hee) Cho and
Thomas F. (Thomas Francis) Budinger and others",
booktitle = "{International Workshop on Physics and Engineering of
Computerized Multidimensional Imaging and Processing:
2--4 April 1986, Newport Beach, California}",
title = "{International Workshop on Physics and Engineering of
Computerized Multidimensional Imaging and Processing:
2--4 April 1986, Newport Beach, California}",
volume = "671",
publisher = pub-SPIE,
address = pub-SPIE:adr,
pages = "viii + 329",
year = "1986",
CODEN = "PSISDG",
ISBN = "0-89252-706-4",
ISBN-13 = "978-0-89252-706-9",
ISSN = "0277-786X (print), 1996-756X (electronic)",
LCCN = "TK8315 .I5451 1986; TK8315 .I57 1986; TA1632 .I62
1986; TS510 .S63; TA1632 .I58 1986",
bibdate = "Wed May 9 19:25:40 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
melvyl.cdlib.org:210/CDL90",
series = "SPIE",
acknowledgement = ack-nhfb,
meetingname = "International Workshop on Physics and Engineering of
Computerized Multidimensional Imaging and Processing
(1986: Newport Beach, Calif.)",
subject = "Image processing; Digital techniques; Congresses;
Imaging systems",
}
@Proceedings{Jones:1987:AIP,
editor = "Hugh W. Jones",
booktitle = "{Acoustical Imaging: Proceedings of the International
Symposium, July 14--16, 1986, Halifax, NS, Canada}",
title = "{Acoustical Imaging: Proceedings of the International
Symposium, July 14--16, 1986, Halifax, NS, Canada}",
volume = "15",
publisher = pub-PLENUM,
address = pub-PLENUM:adr,
pages = "xi + 692",
year = "1987",
CODEN = "ACIGD9",
ISBN = "0-306-42565-3",
ISBN-13 = "978-0-306-42565-3",
ISSN = "0270-5117 (print), 2215-1869 (electronic)",
ISSN-L = "0270-5117",
LCCN = "????",
bibdate = "Wed May 9 19:29:45 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
z3950.bibsys.no:2100/BIBSYS",
series = "Acoustical imaging",
acknowledgement = ack-nhfb,
remark = "Proceedings of the 15th International Symposium on
Acoustical Imaging, held in Halifax, Nova Scotia,
Canada'' - Tittelsidens bakside.",
}
@Proceedings{Bowers:1989:CCP,
editor = "K. Bowers and J. Lund and K. L. (Kenneth L.) Bowers
and J. (John) Lund",
booktitle = "{Computation and control: proceedings of the Bozeman
conference, Bozeman, Montana, August 1--11, 1988}",
title = "{Computation and control: proceedings of the Bozeman
conference, Bozeman, Montana, August 1--11, 1988}",
volume = "1",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "410",
year = "1989",
ISBN = "0-8176-3438-X",
ISBN-13 = "978-0-8176-3438-4",
LCCN = "TA329 .C645 1989",
bibdate = "Wed May 9 08:56:08 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
z3950.loc.gov:7090/Voyager",
series = "Progress in systems and control theory",
acknowledgement = ack-nhfb,
remark = "``Collection of papers \ldots{} delivered at the first
Bozeman Conference on Computation and Control, held at
Montana State University''--Pref.",
subject = "Engineering mathematics; Congresses; Feedback control
systems",
}
@Proceedings{Martin:1990:VSL,
editor = "Clyde Martin and John White",
booktitle = "{Visiting scholars' lectures 1989, Texas Tech
University, Lubbock, TX (USA)}",
title = "{Visiting scholars' lectures 1989, Texas Tech
University, Lubbock, TX (USA)}",
volume = "16",
publisher = "Department of Mathematics, Texas Tech University",
address = "Lubbock, TX, USA",
pages = "113",
year = "1990",
bibdate = "Thu May 10 16:31:10 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
series = "Mathematics Series",
ZMnumber = "0695.00001",
acknowledgement = ack-nhfb,
classmath = "00Bxx (Conference proceedings and collections of
papers)",
keywords = "Lectures; Lubbock, TX (USA); Texas Tech University;
Visiting scholars' lectures",
}
@Proceedings{Wong:1990:ACA,
editor = "R. (Roderick) Wong",
booktitle = "{Asymptotic and computational analysis: conference in
honor of Frank W. J. Olver's 65th birthday}",
title = "{Asymptotic and computational analysis: conference in
honor of Frank W. J. Olver's 65th birthday}",
volume = "124",
publisher = pub-MARCEL-DEKKER,
address = pub-MARCEL-DEKKER:adr,
pages = "xii + 755",
year = "1990",
ISBN = "0-8247-8347-6",
ISBN-13 = "978-0-8247-8347-1",
LCCN = "QA299.6 .A88 1990",
bibdate = "Wed May 9 09:22:13 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
z3950.loc.gov:7090/Voyager",
series = "Lecture notes in pure and applied mathematics",
URL = "http://www.loc.gov/catdir/enhancements/fy0647/90002810-d.html",
abstract = "Papers presented at the International Symposium on
Asymptotic and Computational Analysis, held June 1989,
Winnipeg, Man., sponsored by the Dept. of Applied
Mathematics, University of Manitoba and the Canadian
Applied Mathematics Society.",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Congresses; Asymptotic expansions;
Olver, Frank W. J.",
subject-dates = "1924--",
}
@Proceedings{Bowers:1991:CCI,
editor = "K. L. (Kenneth L.) Bowers and J. (John) Lund",
booktitle = "{Computation and control II: proceedings of the second
Bozeman conference, Bozeman, Montana, August 1--7,
1990}",
title = "{Computation and control II: proceedings of the second
Bozeman conference, Bozeman, Montana, August 1--7,
1990}",
volume = "11",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "369",
year = "1991",
ISBN = "0-8176-3611-0",
ISBN-13 = "978-0-8176-3611-1",
LCCN = "TA329 .C644 1991",
bibdate = "Wed May 9 08:56:08 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$65.00",
series = "Progress in systems and control theory",
acknowledgement = ack-nhfb,
subject = "Engineering mathematics; Congresses; Feedback control
systems",
}
@Proceedings{Espelid:1992:NIR,
editor = "Terje O. Espelid and Alan Genz",
booktitle = "{Numerical integration: recent developments, software
and applications}",
title = "{Numerical integration: recent developments, software
and applications}",
volume = "357",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xii + 367",
year = "1992",
DOI = "https://doi.org/10.1007/978-94-011-2646-5",
ISBN = "0-7923-1583-9",
ISBN-13 = "978-0-7923-1583-4",
LCCN = "QA299.3 .N38 1991",
bibdate = "Wed May 9 09:35:28 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
z3950.bibsys.no:2100/BIBSYS",
series = "NATO ASI series. Series C, Mathematical and physical
sciences",
abstract = "This volume contains the proceedings of the NATO
Advanced Research Workshop on Numerical Integration
that took place in Bergen, Norway, in June 1991. It
