%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.32", %%% date = "02 May 2016", %%% time = "11:24:15 MDT", %%% filename = "stenger-frank.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "http://www.math.utah.edu/~beebe", %%% checksum = "03762 6872 32911 326235", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography; BibTeX; Green's functions; %%% integral equations; multigrid sync methods; %%% numerical approximation; numerical %%% integration; numerical quadrature; ordinary %%% differential equations; partial differential %%% equations; rational approximation; Sinc %%% functions", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a bibliography of publications of %%% Frank Stenger, whose personal Web site %%% can be found at %%% %%% http:://www.cs.utah.edu/~stenger %%% %%% The companion LaTeX file stenger-frank.ltx %%% can be used to typeset this bibliography. %%% %%% At version 1.32, the year coverage looked %%% like this: %%% %%% 1965 ( 3) 1983 ( 2) 2001 ( 0) %%% 1966 ( 6) 1984 ( 15) 2002 ( 4) %%% 1967 ( 1) 1985 ( 2) 2003 ( 1) %%% 1968 ( 5) 1986 ( 4) 2004 ( 2) %%% 1969 ( 1) 1987 ( 4) 2005 ( 0) %%% 1970 ( 3) 1988 ( 5) 2006 ( 0) %%% 1971 ( 7) 1989 ( 5) 2007 ( 2) %%% 1972 ( 5) 1990 ( 6) 2008 ( 2) %%% 1973 ( 5) 1991 ( 2) 2009 ( 2) %%% 1974 ( 6) 1992 ( 2) 2010 ( 0) %%% 1975 ( 7) 1993 ( 11) 2011 ( 2) %%% 1976 ( 5) 1994 ( 6) 2012 ( 0) %%% 1977 ( 2) 1995 ( 7) 2013 ( 4) %%% 1978 ( 3) 1996 ( 1) 2014 ( 2) %%% 1979 ( 4) 1997 ( 5) 2015 ( 3) %%% 1980 ( 3) 1998 ( 4) 2016 ( 2) %%% 1981 ( 3) 1999 ( 4) %%% 1982 ( 4) 2000 ( 8) %%% %%% Article: 111 %%% Book: 10 %%% InCollection: 14 %%% InProceedings: 24 %%% Misc: 1 %%% PhdThesis: 1 %%% Proceedings: 21 %%% TechReport: 10 %%% %%% Total entries: 192 %%% %%% This file is available as part of the BibNet %%% Project. The master copy is available for %%% public access at %%% %%% ftp://ftp.math.utah.edu in the/pub/bibnet/authors/s %%% %%% mirrored to %%% %%% ftp://netlib.bell-labs.com/netlib/bibnet/authors %%% %%% This bibliography was collected from %%% multiple sources: %%% %%% * the author' own files; %%% * the TeX User Group bibliography archives; %%% * the very large Computer Science %%% bibliography collection on ftp.ira.uka.de %%% in /pub/bibliography, to which many people %%% have contributed; %%% * Internet library catalogs, including %%% University of California MELVYL, Library of %%% Congress, and OCLC; %%% * the ACM Portal database; %%% * the AMS MathSciNet database; %%% * the Compendex database; %%% * the European Mathematical Society database; %%% * the IEEE Xplore database; %%% * the INSPEC database; %%% * the JSTOR database; and %%% * the OCLC WorldCat catalog. %%% %%% BibTeX citation tags are uniformly chosen %%% as name:year:abbrev, where name is the %%% family name of the first author or editor, %%% year is a 4-digit number, and abbrev is a %%% 3-letter condensation of important title %%% words. Citation tags were automatically %%% generated by software developed for the %%% BibNet Project. %%% %%% In this bibliography, entries are sorted %%% first by ascending year, and within each %%% year, alphabetically by author or editor, %%% and then, if necessary, by the 3-letter %%% abbreviation at the end of the BibTeX %%% citation tag, using the bibsort -byyear %%% utility. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ==================================================================== @Preamble{ "\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" # "\ifx \undefined \Dbar \def \Dbar {\leavevmode\raise0.2ex\hbox{--}\kern-0.5emD} \fi" # "\ifx \undefined \hckudot \def \hckudot#1{\ifmmode \setbox7 \hbox{\accent20#1}\else \setbox7 \hbox{\accent20#1}\penalty 10000 \relax \fi \raise 1\ht7 \hbox{\raise.2ex \hbox to 1\wd7{\hss.\hss}}\penalty 10000 \hskip-1\wd7 \penalty 10000\box7} \fi" } %%% ==================================================================== %%% Acknowledgement abbreviations: @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/|"} %%% ==================================================================== %%% Journal abbreviations: @String{j-ADV-QUANTUM-CHEM= "Advances in Quantum Chemistry"} @String{j-AEQUATIONES-MATHEMATICAE= "Aequationes Mathematicae"} @String{j-ANZIAM-J= "The ANZIAM Journal"} @String{j-APPL-MATH-COMP= "Applied Mathematics and Computation"} @String{j-APPL-MATH-NOTES= "Applied Mathematics Notes"} @String{j-BULL-AMS= "Bulletin of the American Mathematical Society"} @String{j-CACM= "Communications of the ACM"} @String{j-CAN-APPL-MATH-Q= "Canadian Applied Mathematics Quarterly"} @String{j-COMM-APPL-ANAL= "Communications in Applied Analysis"} @String{j-COMP-GRAPHICS= "Computer Graphics"} @String{j-COMPOS-SCI-TECH= "Composites Science and Technology"} @String{j-FUNKCIAL-EKVAC= "Funkcialaj Ekvacioj. Serio Internacia"} @String{j-IEEE-TRANS-AUTOMAT-CONTR= "IEEE Transactions on Automatic Control"} @String{j-INT-J-APPL-MATH-STAT= "International Journal of Applied Mathematics \& Statistics"} @String{j-INT-J-FRACTURE= "International Journal of Fracture"} @String{j-INT-J-PURE-APPL-MATH= "International Journal of Pure and Applied Mathematics"} @String{j-J-APPL-PHYS= "Journal of Applied Physics"} @String{j-J-APPROX-THEORY= "Journal of Approximation Theory"} @String{j-J-COMP-APPL-MATH= "Journal of Computational and Applied Mathematics"} @String{j-J-COMPLEXITY= "Journal of Complexity"} @String{j-J-INST-MATH-APPL= "Journal of the Institute of Mathematics and its Applications"} @String{j-J-INTEGRAL-EQU-APPL= "Journal of Integral Equations and Applications"} @String{j-J-MATH-ANAL-APPL= "Journal of Mathematical Analysis and Applications"} @String{j-J-RES-NATL-BUR-STAND-B= "Journal of Research of the National Bureau of Standards. Section B, Mathematics and Mathematical Physics"} @String{j-J-STRUCT-ENG= "Journal of Structural Engineering"} @String{j-LECT-NOTES-MATH= "Lecture Notes in Mathematics"} @String{j-LINEAR-ALGEBRA-APPL= "Linear Algebra and its Applications"} @String{j-MATH-COMPUT= "Mathematics of Computation"} @String{j-NUM-MATH= "Numerische Mathematik"} @String{j-NUMER-ALGORITHMS= "Numerical Algorithms"} @String{j-NUMER-HEAT-TRANSFER-B= "Numerical Heat Transfer, Part B (Fundamentals)"} @String{j-NUMER-METHODS-PARTIAL-DIFFER-EQU= "Numerical Methods for Partial Differential Equations"} @String{j-PROC-AM-MATH-SOC= "Proceedings of the American Mathematical Society"} @String{j-PROC-SPIE= "Proceedings of the SPIE --- The International Society for Optical Engineering"} @String{j-QUART-APPL-MATH= "Quarterly of Applied Mathematics"} @String{j-SAMPL-THEORY-SIGNAL-IMAGE-PROCESS= "Sampling Theory in Signal and Image Processing"} @String{j-SIAM-J-MATH-ANA= "SIAM Journal on Mathematical Analysis"} @String{j-SIAM-J-NUM-ANALYSIS-B= "Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis"} @String{j-SIAM-J-NUMER-ANAL= "SIAM Journal on Numerical Analysis"} @String{j-SIAM-REVIEW= "SIAM Review"} @String{j-SIGNUM= "ACM SIGNUM Newsletter"} @String{j-TOMS= "ACM Transactions on Mathematical Software"} @String{j-ULTRASONIC-IMAGING= "Ultrasonic Imaging"} %%% ==================================================================== %%% Publisher abbreviations: @String{pub-ACADEMIC= "Academic Press Inc."