# bibtab

bibtype: article
filename: elefunt.bib
label: Wasilkowski:1989:AIV
author: G. W. Wasilkowski
journal: j-J-COMPLEXITY
volume: 5
number: 3
pages: 363--368
month: sep
monthnumber: 9
year: 1989
CODEN: JOCOEH
ISSN: 0885-064X (print), 1090-2708 (electronic) OR 0885064X (print), 10902708 (electronic)
ISSNL: 0885-064X OR 0885064X
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of complexity
acknowledgement: ack-nhfb
affiliation: Univ. of Kentucky, Lexington, KY
journalURL: http://www.sciencedirect.com/science/journal/0885064X
rawauthor: G. W. Wasilkowski
title:
On adaptive information with varying cardinality for linear problems with elliptically contoured measures

subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES

rawtitle:
On adaptive information with varying cardinality for linear problems with elliptically contoured measures

entry:
@Article{Wasilkowski:1989:AIV,
  author =       "G. W. Wasilkowski",
  title =        "On adaptive information with varying cardinality for
                 linear problems with elliptically contoured measures",
  journal =      j-J-COMPLEXITY,
  volume =       "5",
  number =       "3",
  pages =        "363--368",
  month =        sep,
  year =         "1989",
  CODEN =        "JOCOEH",
  ISSN =         "0885-064X (print), 1090-2708 (electronic)",
  ISSN-L =       "0885-064X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Kentucky, Lexington, KY",
  bibno =        "68756",
  catcode =      "G.1.2; G.1.2; F.1.3",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Nonlinear
                 approximation; F.1.3 Complexity Classes",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Nonlinear approximation; Theory of
                 Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Complexity Classes",
  fjournal =     "Journal of complexity",
  genterm =      "algorithms; theory",
  guideno =      "1989-08045",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0885064X",
  journalabbrev = "J. Complexity",
  jrldate =      "Sept. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.1 COMPUTATION BY ABSTRACT
                 DEVICES",
}


bibtype: article
filename: elefunt.bib
label: Weniger:1989:NST
author: Ernst Joachim Weniger
journal: j-COMPUT-PHYS-REP
volume: 10
number: 5--6
pages: 189--371
month: dec
monthnumber: 12
year: 1989
CODEN: CPHREF
DOI: https://doi.org/10.1016/0167-7977(89)90011-7
ISSN: 0167-7977 (print), 1878-1004 (electronic) OR 01677977 (print), 18781004 (electronic)
ISSNL: 0167-7977 OR 01677977
bibdate: Thu Dec 01 10:13:37 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 10:13:37 ???
note: Available as math.NA/0306302.
fjournal: Computer Physics Reports
keywords: convergence acceleration
acknowledgement: ack-nhfb
rawauthor: Ernst Joachim Weniger
rawnote: Available as math.NA/0306302.
title:
Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series

rawtitle:
Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series

entry:
@Article{Weniger:1989:NST,
  author =       "Ernst Joachim Weniger",
  title =        "Nonlinear sequence transformations for the
                 acceleration of convergence and the summation of
                 divergent series",
  journal =      j-COMPUT-PHYS-REP,
  volume =       "10",
  number =       "5--6",
  pages =        "189--371",
  month =        dec,
  year =         "1989",
  CODEN =        "CPHREF",
  DOI =          "https://doi.org/10.1016/0167-7977(89)90011-7",
  ISSN =         "0167-7977 (print), 1878-1004 (electronic)",
  ISSN-L =       "0167-7977",
  bibdate =      "Thu Dec 01 10:13:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Available as math.NA/0306302.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Reports",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Yortsos:1989:LSI
author: Y. C. Yortsos and F. J. Hickernell
title: Linear stability of immiscible displacement in porous media
journal: j-SIAM-J-APPL-MATH
volume: 49
number: 3
pages: 730--748
month: jun
monthnumber: 6
year: 1989
CODEN: SMJMAP
ISSN: 0036-1399 (print), 1095-712X (electronic) OR 00361399 (print), 1095712X (electronic)
ISSNL: 0036-1399 OR 00361399
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: SIAM Journal on Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/siap
rawauthor: Y. C. Yortsos and F. J. Hickernell
rawtitle: Linear stability of immiscible displacement in porous media
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING

entry:
@Article{Yortsos:1989:LSI,
  author =       "Y. C. Yortsos and F. J. Hickernell",
  title =        "Linear stability of immiscible displacement in porous
                 media",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "49",
  number =       "3",
  pages =        "730--748",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "64942",
  catcode =      "G.1.8; G.1.0; J.2; G.1.2; G.1.4; G.1.8",
  CRclass =      "G.1.8 Partial Differential Equations; G.1.8 Parabolic
                 equations; G.1.0 General; G.1.0 Stability (and
                 instability); J.2 Earth and atmospheric sciences; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.4 Quadrature and Numerical Differentiation; G.1.4
                 Finite difference methods; G.1.8 Partial Differential
                 Equations; G.1.8 Difference methods",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations, Parabolic equations;
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Stability (and instability); Computer Applications,
                 PHYSICAL SCIENCES AND ENGINEERING, Earth and
                 atmospheric sciences; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation,
                 Finite difference methods; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Partial Differential Equations,
                 Difference methods",
  fjournal =     "SIAM Journal on Applied Mathematics",
  genterm =      "algorithms; theory; experimentation",
  guideno =      "1989-09711",
  journal-URL =  "http://epubs.siam.org/siap",
  journalabbrev = "SIAM J. Appl. Math.",
  jrldate =      "June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING",
}


bibtype: article
filename: elefunt.bib
label: Zalik:1989:NIE
author: R. A. Zalik
title: A new inequality for entire functions
journal: j-J-APPROX-THEORY
volume: 58
number: 3
pages: 281--283
month: sep
monthnumber: 9
year: 1989
CODEN: JAXTAZ
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Approximation Theory
subject: G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: R. A. Zalik
rawtitle: A new inequality for entire functions
entry:
@Article{Zalik:1989:NIE,
  author =       "R. A. Zalik",
  title =        "A new inequality for entire functions",
  journal =      j-J-APPROX-THEORY,
  volume =       "58",
  number =       "3",
  pages =        "281--283",
  month =        sep,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72294",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "verification; theory",
  guideno =      "1989-07871",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Sept. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: book
filename: elefunt.bib
label: Ziemer:1989:WDF
author: William P. Ziemer
title: Weakly differentiable functions: Sobolev spaces and functions of bounded variation
volume: 120
publisher: pub-SV
address: pub-SV:adr
pages: xvi + 308
year: 1989
ISBN: 0-387-97017-7 OR 0387970177
ISBN13: 978-0-387-97017-2 OR 9780387970172
LCCN: QA323 .Z53 1989
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
series: Graduate texts in mathematics
acknowledgement: ack-nhfb
affiliation: Indiana Univ., Bloomington
rawauthor: William P. Ziemer
rawtitle: Weakly differentiable functions: {Sobolev} spaces and functions of bounded variation
entry:
@Book{Ziemer:1989:WDF,
  author =       "William P. Ziemer",
  title =        "Weakly differentiable functions: {Sobolev} spaces and
                 functions of bounded variation",
  volume =       "120",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 308",
  year =         "1989",
  ISBN =         "0-387-97017-7",
  ISBN-13 =      "978-0-387-97017-2",
  LCCN =         "QA323 .Z53 1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Graduate texts in mathematics",
  acknowledgement = ack-nhfb,
  affiliation =  "Indiana Univ., Bloomington",
  bibno =        "69369",
  catcode =      "G.1.2; G.1.8; G.1.5",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.8 Partial Differential Equations;
                 G.1.5 Roots of Nonlinear Equations",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Roots of Nonlinear Equations",
  genterm =      "algorithms; theory",
  guideno =      "1989-01732",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Amos:1990:RPP
author: Donald E. Amos
journal: j-TOMS
volume: 16
number: 4
pages: 404--404
month: dec
monthnumber: 12
year: 1990
CODEN: ACMSCU
DOI: https://doi.org/10.1145/98267.98299
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 09 10:26:24 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.03.09 10:26:24 ???
note: See cite Amos:1986:APP,Amos:1995:RAP,Kodama:2007:RA.
URL: http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p404-amos/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; theory
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Donald E. Amos
rawnote: See \cite{Amos:1986:APP,Amos:1995:RAP,Kodama:2007:RA}.
title:
Remark on ``Algorithm 644: a Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order''

subject:
bf F.2.2: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems.