includes papers for all invited talks and a selection
of contributed talks. The papers are organized into
four parts: numerical integration rules, numerical
integration error analysis, numerical integration
applications and numerical integration algorithms and
software; many papers are relevant to more than one
category. The workshop studied the state of the art in
numerical integration (both single and
multidimensional). The book contains a number of survey
papers by experts on themes such as: numerical solution
of integral equations, cubature formulae construction,
handling singularities in finite elements, statistical
applications, lattice rules, error estimates, error
bounds and software.",
acknowledgement = ack-nhfb,
meetingname = "NATO Advanced Research Workshop on Numerical
Integration: Recent Developments, Software and
Applications. Bergen. 1991",
remark = "Proceedings of the NATO Advanced Research Workshop on
Numerical Integration: Recent Developments, Software
and Applications, Bergen, Norway, June 17--21, 1991.",
subject = "Numerical integration; Congresses;
Differensialligninger; Databehandling; Numerisk
l{\o}sning",
tableofcontents = "Preface / xi \\
\\
Numerical Integration Rules \\
\\
Ronald Cools / A Survey of Methods for Constructing
Cubature Formulae / 1 \\
\\
Karin Gatermann / Linear Representations of Finite
Groups and the Ideal Theoretical Construction of
G-Invariant Cubature Formulas / 25 \\
Hans J. Schmid and H. Berens / On the Number of Nodes
of Odd Degree Cubature Formulae for Integrals with
Jacobi Weights on a Simplex / 37 \\
\\
Klaus-J{\"u}rgen Forster / On Quadrature Formulae near
Gaussian Quadrature / 45 \\
\\
Ian Sloan / Numerical Integration in High Dimensions -
the Lattice Rule Approach / 55 \\
\\
Harald Niederreiter / Existence Theorems for Efficient
Lattice Rules / 71 \\
\\
Bernard Bialecki / SINC Quadratures for Cauchy
Principal Value Integrals / 81 \\
\\
Philip Rabinowitz and William E. Smith / Interpolatory
Product Integration in the Presence of Singularities:
Lp Theory / 93 \\
\\
David B. Hunter / The Numerical Evaluation of Definite
Integrals Affected by Singularities Near the Interval
of Integration / 111 \\
\\
Nikolaos I. Ioakimidis / Application of Computer
Algebra Software to the Derivation of Numerical
Integration Rules for Singular and Hypersingular
Integrals / 121 \\
\\
Numerical Integration Error Analysis \\
\\
Walter Gautschi / Remainder Estimates for Analytic
Functions / 133 \\
\\
Helmut Brass / Error Bounds Based on Approximation
Theory / 147 \\
\\
Knut Petras / One Sided LI-Approximation and Bounds for
Peano Kernels / 165 \\
\\
Ricolindo Carino, Ian Robinson and Elise De Doncker /
An Algebraic Study of the Levin Transformation in
Numerical Integration / 175 \\
Numerical Integration Applications \\
\\
G{\"u}nther Hammerlin / Developments in Solving
Integral Equations Numerically / 187 \\
\\
Christoph Schwab and Wolfgang L. Wendland / Numerical
Integration of Singular and Hypersingular Integrals in
Boundary Element Methods / 203 \\
\\
James N. Lyness / On Handling Singularities in Finite
Elements / 219 \\
Ken Hayami / A Robust Numerical Integration Method for
3-D Boundary Element Analysis and its Error Analysis
using Complex Function Theory / 235 \\
\\
Jarle Berntsen / On the Numerical Calculation of
Multidimensional Integrals Appearing in the Theory of
Underwater Acoustics / 249 \\
\\
Alan Genz / Statistics Applications of Subregion
Adaptive Multiple Numerical Integration / 267 \\
\\
Frank Stenger, Brian Keyes, Mike O'Reilly and Ken
Parker / The Sinc Indefinite Integration and Initial
Value Problems / 281 \\
\\
Numerical Integration Algorithms and Software \\
\\
Patrick Keast / Software for Integration over Triangles
and General Simplices / 283 \\
\\
Ricolindo Carino, Ian Robinson and Elise De Doncker /
An Algorithm for Automatic Integration of Certain
Singular Functions over a Triangle / 295 \\
\\
Ronald Cools and Ann Haegemans / CUBPACK: Progress
Report / 305 \\
\\
Elise de Doncker and John Kapenga / Parallel Cubature
on Loosely Coupled Systems / 317 \\
\\
Marc Beckers and Ann Haegemans / Transformation of
Integrands for Lattice Rules / 329 \\
\\
Terje O. Espelid / DQAINT: An Algorithm for Adaptive
Quadrature over a Collection of Finite Intervals / 341
\\
\\
Christoph Schwab / A Note on Variable Knot, Variable
Order Composite Quadrature for Integrands with Power
Singularities / 343 \\
\\
Avram Sidi / Computation of Oscillatory Infinite
Integrals by Extrapolation Methods / 349 \\
\\
Appendix: Final Program / 353 \\
\\
List of Participants / 357 \\
\\
List of Contributors / 361 \\
\\
Index / 365",
}
@Book{Stenger:1993:NMB,
author = "Frank Stenger",
booktitle = "Numerical methods based on {Sinc} and analytic
functions",
title = "Numerical methods based on {Sinc} and analytic
functions",
volume = "20",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xv + 565",
year = "1993",
DOI = "https://doi.org/10.1007/978-1-4612-2706-9",
ISBN = "0-387-94008-1 (New York), 3-540-94008-1 (Berlin)",
ISBN-13 = "978-0-387-94008-3 (New York), 978-3-540-94008-1
(Berlin)",
LCCN = "QA372 .S82 1993",
MRclass = "65-01 (41A05 41A55 65-02)",
MRnumber = "MR1226236 (94k:65003)",
MRreviewer = "B. Boyanov",
bibdate = "Wed Nov 3 09:30:14 MST 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/numana.bib;
http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/numana.bib;
http://www.math.utah.edu/pub/tex/bib/numana1990.bib",
series = "Springer Series in Computational Mathematics",
ZMnumber = "0803.65141",
abstract = "This excellent monograph offers a self-contained
presentation of the sinc method and its application to
the numerical solution of integral and differential
equations. This book will be the standard reference for
the sinc method. It is of interest for mathematicians,
computational scientists and graduate students.\par
Let $ h > 0 $ and $ \text {sinc} (x) : = (\pi x)^{-1}
\sin (\pi x) $. Using the basis functions $$ S(k, h)
(x) : = \text {sinc} \bigl ((x - k h) / h \bigr), $$ a
given function $f$ bounded on the real line is
approximated by the cardinal function $$ C(f, h) (x) :
= \sum^{\infty_{k = - \infty } f(kh) S(k, h) (x)}. $$
First, the approximation of $f$ by means of $ C(f, h) $
was studied by de la Vall{\'e}e Poussin and Whittaker.