} @String{pub-ACADEMIC:adr= "New York, USA"} @String{pub-AMS= "American Mathematical Society"} @String{pub-AMS:adr= "Providence, RI, USA"} @String{pub-BIRKHAUSER= "Birkh{\"{a}}user"} @String{pub-BIRKHAUSER:adr= "Cambridge, MA, USA; Berlin, Germany; Basel, Switzerland"} @String{pub-BIRKHAUSER-BOSTON= "Birkh{\"a}user Boston Inc."} @String{pub-BIRKHAUSER-BOSTON:adr= "Cambridge, MA, USA"} @String{pub-CRC= "CRC Press"} @String{pub-CRC:adr= "2000 N.W. Corporate Blvd., Boca Raton, FL 33431-9868, USA"} @String{pub-IEEE= "IEEE Computer Society Press"} @String{pub-IEEE:adr= "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} @String{pub-KLUWER= "Kluwer Academic Publishers Group"} @String{pub-KLUWER:adr= "Norwell, MA, USA, and Dordrecht, The Netherlands"} @String{pub-MARCEL-DEKKER= "Marcel Dekker"} @String{pub-MARCEL-DEKKER:adr= "New York, NY, USA"} @String{pub-NORTH-HOLLAND= "North-Holland Publishing Co."} @String{pub-NORTH-HOLLAND:adr= "Amsterdam, The Netherlands"} @String{pub-OXFORD= "Oxford University Press"} @String{pub-OXFORD:adr= "Walton Street, Oxford OX2 6DP, UK"} @String{pub-PLENUM= "Plenum Press"} @String{pub-PLENUM:adr= "New York, NY, USA; London, UK"} @String{pub-SPIE= "SPIE Optical Engineering Press"} @String{pub-SPIE:adr= "Bellingham, WA, USA"} @String{pub-SV= "Spring{\-}er-Ver{\-}lag"} @String{pub-SV:adr= "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-WORLD-SCI= "World Scientific Publishing Co. Pte. Ltd."} @String{pub-WORLD-SCI:adr= "P. O. Box 128, Farrer Road, Singapore 9128"} %%% ==================================================================== %%% Series abbreviations: @String{ser-LECT-NOTES-MATH= "Lecture Notes in Mathematics"} %%% ==================================================================== %%% Part 1 (of 2) %%% %%% Publications by Frank Stenger, sorted by year and then by citation %%% label, with ``bibsort -byyear'': %%% http://www.zentralblatt-math.org/zmath/en/search/ %%% au:stenger, frank & py:1960-1965 %%% ZM has more: 1972 (1), 1976 (4), 1995 (2) @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 = "http://dx.doi.org/10.1137/0702018", ISSN = "0887-459X (print), 1095-7170 (electronic)", 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", } @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, } @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, } @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, } @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 = "http://dx.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", } @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 = "http://dx.doi.org/10.6028/jres.070b.017", ISSN = "0022-4340", 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", } @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 = "http://dx.doi.org/10.6028/jres.070b.018", ISSN = "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", } @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 = "http://dx.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", } @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, } @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 = "http://dx.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", } @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, } @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 = "http://dx.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", } @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 = "http://dx.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", } @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 = "http://dx.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", } @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 = "http://dx.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", } @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 = "http://dx.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/", } @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 = "http://dx.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", } @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", publisher = "Kobe University, Faculty of Science, Department of Mathematics", address = "Kobe, Japan", pages = "1--18", year = "1970", CODEN = "FESIAT", ISSN = "0532-8721", bibdate = "Thu Nov 6 17:29:47 2014", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib", ZMnumber = "0204.40301", acknowledgement = ack-nhfb, fjournal = "Funkcialaj Ekvacioj. Serio Internacia", journal-URL = "http://www.math.kobe-u.ac.jp/~fe/", } @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", 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 = "://links.jstor.org/sici?sici=0025-5718(197110)25:116<935:TOCFSN>2.0.CO%3B2-B", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @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", 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", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @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 = "http://dx.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", } @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 = "http://dx.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", } @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 = "http://dx.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", } @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 = "http://dx.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", } @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 = "http://dx.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", } @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 = "http://dx.doi.org/10.1090/s0025-5718-1972-0319356-4; http://dx.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", 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 = "http://dx.