rawtitle:
Remark on ``{Algorithm 644}: a Portable Package for {Bessel} Functions of a Complex Argument and Nonnegative Order''

entry:
@Article{Amos:1990:RPP,
  author =       "Donald E. Amos",
  title =        "Remark on ``{Algorithm 644}: a Portable Package for
                 {Bessel} Functions of a Complex Argument and
                 Nonnegative Order''",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "404--404",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/98267.98299",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:26:24 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See
                 \cite{Amos:1986:APP,Amos:1995:RAP,Kodama:2007:RA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p404-amos/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf F.2.2}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems.",
}


bibtype: article
filename: elefunt.bib
label: Anderson:1990:FIC
author: G. D. Anderson and M. K. Vamanamurthy and M. Vuorinen
title: Functional Inequalities for Complete Elliptic Integrals and Their Ratios
journal: j-SIAM-J-MATH-ANA
volume: 21
number: 2
pages: 536--549
month: mar
monthnumber: 3
year: 1990
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 33E05 (30C62 33C75)
MRnumber: 91d:33039
MRreviewer: K. C. Gupta
bibdate: Sat Dec 5 18:14:13 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.12.05 18:14:13 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: G. D. Anderson and M. K. Vamanamurthy and M. Vuorinen
rawtitle: Functional Inequalities for Complete Elliptic Integrals and Their Ratios
entry:
@Article{Anderson:1990:FIC,
  author =       "G. D. Anderson and M. K. Vamanamurthy and M.
                 Vuorinen",
  title =        "Functional Inequalities for Complete Elliptic
                 Integrals and Their Ratios",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "21",
  number =       "2",
  pages =        "536--549",
  month =        mar,
  year =         "1990",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33E05 (30C62 33C75)",
  MRnumber =     "91d:33039",
  MRreviewer =   "K. C. Gupta",
  bibdate =      "Sat Dec 5 18:14:13 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: article
filename: elefunt.bib
label: Anonymous:1990:BRPb
author: Anonymous
journal: j-MATH-COMPUT-SIMUL
volume: 32
number: 4
pages: 420--420
month: oct
monthnumber: 10
year: 1990
CODEN: MCSIDR
DOI: https://doi.org/10.1016/0378-4754(90)90150-H
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
bibdate: Mon Aug 18 12:50:00 MDT 2025
bibtimestamp: 2025.08.18 12:50:00 MDT
URL: https://www.sciencedirect.com/science/article/pii/037847549090150H
fjournal: Mathematics and Computers in Simulation
acknowledgement: ack-nhfb
ajournal: Math. Comput. Simul.
journalURL: https://www.sciencedirect.com/science/journal/03784754
rawauthor: Anonymous
title:
Book Review: booktitle Properties of estimators for the gamma function: K. O. Bowman and L. R. Shenton, Marcel Dekker, New York, 1988. 268 pp., ISBN 0-8247-7556-2

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1990.bib

rawtitle:
Book Review: {{\booktitle{Properties of estimators for the gamma function}}: K. O. Bowman and L. R. Shenton, Marcel Dekker, New York, 1988. 268 pp., ISBN 0-8247-7556-2}

entry:
@Article{Anonymous:1990:BRPb,
  author =       "Anonymous",
  title =        "Book Review: {{\booktitle{Properties of estimators for
                 the gamma function}}: K. O. Bowman and L. R. Shenton,
                 Marcel Dekker, New York, 1988. 268 pp., ISBN
                 0-8247-7556-2}",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "32",
  number =       "4",
  pages =        "420--420",
  month =        oct,
  year =         "1990",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/0378-4754(90)90150-H",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Mon Aug 18 12:50:00 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1990.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/037847549090150H",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}