Later, Shannon's sampling theorem gave an essential
impulse to application of this theory in signal
processing. The author has special merits in this
topic, since he has studied the sinc method over 30
years intensively. Thus, many results presented in this
book are new. Note that the sinc method is closely
related to the approximation by translates, wavelet
theory, and multiscale technique.\par
Basic facts on analytic functions, polynomial
approximation, and Fourier technique are presented in
the first two chapters. Chapter 3 deals with the
approximation of $f$ by $ C(f, h) $, where $f$ is
analytic on a strip containing the real line.
Interpolation, quadrature, Fourier and Hilbert
transforms, derivatives, and indefinite integrals are
determined approximately. All of these procedures
converge at exponential and close to optimal rate.
Using a conformal mapping, the results of Chapter 3 are
extended in Chapter 4 to approximations over a contour
such that a finite or semi-infinite interval is a
special case.\par
In Chapter 5, procedures related to sinc methods are
discussed. Chapter 6 illustrates the application of
sinc methods to the approximate solution of integral
equations. The author considers nonlinear Volterra
integral equations, Cauchy singular integral equations,
convolution equations, Wiener--Hopf integral equations,
and the inversion of Laplace transform. If there exists
an analytic solution, then it is shown that an
exponential convergence rate is reachable by sinc
methods.\par
Finally, Chapter 7 demonstrates the use of sinc methods
to obtain approximate solutions of ordinary and partial
differential equations for both initial and boundary
value problems. It is pointed out that Galerkin, finite
element, spectral, and collocation methods are
essential the same for the sinc methods, since they all
yield nearly the same system of linear equations, whose
solutions have the same order of accuracy.\par
Each section ends with some problems. Each chapter
closes with historical remarks. This book is completed
by a detailed list of references containing 296
items.",
acknowledgement = ack-nhfb,
classmath = "65T40 (Trigonometric approximation and interpolation)
65-02 (Research monographs (numerical analysis)) 42C05
(General theory of orthogonal functions and
polynomials) 65N30 (Finite numerical methods (BVP of
PDE)) 65N35 (Collocation methods (BVP of PDE)) 65L60
(Finite numerical methods for ODE) 65M70 (Spectral,
collocation and related methods (IVP of PDE)) 65R20
(Integral equations (numerical methods)) 42A38 (Fourier
type transforms, one variable) 94A12 (Signal theory)
65Dxx (Numerical approximation) 44A10 (Laplace
transform) 45Exx (Singular integral equations) 45G10
(Nonsingular nonlinear integral equations)",
keywords = "cardinal function; Cauchy singular integral equations;
collocation method; convolution equations; derivatives;
differential equations; exponential convergence rate;
finite element method; Fourier and Hilbert transforms;
Galerkin method; Galerkin methods; indefinite
integrals; interpolation; inversion of Laplace
transform; monograph; multiscale technique; nonlinear
Volterra integral equations; numerical solutions;
quadrature; Shannon's sampling theorem; signal
processing; sinc method; spectral method; translates;
wavelet theory; Wiener--Hopf integral equations",
ORCID-numbers = "Stenger, Frank/0000-0002-2947-3018",
reviewer = "M. Tasche (Rostock)",
subject = "Galerkin methods; Differential equations; Numerical
solutions",
summary = "Many mathematicians, scientists, and engineers are
familiar with the Fast Fourier Transform, a method
based upon the Discrete Fourier Transform. Perhaps not
so many mathematicians, scientists, and engineers
recognize that the Discrete Fourier Transform is one of
a family of symbolic formulae called Sinc methods. Sinc
methods are based upon the Sinc function, a
wavelet-like function replete with identities which
yield approximations to all classes of computational
problems. Such problems include problems over finite,
semi-infinite, or infinite domains, problems with
singularities, and boundary layer problems. Written by
the principle authority on the subject, this book
introduces Sinc methods to the world of computation. It
serves as an excellent research sourcebook as well as a
textbook which uses analytic functions to derive Sinc
methods for the advanced numerical analysis and applied
approximation theory classrooms. Problem sections and
historical notes are included.",
tableofcontents = "1 Mathematical Preliminaries / 1 \\
1.1 Properties of Analytic Functions / 1 \\
Problems for Section 1.1 / 18 \\
1.2 Hilbert Transforms / 22 \\
Problems for Section 1.2 / 27 \\
1.3 Riemann--Hilbert Problems / 29 \\
1.3.1 Some Definitions / 30 \\
1.3.2 The Index of a Function / 31 \\
1.3.3 Homogeneous Problem / 35 \\
1.3.4 Solution of the Non-Homogeneous Problem / 38 \\
Problems for Section 1.3 / 39 \\
1.4 Fourier Transforms / 42 \\
Problems for Section 1.4 / 52 \\
1.5 Laplace Transforms / 55 \\
Problems for Section 1.5 / 56 \\
1.6 Fourier Series / 56 \\
Problems for Section 1.6 / 62 \\
1.7 Transformations of Functions / 65 \\
Problems for Section 1.7 / 70 \\
1.8 Spaces of Analytic Functions / 74 \\
1.8.1 Functions Analytic on the Unit Disc / 74 \\
1.8.2 Functions Analytic on $\Omega_+$ / 77 \\
1.8.3 Functions Analytic in the Strip ${\cal D}_d$ / 80
\\
Problems for Section 1.8 / 84 \\
1.9 The Paley--Wiener Theorem / 87 \\
Problems for Section 1.9 / 90 \\
1.10 The Cardinal Function / 91 \\
Problems for Section 1.10 / 97 \\
Historical Remarks on Chapter 1 / 102 \\
2 Polynomial Approximation / 105 \\
2.1 Chebyshev Polynomials / 105 \\
Problems for Section 2.1 / 108 \\
2.2 Discrete Fourier Polynomials / 110 \\
Problems for Section 2.2 / 115 \\
2.3 The Lagrange Polynomial / 118 \\
Problems for Section 2.3 / 122 \\
2.4 Faber Polynomials / 127 \\
Problems for Section 2.4 / 129 \\
Historical Remarks on Chapter 2 / 130 \\
\\
3 Sinc Approximation in Strip / 131 \\