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", } @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 = "http://dx.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", } @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 = "http://dx.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", } @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 = "http://dx.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", } @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 = "http://dx.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", 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 = "http://dx.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", } @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 = "http://dx.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", } @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 = "http://dx.doi.org/10.1093/imamat/12.1.103", ISSN = "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", } @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", 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", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @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, } @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 = "http://dx.doi.org/10.1090/s0002-9939-1974-0333123-0; http://dx.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", } @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 = "http://dx.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 = "http://dx.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", } @TechReport{Stenger:1974:CTD, author = "Frank Stenger", title = "Computing the topological degree of a mapping in {$ {\cal R}^n $}", type = "Report", institution = "National Oceanic and Atmospheric Administration", address = "Washington, DC, USA", year = "1974", bibdate = "Thu May 10 10:10:06 2007", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib", acknowledgement = ack-nhfb, } @Article{Chauvette:1975:ASN, author = "Jean Chauvette and Frank Stenger", title = "The approximate solution of the nonlinear equation {$ \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 = "http://dx.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", } @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 = "http://dx.doi.org/10.1090/s0025-5718-1975-0375068-5; http://dx.doi.org/10.2307/2005558", ISSN = "0025-5718 (paper), 1088-6842 (electronic)", ISSN-L = "0025-5718", 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", 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", 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 = "http://dx.doi.org/10.1137/0712022", 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; 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", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", } @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 = "http://dx.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", acknowledgement = ack-nhfb, fjournal = "Bulletin of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/bull/", } @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 = "http://dx.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", } @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 = "http://dx.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", 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", year = "1975", CODEN = "MCMPAF", 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", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @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", 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", 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", } @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, } @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, 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", 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", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @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 = "http://dx.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", } @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", 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", ZMnumber = "0367.10046", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", } @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 = "http://dx.doi.org/10.1093/imamat/19.2.145", ISSN = "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", } @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 = "??", pages = "359--361", year = "1978", CODEN = "JMTAA8", ISSN = "0020-2932", 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}.", 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{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 = "http://dx.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", 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 = "http://dx.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/", } @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", 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", ZMnumber = "0399.41018", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Mathematical Analysis", journal-URL = "http://epubs.siam.org/sima", } @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 = "http://dx.doi.org/10.1090/s0025-5718-1979-0514812-4; http://dx.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", 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", 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", } @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", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "55M25 (65H10)", MRnumber = "80m:55002", 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", 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", } @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 = "http://dx.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, } @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", 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", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", } @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 = "http://dx.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", } @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 = "http://dx.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", } @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", ISSN = "0025-5718 (paper), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65D30", MRnumber = "83a:65021", 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", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @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 = "http://dx.