bibtype: article
filename: elefunt.bib
label: Bellalij:1990:SPC
author: M. Bellalij
title: A simultaneous process for convergence acceleration and error control
journal: j-J-COMPUT-APPL-MATH
volume: 33
number: 2
pages: 217--231
day: 21
month: dec
monthnumber: 12
year: 1990
CODEN: JCAMDI
DOI: https://doi.org/10.1016/0377-0427(90)90370-F
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 65B99 (65G10)
MRnumber: 1090897 (92a:65029)
MRreviewer: Thomas A. Atchison
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
fjournal: Journal of Computational and Applied Mathematics
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. Bellalij
rawtitle: A simultaneous process for convergence acceleration and error control
entry:
@Article{Bellalij:1990:SPC,
  author =       "M. Bellalij",
  title =        "A simultaneous process for convergence acceleration
                 and error control",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "33",
  number =       "2",
  pages =        "217--231",
  day =          "21",
  month =        dec,
  year =         "1990",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(90)90370-F",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65B99 (65G10)",
  MRnumber =     "1090897 (92a:65029)",
  MRreviewer =   "Thomas A. Atchison",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Bronstein:1990:IEF
author: Manuel Bronstein
title: Integration of elementary functions
journal: j-J-SYMBOLIC-COMP
volume: 9
number: 2
pages: 117--173
month: feb
monthnumber: 2
year: 1990
CODEN: JSYCEH
ISSN: 0747-7171 (print), 1095-855X (electronic) OR 07477171 (print), 1095855X (electronic)
ISSNL: 0747-7171 OR 07477171
MRclass: 12H05 (68Q40)
MRnumber: 91h:12017
MRreviewer: Alexandru Buium
bibdate: Sat May 10 15:54:09 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; Theory/cathode.bib
bibtimestamp: 1997.05.10 15:54:09 MDT
fjournal: Journal of Symbolic Computation
acknowledgement: ack-nhfb
classcodes: C1120 (Analysis); C4160 (Numerical integration and differentiation)
corpsource: Dept. of Math. Sci, IBM Res. Div., Thomas J. Watson Res. Center, Yorktown Heights, NY, USA
journalURL: http://www.sciencedirect.com/science/journal/07477171
treatment: T Theoretical or Mathematical
rawauthor: Manuel Bronstein
rawtitle: Integration of elementary functions
keywords:
algebraic extension; algebraic function; decision procedure; elementary function field; elementary functions; exponential; finite terms; indefinite; integration; integration Risch ODEs oderef; logarithm; proof; Trager

entry:
@Article{Bronstein:1990:IEF,
  author =       "Manuel Bronstein",
  title =        "Integration of elementary functions",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "9",
  number =       "2",
  pages =        "117--173",
  month =        feb,
  year =         "1990",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  MRclass =      "12H05 (68Q40)",
  MRnumber =     "91h:12017",
  MRreviewer =   "Alexandru Buium",
  bibdate =      "Sat May 10 15:54:09 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Theory/cathode.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C1120 (Analysis); C4160 (Numerical integration and
                 differentiation)",
  corpsource =   "Dept. of Math. Sci, IBM Res. Div., Thomas J. Watson
                 Res. Center, Yorktown Heights, NY, USA",
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
  keywords =     "algebraic extension; algebraic function; decision
                 procedure; elementary function field; elementary
                 functions; exponential; finite terms; indefinite;
                 integration; integration Risch ODEs oderef; logarithm;
                 proof; Trager",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Carre:1990:PEF
author: C. Carre
title: Plethysm of elementary functions
journal: Bayreuth. Math. Schr.
volume: 31
pages: 1--18
year: 1990
ISSN: 0172-1062 OR 01721062
MRclass: 20C30 (05E05 22E45)
MRnumber: 91f:20013
MRreviewer: John R. Stembridge
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: C. Carre
rawtitle: Plethysm of elementary functions
entry:
@Article{Carre:1990:PEF,
  author =       "C. Carre",
  title =        "Plethysm of elementary functions",
  journal =      "Bayreuth. Math. Schr.",
  volume =       "31",
  pages =        "1--18",
  year =         "1990",
  ISSN =         "0172-1062",
  MRclass =      "20C30 (05E05 22E45)",
  MRnumber =     "91f:20013",
  MRreviewer =   "John R. Stembridge",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Ciminiera:1990:HRS
author: L. Ciminiera and P. Montuschi
title: Higher radix square rooting
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 10
pages: 1220--1231
month: oct
monthnumber: 10
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.59853
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:04 MDT 2011
bibtimestamp: 2011.07.07 14:20:04 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=59853
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: L. Ciminiera and P. Montuschi
rawtitle: Higher radix square rooting
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Ciminiera:1990:HRS,
  author =       "L. Ciminiera and P. Montuschi",
  title =        "Higher radix square rooting",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "10",
  pages =        "1220--1231",
  month =        oct,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.59853",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:04 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=59853",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A general discussion on nonrestoring square root
                 algorithms is presented, showing bounds and constraints
                 delimiting the space of feasible algorithms, for all
                 the choices of radix, digit set and representation of
                 the partial remainder. Two classes of \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Cody:1990:PEP
author: W. J. Cody
title: Performance Evaluation of Programs for the Error and Complementary Error Functions
journal: j-TOMS
volume: 16
number: 1
pages: 29--37
month: mar
monthnumber: 3
year: 1990
CODEN: ACMSCU
DOI: https://doi.org/10.1145/77626.77628
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65-04 (65G05)
MRnumber: 1 073 407
bibdate: Tue Oct 09 09:29:47 2007
bibtimestamp: 2007.10.09 09:29:47 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
affiliation: Argonne Nat. Lab., IL, USA
journalURL: https://dl.acm.org/loi/toms
thesaurus: Error analysis; Function approximation; Performance evaluation
rawauthor: W. J. Cody
rawtitle: Performance Evaluation of Programs for the Error and Complementary Error Functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