3.1 Sine Approximation in ${\cal D}_d$ / 131 \\
Problems for Section 3.1 / 141 \\
3.2 Sine Quadrature on $(-\infty,\infty)$ / 143 \\
Problems for Section 3.2 / 146 \\
3.3 Discrete Fourier Transforms on $(-\infty,\infty)$ /
147 \\
Problems for Section 3.3 / 151 \\
3.4 Cauchy-Like Transforms on $(-\infty,\infty)$ / 152
\\
Problems for Section 3.4 / 160 \\
3.5 Approximation of Derivatives in ${\cal D}_d$ / 162
\\
Problems for Section 3.5 / 166 \\
3.6 The Indefinite Integral on $(-\infty,\infty)$ / 167
\\
Problems for Section 3.6 / 177 \\
Historical Remarks on Chapter 3 / 178 \\
\\
4 Sine Approximation on $\Gamma$ / 179 \\
4.1 Basic Definitions / 179 \\
Problems for Section 4.1 / 182 \\
4.2 Interpolation and Quadrature on $\Gamma$ / 183 \\
Problems for Section 4.2 / 197 \\
4.3 Hilbert and Related Transforms on $\Gamma$ / 201
\\
Problems for Section 4.3 / 204 \\
4.4 Approximation of Derivatives on $\Gamma$ / 207 \\
Problems for Section 4.4 / 217 \\
4.5 Indefinite Integral Over $\Gamma$ / 218 \\
Problems for Section 4.5 / 220 \\
4.6 Indefinite Convolution Over $\Gamma$ / 221 \\
4.6.1 Approximation Procedure / 222 \\
4.6.2 Formula Derivation / 225 \\
4.6.3 Convergence / 228 \\
4.6.4 Applications / 234 \\
Problems for Section 4.6 / 240 \\
Historical Remarks on Chapter 4 / 240 \\
5 Sine-Related Methods / 243 \\
5.1 Introduction / 243 \\
5.2 Variations of the Sine Basis / 245 \\
Problems for Section 5.2 / 252 \\
5.3 Elliptic Function Interpolants / 252 \\
Problems for Section 5.3 / 257 \\
5.4 Inversion of the Laplace Transform / 258 \\
Problems for Section 5.4 / 261 \\
5.5 Sine-Like Rational Approximation / 262 \\
Problems for Section 5.5 / 276 \\
5.6 Rationals and Extrapolation / 276 \\
5.6.1 Pad{\'e} Approximation / 277 \\
5.6.2 Continued Fractions / 280 \\
5.6.3 The Epsilon Algorithm and Aitken's $\Delta^2$
Process / 283 \\
5.6.4 Chebyshev Acceleration / 284 \\
5.6.5 Thiele's Algorithm / 285 \\
Problems for Section 5.6 / 291 \\
5.7 Heaviside and Filter Rationals / 294 \\
5.7.1 Approximation of the Heaviside Function / 295 \\
5.7.2 Approximation of the Filter Function / 298 \\
5.7.3 Approximation of the Delta Function / 299 \\
Problems for Section 5.7 / 302 \\
5.8 Positive Base Approximation / 304 \\
Problems for Section 5.8 / 310 \\
Historical Remarks on Chapter 5 / 310 \\
\\
6 Integral Equations / 311 \\
6.1 Introduction / 311 \\
6.2 Mathematical Preliminaries / 313 \\
6.2.1 Use of Functional Analysis / 313 \\
6.2.2 Approximation, Convergence, and Error / 317 \\
6.2.3 Fredholm Alternative / 320 \\
6.2.4 Perturbed Equations / 325 \\
6.2.5 Tikhonov Regularization / 326 \\
Problems for Section 6.2 / 329 \\
6.3 Reduction to Algebraic Equations / 331 \\
6.3.1 Galerkin Method / 331 \\
6.3.2 Nystr{\"o}m's Method / 331 \\
6.3.3 The Generalized Inverse Procedure / 332 \\
6.3.4 Errors in the Numerical Solution / 335 \\
Problems for Section 6.3 / 336 \\
6.4 Volterra Integral Equations / 338 \\
6.4.1 Linear Volterra Equations / 338 \\
6.4.2 Non-Linear Equations via Neumann Series / 340 \\
6.4.3 Non-Linear Equations by Newton's Method / 343 \\
Problems for Section 6.4 / 346 \\
6.5 Potential Theory Problems / 349 \\
6.5.1 Problem Description / 349 \\
6.5.2 Spaces for Sine Approximation / 350 \\
6.5.3 Sine Approximation / 351 \\
6.5.4 Properties of the Integral Equation / 354 \\
6.5.5 Galerkin Approximation / 360 \\
6.5.6 Several Surface Patches-Domain Decomposition /
361 \\
6.5.7 An Explicit Example / 364 \\
6.5.8 Kernel Singularities and Integration / 374 \\
Problems for Section 6.5 / 376 \\
6.6 Reduced Wave Equation on a Half-Space / 379 \\
6.6.1 Problem Description / 380 \\
6.6.2 Spaces for Sine Approximation / 381 \\
6.6.3 Sine Approximation / 383 \\
6.6.4 Properties of the Integral Equation / 385 \\
6.6.5 Galerkin Approximation / 391 \\
6.6.6 Evaluation of Moment Integrals / 392 \\
6.6.7 Numerical Evaluation of Solution / 395 \\
6.6.8 An Explicit Example / 396 \\
Problems for Section 6.6 / 398 \\
6.7 Cauchy Singular Integral Equations / 400 \\
6.7.1 The Problem / 401 \\
6.7.2 The Method of Regularization / 401 \\
6.7.3 Properties of the Fredholm Equation / 404 \\
6.7.4 Approximation via Nystr{\"o}m's Method / 406 \\
Problems for Section 6.7 / 407 \\
6.8 Convolution-Type Equations / 407 \\
6.8.1 The Problems and Theoretical Solutions / 407 \\
6.8.2 Approximate Solution / 410 \\
6.8.3 Explicit Examples / 418 \\
Problems for Section 6.8 / 421 \\
6.9 The Laplace Transform and Its Inversion / 422 \\
Problems for Section 6.9 / 437 \\
Historical Remarks on Chapter 6 / 439 \\
\\
7 Differential Equations / 441 \\
7.1 ODE--IVP / 444 \\
7.1.1 Linear Initial Value Problems / 445 \\
7.1.2 Non-Linear Initial Value Problems / 453 \\
Problems for Section 7.1 / 459 \\
7.2 ODE--BVP / 465 \\
7.2.1 Sinc--Galerkin and Collocation / 467 \\
7.2.2 Integration by Parts / 469 \\
7.2.3 Collocation and Integration by Parts / 470 \\
7.2.4 Convergence of Sinc--Galerkin Methods / 471 \\
7.2.5 Non-Linear Equations / 483 \\
7.2.6 Non-Homogeneous Boundary Conditions / 484 \\
7.2.7 Symmetric Sinc--Galerkin Method / 486 \\
7.2.8 More Examples / 492 \\
Problems for Section 7.2 / 497 \\
7.3 Analytic Solutions of PDE / 500 \\
7.3.1 Analyticity of Solutions in All Variables / 501
\\
7.3.2 Analyticity for Sinc Approximation / 501 \\
7.3.3 Singularities Due to Corners and Edges / 506 \\
Problems for Section 7.3 / 509 \\
7.4 Elliptic Problems / 511 \\
Problems for Section 7.4 / 521 \\
7.5 Hyperbolic Problems / 521 \\
Problems for Section 7.5 / 523 \\
7.6 Parabolic Problems / 524 \\
Problems for Section 7.6 / 529 \\
Historical Remarks on Chapter 7 / 529 \\
\\
References / 533 \\
\\
Index 563",
}
@Proceedings{Zahar:1994:ACF,
editor = "R. V. M. (Ramsay Vincent Michael) Zahar",
booktitle = "{Approximation and computation: a festschrift in honor
of Walter Gautschi: proceedings of the Purdue
conference, December 2--5, 1993}",
title = "{Approximation and computation: a festschrift in honor
of Walter Gautschi: proceedings of the Purdue
conference, December 2--5, 1993}",