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, } @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", 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", 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", 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 = "http://dx.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", 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 = "http://dx.doi.org/10.1007/978-1-4684-1137-9", } @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 = "http://dx.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, } @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 = "http://doi.acm.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", URL = "http://doi.acm.org/10.1145/2701.2705", 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", } @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, } @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 = "http://dx.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", } @InProceedings{Johnson:1984:RDS, author = "S. A. Johnson and M. J. Berggren and F. Stenger and C. H. Wilcox and E. Jensen", editor = "????", 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., Kansas City, MO, USA", title = "Recent Developments in Solving the Exact Acoustic Inverse Scattering Problem", publisher = "American Inst of Ultrasound in Medicine", address = "????", 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, } @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 = "http://dx.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, } @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 = "http://doi.acm.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", URL = "http://doi.acm.org/10.1145/399.449", 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", 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 = "140--160", month = jun, year = "1984", CODEN = "ACMSCU", 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", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", } @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 = "http://doi.acm.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", URL = "http://doi.acm.org/10.1145/399.448", 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", 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 = "http://dx.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 = "http://dx.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", } @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, } @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", 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 = "http://dx.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, } @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, } @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 = "http://dx.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", 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 = "http://dx.doi.org/10.1090/s0025-5718-1986-0842132-0; http://dx.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", 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", editor = "????", booktitle = "Acoustical Imaging: Proceedings of the International Symposium (Halifax, NS, Canada)", title = "Performance of Fast Inverse Scattering Solutions for the Exact {Helmholtz} Equation using Multiple Frequencies and Limited Views", publisher = "????", address = "????", pages = "193--201", year = "1987", CODEN = "ACIGD9", ISBN = "0-306-42565-3", ISBN-13 = "978-0-306-42565-3", ISSN = "0270-5117", LCCN = "????", 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, } @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, } @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, } @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-COMP-APPL-MATH, volume = "23", number = "2", pages = "245--255", month = aug, year = "1988", CODEN = "JCAMDI", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", MRclass = "35R35 (65P05)", MRnumber = "MR959479 (89h:35350)", bibdate = "Thu May 10 16:31:10 2007", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib", 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", } @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 = "http://dx.doi.org/10.1090/s0025-5718-1988-0942147-x; http://dx.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", 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 = "http://dx.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", } @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 = "http://dx.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", } @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", 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", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @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 = "http://dx.doi.org/10.1090/s0025-5718-1989-0983558-7; http://dx.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", 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 = "http://dx.doi.org/10.1007/978-94-009-0927-4_11; http://dx.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", } @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 = "http://dx.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", } @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 = "http://dx.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", 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", 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 = "http://dx.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", } @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", 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", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @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)", } @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 = "http://dx.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", 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 = "http://dx.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", } @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 = "http://dx.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", } @InCollection{Stenger:1993:DE, author = "Frank Stenger", title = "Differential Equations", crossref = "Stenger:1993:NMB", chapter = "7", pages = "441--532", year = "1993", DOI = "http://dx.