URL:
http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p29-cody/; http://www.acm.org/pubs/toc/Abstracts/0098-3500/77628.html

abstract:
This paper presents methods for performance evaluation of computer programs for the functions $ textrm erf(x) $, $ textrm erfc(x) $, and $ ^x^2 textrm erfc(x) $. Accuracy estimates are based on comparisons using power series expansions and an expansion in the repeated integrals of $ textrm erfc(x) $. Some suggestions for checking robustness are also given. Details of a specific implementation of a test program are included.

keywords:
Complementary error functions; Computer programs; FORTRAN; Power series expansions; Repeated integrals; Robustness; Test program

subject:
bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.

rawabstract:
This paper presents methods for performance evaluation of computer programs for the functions $ \textrm {erf}(x) $, $ \textrm {erfc}(x) $, and $ \e^{x^2} \textrm {erfc}(x) $. Accuracy estimates are based on comparisons using power series expansions and an expansion in the repeated integrals of $ \textrm {erfc}(x) $. Some suggestions for checking robustness are also given. Details of a specific implementation of a test program are included.

entry:
@Article{Cody:1990:PEP,
  author =       "W. J. Cody",
  title =        "Performance Evaluation of Programs for the Error and
                 Complementary Error Functions",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "29--37",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.77628",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65G05)",
  MRnumber =     "1 073 407",
  bibdate =      "Tue Oct 09 09:29:47 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p29-cody/;
                 http://www.acm.org/pubs/toc/Abstracts/0098-3500/77628.html",
  abstract =     "This paper presents methods for performance evaluation
                 of computer programs for the functions $ \textrm
                 {erf}(x) $, $ \textrm {erfc}(x) $, and $ \e^{x^2}
                 \textrm {erfc}(x) $. Accuracy estimates are based on
                 comparisons using power series expansions and an
                 expansion in the repeated integrals of $ \textrm
                 {erfc}(x) $. Some suggestions for checking robustness
                 are also given. Details of a specific implementation of
                 a test program are included.",
  acknowledgement = ack-nhfb,
  affiliation =  "Argonne Nat. Lab., IL, USA",
  classification = "B0290B (Error analysis in numerical methods); B0290F
                 (Interpolation and function approximation); C4110
                 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Complementary error functions; Computer programs;
                 FORTRAN; Power series expansions; Repeated integrals;
                 Robustness; Test program",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms.",
  thesaurus =    "Error analysis; Function approximation; Performance
                 evaluation",
}