volume = "119",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xlvi + 591",
year = "1994",
ISBN = "0-8176-3753-2",
ISBN-13 = "978-0-8176-3753-8",
LCCN = "QA221 .A634 1994",
bibdate = "Wed May 9 09:01:57 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "International series of numerical mathematics",
acknowledgement = ack-nhfb,
subject = "Approximation theory; Congresses; Orthogonal
polynomials; Numerical integration; Functions,
Special",
}
@Proceedings{Ang:1995:IPA,
editor = "{\Dbar}{\hckudot{a}}ng {\Dbar}i{\~n}h {\'A}ng and
others",
title = "{Inverse problems and applications to geophysics,
industry, medicine and technology: proceedings of the
International Workshop on Inverse Problems, 17--19
January 1995, Ho Chi Minh City}",
volume = "2",
publisher = "Vietnam Mathematical Society",
address = "Ho Chi Minh City, Vietnam",
pages = "226",
year = "1995",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Wed May 09 17:36:40 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
series = "Publications of the Ho Chi Minh City Mathematical
Society",
acknowledgement = ack-nhfb,
}
@Proceedings{Ismail:1995:MAW,
editor = "Mourad Ismail and others",
booktitle = "{Mathematical analysis, wavelets, and signal
processing: an International Conference on Mathematical
Analysis and Signal Processing, January 3--9, 1994,
Cairo University, Cairo, Egypt}",
title = "{Mathematical analysis, wavelets, and signal
processing: an International Conference on Mathematical
Analysis and Signal Processing, January 3--9, 1994,
Cairo University, Cairo, Egypt}",
volume = "190",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "x + 354",
year = "1995",
ISBN = "0-8218-0384-0",
ISBN-13 = "978-0-8218-0384-4",
ISSN = "0271-4132 (print), 1098-3627 (electronic)",
LCCN = "QA299.6 .M38 1995",
bibdate = "Wed May 9 08:38:41 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
z3950.loc.gov:7090/Voyager",
series = "Contemporary mathematics",
acknowledgement = ack-nhfb,
meetingname = "International Conference on Mathematical Analysis and
Signal Processing (1994: Cairo, Egypt)",
subject = "Mathematical analysis; Congresses; Wavelets
(Mathematics); Signal processing; Mathematics",
}
@Proceedings{Papamichael:1999:CMF,
editor = "N. (Nicolas) Papamichael and Stephan Ruscheweyh and E.
B. Saff",
booktitle = "{Computational methods and function theory 1997:
proceedings of the Third CMFT Conference, 13--17
October 1997, Nicosia, Cyprus}",
title = "{Computational methods and function theory 1997:
proceedings of the Third CMFT Conference, 13--17
October 1997, Nicosia, Cyprus}",
volume = "11",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xi + 652",
year = "1999",
ISBN = "981-02-3626-3",
ISBN-13 = "978-981-02-3626-7",
LCCN = "QA297 .I473 1997",
bibdate = "Wed May 9 09:40:29 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
z3950.loc.gov:7090/Voyager",
series = "Series in approximations and decompositions",
acknowledgement = ack-nhfb,
meetingname = "CMFT Conference (3rd: 1997: Nicosia, Cyprus)",
subject = "Numerical analysis; Congresses; Functions of complex
variables",
}
@Proceedings{Kromann:2000:ISI,
editor = "Gary B. Kromann and J. Richard Culham and Koneru
Ramakrishna",
booktitle = "{ITherm 2000: the Seventh Intersociety Conference on
Thermal and Thermomechanical Phenomena in Electronic
Systems, presented at Las Vegas, Nevada, USA, May
23--26, 2000}",
title = "{ITherm 2000: the Seventh Intersociety Conference on
Thermal and Thermomechanical Phenomena in Electronic
Systems, presented at Las Vegas, Nevada, USA, May
23--26, 2000}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + viii + 819",
year = "2000",
ISBN = "0-7803-5912-7 (softcover), 0-7803-5913-5 (casebound),
0-7803-5914-3 (microfiche)",
ISBN-13 = "978-0-7803-5912-3 (softcover), 978-0-7803-5913-0
(casebound), 978-0-7803-5914-7 (microfiche)",
LCCN = "TK7870.25 .I6 2000",
bibdate = "Wed May 09 18:22:15 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
note = "Two volumes. IEEE catalog number 00CH37069.",
acknowledgement = ack-nhfb,
}
@Proceedings{Nashed:2002:IPI,
editor = "M. Zuhair Nashed and Otmar Scherzer",
booktitle = "{Inverse problems, image analysis, and medical
imaging: AMS Special Session on Interaction of Inverse
Problems and Image Analysis, January 10--13, 2001, New
Orleans, Louisiana}",
title = "{Inverse problems, image analysis, and medical
imaging: AMS Special Session on Interaction of Inverse
Problems and Image Analysis, January 10--13, 2001, New
Orleans, Louisiana}",
volume = "313",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "ix + 305",
year = "2002",
ISBN = "0-8218-2979-3",
ISBN-13 = "978-0-8218-2979-0",
ISSN = "0271-4132 (print), 1098-3627 (electronic)",
ISSN-L = "0271-4132",
LCCN = "TA1637 .A47 2001",
bibdate = "Wed May 9 09:41:07 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
z3950.loc.gov:7090/Voyager",
series = "Contemporary mathematics",
acknowledgement = ack-nhfb,
meetingname = "AMS Special Session on Interaction of Inverse Problems
and Image Analysis (2001: New Orleans, LA)",
subject = "Image processing; Digital techniques; Mathematical
models; Congresses; Image analysis; Inverse problems
(Differential equations); Diagnostic imaging;
Mathematic models",
}
@Book{Shen:2013:MSA,
editor = "Xiaoping Shen and Ahmed I. Zayed",
booktitle = "Multiscale Signal Analysis and Modeling",
title = "Multiscale Signal Analysis and Modeling",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvii + 378",
year = "2013",
DOI = "https://doi.org/10.1007/978-1-4614-4145-8",
ISBN = "1-4614-4144-7, 1-4614-4145-5 (e-book)",
ISBN-13 = "978-1-4614-4144-1, 978-1-4614-4145-8 (e-book)",
LCCN = "TA342 .M855 2013",
bibdate = "Fri Nov 7 06:43:00 MST 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
abstract = "\booktitle{Multiscale Signal Analysis and Modeling}
presents recent advances in multiscale analysis and
modeling using wavelets and other systems. This book
also presents applications in digital signal processing
using sampling theory and techniques from various