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, } @InCollection{Stenger:1993:IE, author = "Frank Stenger", title = "Integral Equations", crossref = "Stenger:1993:NMB", chapter = "6", pages = "311--440", year = "1993", DOI = "http://dx.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, } @InCollection{Stenger:1993:MP, author = "Frank Stenger", title = "Mathematical Preliminaries", crossref = "Stenger:1993:NMB", chapter = "1", pages = "1--103", year = "1993", DOI = "http://dx.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, } @InCollection{Stenger:1993:PA, author = "Frank Stenger", title = "Polynomial Approximation", crossref = "Stenger:1993:NMB", chapter = "2", pages = "105--130", year = "1993", DOI = "http://dx.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, } @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", 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", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @InCollection{Stenger:1993:SA, author = "Frank Stenger", title = "Sinc Approximation on {$ \Gamma $}", crossref = "Stenger:1993:NMB", chapter = "4", pages = "179--242", year = "1993", DOI = "http://dx.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, } @InCollection{Stenger:1993:SAS, author = "Frank Stenger", title = "Sinc Approximation in Strip", crossref = "Stenger:1993:NMB", chapter = "3", pages = "131--178", year = "1993", DOI = "http://dx.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, } @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, } @InCollection{Stenger:1993:SRM, author = "Frank Stenger", title = "Sinc-Related Methods", crossref = "Stenger:1993:NMB", chapter = "5", pages = "243--310", year = "1993", DOI = "http://dx.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, } @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 = "http://dx.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", 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", 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", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @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 = "http://dx.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/", } @InProceedings{Stenger:1994:NMT, author = "Frank Stenger", title = "Numerical methods via transformations", crossref = "Zahar:1994:ACF", pages = "543--550", year = "1994", DOI = "http://dx.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", 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", 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)", } @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 = "http://dx.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 = "289--303", acknowledgement = ack-nhfb, } @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 = "http://dx.doi.org/10.1090/s0025-5718-1995-1270624-7; http://dx.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/", } @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 = "http://dx.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", 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", } @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 = "http://dx.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/", } @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", 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", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @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", 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", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Article{Stenger:1997:MSM, author = "Frank Stenger", title = "Matrices of {Sinc} methods", journal = j-J-COMP-APPL-MATH, volume = "86", number = "1", pages = "297--310", day = "28", month = nov, year = "1997", CODEN = "JCAMDI", DOI = "http://dx.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 = "Thu May 10 16:31:10 2007", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib", note = "Special issue dedicated to William B. Gragg (Monterey, CA, 1996)", 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", 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 = "http://dx.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/", } @Article{Stenger:1997:RIE, author = "Frank Stenger", title = "Review: {{\em 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", 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", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @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 = "http://dx.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", } @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 = "http://dx.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", 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", 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", 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", } @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 = "http://dx.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", } @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 = "http://dx.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/", } @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", 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", 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", 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", } @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 = "http://dx.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, } @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", year = "2000", CODEN = "AEMABN", 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", 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", 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 = "http://dx.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", } @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", year = "2000", CODEN = "AJNOA2", DOI = "http://dx.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", note = "Papers in honour of David Elliott on the occasion of his sixty-fifth birthday.", 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, 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", reviewer = "I. V. Boikov (Penza)", } @Article{Stenger:2000:SSN, author = "Frank Stenger", title = "Summary of {Sinc} numerical methods", journal = j-J-COMP-APPL-MATH, volume = "121", number = "1--2", pages = "379--420", month = sep, year = "2000", CODEN = "JCAMDI", DOI = "http://dx.doi.org/10.1016/s0377-0427(00)00348-4; http://dx.