function spaces, filter design, feature extraction and
classification, signal and image
representation/transmission, coding, nonparametric
statistical signal processing, and statistical learning
theory. This book also: (1) Discusses recently
developed signal modeling techniques, such as the
multiscale method for complex time series modeling,
multiscale positive density estimations, Bayesian
Shrinkage Strategies, and algorithms for data adaptive
statistics; (2) Introduces new sampling algorithms for
multidimensional signal processing; (3) Provides
comprehensive coverage of wavelets with presentations
on waveform design and modeling, wavelet analysis of
ECG signals and wavelet filters; (4) Reviews features
extraction and classification algorithms for multiscale
signal and image processing using Local Discriminant
Basis (LDB); (5) Develops multi-parameter regularized
extrapolating estimators in statistical learning
theory. \booktitle{Multiscale Signal Analysis and
Modeling} is an ideal book for graduate students and
practitioners, especially those working in or studying
the field of signal/image processing, telecommunication
and applied statistics. It can also serve as a
reference book for engineers, researchers and educators
interested in mathematical and statistical modeling.",
acknowledgement = ack-nhfb,
remark = "This monograph is a collection of chapters authored or
coauthored by friends and colleagues of Professor
Gilbert Walter in celebration of his 80th birthday.",
subject = "Multiscale modeling; Signal processing; Digital
techniques; Mathematics; Sampling (Statistics);
Multiscale modeling.; Sampling (Statistics);
Mathematics.",
tableofcontents = "Part 1: Sampling \\
Convergence of Classical Cardinal Series / W. R. Madych
\\
Improved Approximation via Use of Transformations /
Frank Stenger, Maha Youssef and Jenny Niebsch \\
Generalized Sampling in $L^2(R^d)$ Shift-Invariant
Subspaces with Multiple Stable Generators / H. R.
Fern{\'a}ndez-Morales, A. G. Garc{\'i}a and G.
P{\'e}rez-Villal{\'o}n \\
Function Spaces for Sampling Expansions / M. Zuhair
Nashed and Qiyu Sun \\
Coprime Sampling and Arrays in One and Multiple
Dimensions / P. P. Vaidyanathan and Piya Pal \\
Chromatic Expansions and the Bargmann Transform / Ahmed
I. Zayed \\
Representation Formulas for Hardy Space Functions
Through the Cuntz Relations and New Interpolation
Problems / Daniel Alpay, Palle Jorgensen, Izchak
Lewkowicz and Itzik Marziano \\
Constructions and a Generalization of Perfect
Autocorrelation Sequences on $\mathbb{Z}$ / John J.
Benedetto and Somantika Datta \\
Part 2: Multiscale Analysis \\
On the Application of the SDLE to the Analysis of
Complex Time Series / Jianbo Gao, Jing Hu and Wen-wen
Tung \\
Wavelet Analysis of ECG Signals / En-Bing Lin, Megan
Haske, Marilyn Smith and Darren Sowards \\
Multiscale Signal Processing with Discrete Hermite
Functions / Dale H. Mugler and Anandi Mahadevan \\
Earth Mover's Distance-Based Local Discriminant Basis /
Bradley Marchand and Naoki Saito \\
Part 3: Statistical Analysis \\
Characterizations of Certain Continuous Distributions /
G. G. Hamedani \\
Bayesian Wavelet Shrinkage Strategies: A Review /
Norbert Rem{\'e}nyi and Brani Vidakovic \\
Multiparameter Regularization for Construction of
Extrapolating Estimators in Statistical Learning Theory
/ Shuai Lu, Sergiy Pereverzyev Jr. and Sivananthan
Sampath",
}
@Book{Zayed:2014:NPA,
editor = "Ahmed I. Zayed and Gerhard Schmeisser",
booktitle = "New Perspectives on Approximation and Sampling Theory:
{Festschrift} in Honor of {Paul Butzer}'s {85th}
Birthday",
title = "New Perspectives on Approximation and Sampling Theory:
{Festschrift} in Honor of {Paul Butzer}'s {85th}
Birthday",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxii + 472",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-319-08801-3",
ISBN = "3-319-08800-9, 3-319-08801-7 (e-book)",
ISBN-13 = "978-3-319-08800-6, 978-3-319-08801-3 (e-book)",
ISSN = "2296-5009 (print), 2296-5017 (electronic)",
LCCN = "????",
bibdate = "Fri Nov 7 10:11:27 MST 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
acknowledgement = ack-nhfb,
tableofcontents = "1: Abstract Exact and Approximate Sampling Theorems
/ M. M. Dodson / 1 \\
2: Sampling in Reproducing Kernel Hilbert Space / J. R.
Higgins / 23 \\
3: Boas-Type Formulas and Sampling in Banach Spaces
with Applications to Analysis on Manifolds / Isaac Z.
Pesenson / 39 \\
4: On Window Methods in Generalized Shannon Sampling
Operators / Andi Kivinukk and Gert Tamberg / 63 \\
5: Generalized Sampling Approximation for Multivariate
Discontinuous Signals and Applications to Image
Processing / Carlo Bardaro, Ilaria Mantellini, Rudolf
Stens, J{\"o}rg Vautz, and Gianluca Vinti / 87 \\
6: Signal and System Approximation from General
Measurements / Holger Boche and Ullrich J. M{\"o}nich /
115 \\
7: Sampling in Image Representation and Compression /
John J. Benedetto and Alfredo Nava-Tudela / 149 \\
8: Sparse Signal Processing. / Masoumeh Azghani and
Farokh Marvasti / 189 \\
9: Signal Sampling and Testing Under Noise /
Miros{\l}aw Pawlak / 215 \\
10: Superoscillations / Paulo J. S. G. Ferreira / 247
\\
11: General Moduli of Smoothness and Approximation by
Families of Linear Polynomial Operators / K. Runovski
and H.-J. Schmeisser / 269 \\
12: Variation and Approximation in Multidimensional
Setting for Mellin Integral Operators / Laura Angeloni
and Gianluca Vinti / 299 \\
13: The Lebesgue Constant for Sinc Approximations /
Frank Stenger, Hany A. M. El-Sharkawy, and Gerd Baumann
/ 319 \\
14: Six (Seven) Problems in Frame Theory / Ole
Christensen / 337 \\
15: Five Good Reasons for Complex-Valued Transforms in
Image Processing / Brigitte Forster / 359 \\
16: Frequency Determination Using the Discrete Hermite
Transform / Dale H. Mugler and Stuart Clary / 383 \\
17: Fractional Operators, Dirichlet Averages, and
Splines / Peter Massopust / 399 \\
18: A Distributional Approach to Generalized Stochastic
Processes on Locally Compact Abelian Groups / H. G.