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 = "Thu May 10 16:31:10 2007", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib", note = "Numerical analysis in the 20th century, Vol.\ I, Approximation theory", 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", 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, } @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, } @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 = "http://dx.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", } @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", 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", } @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 = "http://dx.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", 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 = "http://dx.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", } @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, } @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", 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", 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", } @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", 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", } @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", 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", } @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 = "http://dx.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", } @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", 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", } @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 = "http://dx.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", 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 = "http://dx.doi.org/10.2478/s13540-011-0035-3", ISSN = "1311-0454 (print), 1314-2444 (electronic)", 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/", } @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 = "http://dx.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", 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, 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 = "http://dx.doi.org/10.2478/s13540-013-0046-3", ISSN = "1311-0454 (print), 1314-2444 (electronic)", MRclass = "65R20 (26A33 35R11 45G05)", MRnumber = "3071211", bibdate = "Mon Apr 21 17:27:35 2014", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib", 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/", } @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 = "http://dx.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", } @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 = "http://dx.doi.org/10.1007/978-1-4614-4145-8_2", bibdate = "Fri Nov 07 06:46:49 2014", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib", acknowledgement = ack-nhfb, } @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 = "http://dx.doi.org/10.1007/978-3-319-08801-3_13", bibdate = "Fri Nov 7 08:39:52 MST 2014", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib", acknowledgement = ack-nhfb, } @Article{Stenger:2015:CEC, author = "Frank Stenger and Gerd Baumann and Vasilios G. Koures", title = "Chapter Eleven --- Computational Methods for Chemistry and Physics, and {Schr{\"o}dinger} in $ 3 + 1^1 $", journal = j-ADV-QUANTUM-CHEM, volume = "71", pages = "265--298", year = "2015", CODEN = "AQCHA9", ISSN = "0065-3276", 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/", } %%% ==================================================================== %%% Part 2 (of 2) %%% %%% Publications about Frank Stenger and his works, sorted by year and %%% then by citation label, with ``bibsort -byyear'': @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 = "http://dx.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{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 = "http://dx.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", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "December 1994", } @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 = "http://dx.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", } @TechReport{Stenger:2015:CMC, author = "Frank Stenger and Gerd Baumann and Vasilios G. Koures", title = "Computational Methods for Chemistry and Physics, and Schr{\"o}dinger in $ 3 + 1 $", type = "Preprint", institution = "University of Utah; German University in Cairo; IISAM L3C", address = "Salt Lake City, UT, USA; New Cairo City, Egypt; Oklahoma City, OK, USA", pages = "44", day = "24", month = feb, year = "2015", bibdate = "Thu Feb 26 07:59:05 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib", note = "To be published in the proceedings of a conference of December 2014 honoring the 85th birthday of Frank E. Harris.", acknowledgement = ack-nhfb, } @Book{Stenger:2016:NSE, author = "Frank Stenger and Don Tucker and Gerd Baumann", title = "{Navier--Stokes} Equations on {$ R^3 \times [0, T] $}", publisher = pub-SV, address = pub-SV:adr, pages = "xi + 219", year = "2016", DOI = "http://dx.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 = "????", bibdate = "Mon May 02 11:20:53 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib", URL = "http://www.springer.com/us/book/9783319275246", acknowledgement = ack-nhfb, } %%% ==================================================================== %%% Cross-referenced entries must come last: @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 = "http://dx.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 = "http://dx.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", 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 = "http://dx.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", 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 = "http://dx.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 = "http://dx.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", 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", 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 = "http://dx.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 = "http://dx.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", 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/s/stenger-frank.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 = "http://dx.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 = "http://dx.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", 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.", }