Feichtinger and W. H{\"o}rmann / 423 \\
19: On a Discrete Tur{\'a}n Problem for $\ell - 1$
Radial Functions / Elena E. Berdysheva and Hubert
Berens / 447",
}
@Book{Sabin:2015:CMP,
editor = "John R. Sabin and Remigio Cabrera-Trujillo",
title = "Concepts of mathematical physics in chemistry: a
tribute to {Frank E. Harris}",
volume = "71",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xv + 382",
year = "2015",
ISBN = "0-12-802824-6, 0-12-802868-8 (e-book)",
ISBN-13 = "978-0-12-802824-7, 978-0-12-802868-1 (e-book)",
LCCN = "QC19.2",
bibdate = "Fri Aug 28 07:06:45 MDT 2015",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/advquantumchem.bib",
acknowledgement = ack-nhfb,
subject = "Quantum chemistry",
tableofcontents = "1. Frank Harris, a Master of Mountains / Per
Kaijser \\
2. System-Size Dependence in Grand Canonical and
Canonical Ensembles / Debajit Chakraborty, James Dufty,
Valentin V. Karasiev \\
3. The Mean Excitation Energy of Atomic Ions / Stephan
P. A. Sauer, Jens Oddershede, John R. Sabin \\
4. Hybrid Functionals with Variationally Fitted Exact
Exchange / Daniel Mej{\'i}a-Rodr{\'i}guez, Xiaomin
Huang, Jorge M. del Campo, Andreas M. K{\"o}ster \\
5. The Hydrogen H$_2^+$ and HeH$_2^+$ Molecular Ions
Confined in Dihedral Angles / Salvador A. Cruz, Eugenio
Ley-Koo \\
6. Angular Momentum Theory in Bases of Lam{\'e}
Spheroconal Harmonics / Ricardo M{\'e}ndez-Fragoso,
Eugenio Ley-Koo \\
7. The Fourier Space Restricted Hartree--Fock Method
for the Electronic Structure Calculation of
One-Dimensionally Periodic Systems / Joseph G. Fripiat,
Beno{\^i}t Champagne, Frank E. Harris \\
8. Generalized Response Theory for a Photoexcited
Many-Atom System / David A. Micha \\
9. Frank Discussion of the Status of Ground-State
Orbital-Free DFT / Valentin V. Karasiev, Samuel B.
Trickey \\
10. Statistical Inference with Minimum Relative
Entropy: A Robust Numerical Algorithm Employing Sinc
Quadrature / Vasilios G. Koures \\
11. Computational Methods for Chemistry and Physics,
and Schr{\"o}dinger in $3 + 1^1$ / Frank Stenger, Gerd
Baumann, Vasilios G. Koures \\
12. Approximate Coherent States for Nonlinear Systems /
Ricardo Rom{\'a}n-Ancheyta, Jos{\'e} R{\'e}camier \\
13. Electronic Properties in Supercritical Fluids: The
Absorption Spectrum of p-Nitroaniline in Supercritical
Water / Marcelo Hidalgo Cardenuto, Kaline Coutinho,
Benedito J. C. Cabral, Sylvio Canuto \\
14. On a Hyperbolic Solution to the Nonlinear
Schr{\"o}dinger Equation for a Square Well Potential
Coupled to a Contact Impurity at the Delocalization
Threshold / Ricardo M{\'e}ndez-Fragoso, Remigio
Cabrera-Trujillo \\
15. Multiresolution Approach for Laser-Modified
Collisions of Atoms and Ions / Fco. Javier
Dom{\'i}nguez-Guti{\'e}rrez, Predrag S. Krsti{\'c},
Remigio Cabrera-Trujillo",
}
@Book{Sabin:2016:CMP,
editor = "John R. Sabin and Remigio Cabrera-Trujillo",
title = "Concepts of mathematical physics in chemistry: a
tribute to {Frank E. Harris}. {Part B}",
volume = "72",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xii + 235",
year = "2016",
ISBN = "0-12-803984-1, 0-12-803985-X (e-book)",
ISBN-13 = "978-0-12-803984-7, 978-0-12-803985-4 (e-book)",
ISSN = "0065-3276 (print), 2162-8815 (electronic)",
LCCN = "QC19.2",
bibdate = "Thu Jan 21 15:33:05 MST 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/advquantumchem.bib",
series = "Advances in quantum chemistry",
abstract = "This volume presents a series of articles concerning
current important topics in quantum chemistry.",
acknowledgement = ack-nhfb,
subject = "Mathematical physics; Chemistry; Mathematics; SCIENCE
/ Energy; SCIENCE / Mechanics / General; SCIENCE /
Physics / General; Mathematics.; Mathematical
physics.",
}
@Book{Govil:2017:PAT,
editor = "Narendra Kumar Govil and Ram Mohapatra and Mohammed A.
Qazi and Gerhard Schmeisser",
booktitle = "Progress in Approximation Theory and Applicable
Complex Analysis: In Memory of {Q. I. Rahman}",
title = "Progress in Approximation Theory and Applicable
Complex Analysis: In Memory of {Q. I. Rahman}",
volume = "117",
publisher = pub-SV,
address = pub-SV:adr,
pages = "",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-49242-1",
ISBN = "3-319-49240-3 (print), 3-319-49242-X (e-book)",
ISBN-13 = "978-3-319-49240-7 (print), 978-3-319-49242-1
(e-book)",
LCCN = "QA402.5-402.6",
bibdate = "Sat Feb 10 18:46:45 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Springer Optimization and Its Applications",
URL = "https://link.springer.com/chapter/10.1007/978-3-319-49242-1",
abstract = "Current and historical research methods in
approximation theory are presented in this book
beginning with the 1800s and following the evolution of
approximation theory via the refinement and extension
of classical methods and ending with recent techniques
and methodologies. Graduate students, postdocs, and
researchers in mathematics, specifically those working
in the theory of functions, approximation theory,
geometric function theory, and optimization will find
new insights as well as a guide to advanced topics. The
chapters in this book are grouped into four themes; the
first, polynomials (Chapters 1--8), includes
inequalities for polynomials and rational functions,
orthogonal polynomials, and location of zeros. The
second, inequalities and extremal problems are
discussed in Chapters 9--13. The third, approximation
of functions, involves the approximants being
polynomials, rational functions, and other types of
functions and are covered in Chapters 14--19. The last
theme, quadrature, cubature and applications, comprises
the final three chapters and includes an article
coauthored by Rahman. This volume serves as a memorial
volume to commemorate the distinguished career of Qazi
Ibadur Rahman (1934--2013) of the Universit{\'e} de
Montr{\'e}al. Rahman was considered by his peers as one
of the prominent experts in analytic theory of
polynomials and entire functions. The novelty of his
work lies in his profound abilities and skills in
applying techniques from other areas of mathematics,
such as optimization theory and variational principles,
to obtain final answers to countless open problems.",
acknowledgement = ack-nhfb,
series-URL = "https://link.springer.com/bookseries/7393",
tableofcontents = "On the $L_2$ Markov Inequality with Laguerre Weight
\\
Markov-Type Inequalities for Products of Muntz
Polynomials Revisited \\
On Bernstein-Type Inequalities for the Polar Derivative
of a Polynomial \\
On Two Inequalities for Polynomials in the Unit Disk
\\
Inequalities for Integral Norms of Polynomials via
Multipliers \\
Some Rational Inequalities Inspired by Rahman's
Research \\
On an Asymptotic Equality for Reproducing Kernels and
Sums of Squares of Orthonormal Polynomials \\
Two Walsh-Type Theorems for the Solutions of
Multi-Affine Symmetric Polynomials \\
Vector Inequalities for a Projection in Hilbert Spaces
and Applications \\
A Half-Discrete Hardy--Hilbert-Type Inequality with a
Best Possible Constant Factor Related to the Hurwitz
Zeta Function \\
Quantum Integral Inequalities for Generalized Convex
Functions \\
Quantum integral inequalities for generalized preinvex
functions \\
On the Bohr inequality \\
Bernstein-Type Polynomials on Several Intervals \\
Best Approximation by Logarithmically Concave Classes
of Functions \\
Local approximation using Hermite functions \\
Approximating the Riemann Zeta and Related Functions
\\
Overconvergence of Rational Approximants of Meromorphic
Functions \\
Approximation by Bernstein--Faber--Walsh and
Sz{\'a}sz--Mirakjan--Faber--Walsh Operators in Multiply
Connected Compact Sets of $\mathbb{C}$ \\
Summation Formulas of Euler--Maclaurin and Abel--Plana:
Old and New Results and Applications \\
A New Approach to Positivity and Monotonicity for the
Trapezoidal Method and Related Quadrature Methods \\
A Unified and General Framework for Enriching Finite
Element Approximations",
}
@Book{Baumann:2021:NSM,
editor = "Gerd Baumann",
booktitle = "New Sinc methods of numerical analysis: Festschrift in
honor of {Frank Stenger}'s 80th birthday",
title = "New Sinc methods of numerical analysis: Festschrift in
honor of {Frank Stenger}'s 80th birthday",
publisher = "Birkh{\"a}user",
address = "Cham, Switzerland",
pages = "xvi + 404",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-49716-3",
ISBN = "3-030-49715-1 (hardcover), 3-030-49716-X (e-book)",
ISBN-13 = "978-3-030-49715-6 (hardcover), 978-3-030-49716-3
(e-book)",
ISSN = "2297-0215",
LCCN = "QA372",
bibdate = "Mon May 3 06:40:07 MDT 2021",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib",
series = "Trends in mathematics",
abstract = "This contributed volume honors the 80th birthday of
Frank Stenger who established new Sinc methods in
numerical analysis.The contributions, written
independently from each other, show the new
developments in numerical analysis in connection with
Sinc methods and approximations of solutions for
differential equations, boundary value problems,
integral equations, integrals, linear transforms,
eigenvalue problems, polynomial approximations,
computations on polyhedra, and many applications. The
approximation methods are exponentially converging
compared with standard methods and save resources in
computation. They are applicable in many fields of
science including mathematics, physics, and
engineering.The ideas discussed serve as a starting
point in many different directions in numerical
analysis research and applications which will lead to
new and unprecedented results. This book will appeal to
a wide readership, from students to specialized
experts.",
acknowledgement = ack-nhfb,
subject = "Galerkin methods",
tableofcontents = "Front Matter / i-xvi \\
Part I: Applications \\
Front Matter / 1--1 \\
1: Sinc-Gaussian Approach for Solving the Inverse Heat
Conduction Problem / M. H. Annaby, R. M. Asharabi /
3--21 \\
2: Poly-Sinc Collocation Method for Solving Coupled
Burgers Equations with a Large Reynolds Number / Maha
Youssef / 23--34 \\
3: Sinc Projection Solutions of Fredholm Integral
Equations / Khadijeh Nedaiasl / 35--53 \\
4: L{\'e}vy--Schr{\"o}dinger Equation: Their
Eigenvalues and Eigenfunctions Using Sinc Methods /
Gerd Baumann / 55--98 \\
5: Application of Sinc on the Multi-Order Fractional
Differential Equations / J. Rashidinia, A. Parsa, R.
Salehi / 99--122 \\
6: Election Integrity Audits to Ensure Election Outcome
Accuracy / Kathy Dopp / 123--145 \\
7: Numerical Solution of the Falkner--Skan Equation
Arising in Boundary Layer Theory Using the
Sinc-Collocation Method / Basem Attili / 147--162 \\
8: Sinc Methods on Polyhedra / Marc Stromberg /
163--224 \\
Part II: New Developments \\
Front Matter / 225--225 \\
9: Indefinite Integration Operators Identities, and
Their Approximations / Frank Stenger / 227--254 \\
10: An Overview of the Computation of the Eigenvalues
Using Sinc-Methods / M. H. Annaby, R. M. Asharabi, M.
M. Tharwat / 255--298 \\
11: Completely Monotonic Fredholm Determinants / Mourad
E. H. Ismail, Ruiming Zhang / 299--321 \\
12: The Influence of Jumps on the Sinc Interpolant, and
Ways to Overcome It / Jean-Paul Berrut / 323--339 \\
13: Construction of Approximation Formulas for Analytic
Functions by Mathematical Optimization / Ken'ichiro
Tanaka, Masaaki Sugihara / 341--368 \\
14: $L U$ Factorization of Any Matrix / Marc Stromberg
/ 369--382 \\
Part III: Frank Stenger's Work \\
Front Matter / 383--383 \\
15: Publications by, and About, Frank Stenger / Nelson
H. F. Beebe / 385--399 \\
Index / 401--404",
}