bibtype: techreport
filename: elefunt.bib
label: DiDonato:1990:SDC
author: Armido R. DiDonato
title: Significant Digit Computation of the Elliptical Coverage Function
type: Technical Report
number: NAVSWC TR 90-513
institution: Naval Surface Warfare Center
address: Dahlgren, VA 22448-5000, USA and Silver Spring, MD 20903-5000, USA
pages: v + 13 + A-7 + B-9 + 5
month: sep
monthnumber: 9
year: 1990
bibdate: Sat Nov 15 10:55:35 2014
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2014.11.15 10:55:35 ???
URL: http://www.dtic.mil/dtic/tr/fulltext/u2/a230523.pdf
acknowledgement: ack-nhfb
rawauthor: Armido R. DiDonato
rawtitle: Significant Digit Computation of the Elliptical Coverage Function
entry:
@TechReport{DiDonato:1990:SDC,
  author =       "Armido R. DiDonato",
  title =        "Significant Digit Computation of the Elliptical
                 Coverage Function",
  type =         "Technical Report",
  number =       "NAVSWC TR 90-513",
  institution =  "Naval Surface Warfare Center",
  address =      "Dahlgren, VA 22448-5000, USA and Silver Spring, MD
                 20903-5000, USA",
  pages =        "v + 13 + A-7 + B-9 + 5",
  month =        sep,
  year =         "1990",
  bibdate =      "Sat Nov 15 10:55:35 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.dtic.mil/dtic/tr/fulltext/u2/a230523.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Dunham:1990:FPF
author: C. B. Dunham
title: Feasibility of ``perfect'' function evaluation
journal: j-SIGNUM
volume: 25
number: 4
pages: 25--26
month: oct
monthnumber: 10
year: 1990
CODEN: SNEWD6
DOI: https://doi.org/10.1145/122272.122276
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:19 MDT 2005
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.12 07:50:19 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: C. B. Dunham
rawtitle: Feasibility of ``perfect'' function evaluation
entry:
@Article{Dunham:1990:FPF,
  author =       "C. B. Dunham",
  title =        "Feasibility of ``perfect'' function evaluation",
  journal =      j-SIGNUM,
  volume =       "25",
  number =       "4",
  pages =        "25--26",
  month =        oct,
  year =         "1990",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/122272.122276",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:19 MDT 2005",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}


bibtype: article
filename: elefunt.bib
label: Dvorak:1990:NCI
author: Steven L. Dvorak and Edward F. Kuester
title: Numerical computation of the incomplete Lipschitz--Hankel integral $ rm Je_0 (a, z) $
journal: j-J-COMPUT-PHYS
volume: 87
number: 2
pages: 301--327
month: apr
monthnumber: 4
year: 1990
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(90)90255-Y
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Mon Jan 2 07:55:40 MST 2012
bibtimestamp: 2012.01.02 07:55:40 MST
URL: http://www.sciencedirect.com/science/article/pii/002199919090255Y
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Steven L. Dvorak and Edward F. Kuester
rawtitle: Numerical computation of the incomplete {Lipschitz--Hankel} integral {$ {\rm Je}_0 (a, z) $}
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib

entry:
@Article{Dvorak:1990:NCI,
  author =       "Steven L. Dvorak and Edward F. Kuester",
  title =        "Numerical computation of the incomplete
                 {Lipschitz--Hankel} integral {$ {\rm Je}_0 (a, z) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "87",
  number =       "2",
  pages =        "301--327",
  month =        apr,
  year =         "1990",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(90)90255-Y",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:55:40 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/002199919090255Y",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Ercegovac:1990:RSR
author: M. D. Ercegovac and T. Lang
title: Radix-$4$ square root without initial PLA
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 8
pages: 1016--1024
month: aug
monthnumber: 8
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.57040
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:03 MDT 2011
bibtimestamp: 2011.07.07 14:20:03 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57040
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. D. Ercegovac and T. Lang
rawtitle: Radix-$4$ square root without initial {PLA}
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Ercegovac:1990:RSR,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "Radix-$4$ square root without initial {PLA}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1016--1024",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57040",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57040",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Germain-Bonne:1990:CAN
author: B. Germain-Bonne
title: Convergence acceleration of number-machine sequences
journal: j-J-COMPUT-APPL-MATH
volume: 32
number: 1--2
pages: 83--88
day: 26
month: nov
monthnumber: 11
year: 1990
CODEN: JCAMDI
DOI: https://doi.org/10.1016/0377-0427(90)90419-Z
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 65B05
MRnumber: 1091778 (91m:65007)
MRreviewer: W. Govaerts
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
note: Extrapolation and rational approximation (Luminy, 1989)
fjournal: Journal of Computational and Applied Mathematics
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: B. Germain-Bonne
rawnote: Extrapolation and rational approximation (Luminy, 1989)
rawtitle: Convergence acceleration of number-machine sequences
entry:
@Article{Germain-Bonne:1990:CAN,
  author =       "B. Germain-Bonne",
  title =        "Convergence acceleration of number-machine sequences",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "32",
  number =       "1--2",
  pages =        "83--88",
  day =          "26",
  month =        nov,
  year =         "1990",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(90)90419-Z",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65B05",
  MRnumber =     "1091778 (91m:65007)",
  MRreviewer =   "W. Govaerts",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Extrapolation and rational approximation (Luminy,
                 1989)",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Hashemian:1990:SRA
author: R. Hashemian
title: Square Rooting Algorithms for Integer and Floating-Point Numbers
journal: j-IEEE-TRANS-COMPUT
volume: C-39
number: 8
pages: 1025--1029
month: aug
monthnumber: 8
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.57041
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
affiliation: Dept. of Electr. Eng., Northern Illinois Univ., Dekalb, IL, USA
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
thesaurus: Digital arithmetic; Iterative methods; Number theory
rawauthor: R. Hashemian
rawtitle: Square Rooting Algorithms for Integer and Floating-Point Numbers
abstract:
An algorithm for evaluating the square root of integers and real numbers is developed. The procedure consists of two parts: one to obtain a close estimate of the square root and the other to modify the initial value, iteratively, until a precise root is evaluated. The major effort in this development has been concentrated on two objectives: high speed and no division operation other than division by 2. The first objective is achieved through a simple two-step procedure for getting the first estimate, and then modifying it by employing a fast converging iteration technique. The second objective is also fulfilled through applying bit-shift operation rather than division operation. The algorithm is simulated for both integer and real numbers, and the results are compared to two methods being widely used. The results (tabulated) show considerable improvement in speed compared to these other two methods.

keywords:
Bit-shift operation; Close estimate; Division by 2; Fast converging iteration; Floating-point numbers; Initial value modification; Integer numbers; Precise root; Real numbers; Square rooting algorithms

rawabstract:
An algorithm for evaluating the square root of integers and real numbers is developed. The procedure consists of two parts: one to obtain a close estimate of the square root and the other to modify the initial value, iteratively, until a precise root is evaluated. The major effort in this development has been concentrated on two objectives: high speed and no division operation other than division by 2. The first objective is achieved through a simple two-step procedure for getting the first estimate, and then modifying it by employing a fast converging iteration technique. The second objective is also fulfilled through applying bit-shift operation rather than division operation. The algorithm is simulated for both integer and real numbers, and the results are compared to two methods being widely used. The results (tabulated) show considerable improvement in speed compared to these other two methods.

entry:
@Article{Hashemian:1990:SRA,
  author =       "R. Hashemian",
  title =        "Square Rooting Algorithms for Integer and
                 Floating-Point Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-39",
  number =       "8",
  pages =        "1025--1029",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57041",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "An algorithm for evaluating the square root of
                 integers and real numbers is developed. The procedure
                 consists of two parts: one to obtain a close estimate
                 of the square root and the other to modify the initial
                 value, iteratively, until a precise root is evaluated.
                 The major effort in this development has been
                 concentrated on two objectives: high speed and no
                 division operation other than division by 2. The first
                 objective is achieved through a simple two-step
                 procedure for getting the first estimate, and then
                 modifying it by employing a fast converging iteration
                 technique. The second objective is also fulfilled
                 through applying bit-shift operation rather than
                 division operation. The algorithm is simulated for both
                 integer and real numbers, and the results are compared
                 to two methods being widely used. The results
                 (tabulated) show considerable improvement in speed
                 compared to these other two methods.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Dept. of Electr. Eng., Northern Illinois Univ.,
                 Dekalb, IL, USA",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C1160 (Combinatorial mathematics); C4130
                 (Interpolation and function approximation); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Bit-shift operation; Close estimate; Division by 2;
                 Fast converging iteration; Floating-point numbers;
                 Initial value modification; Integer numbers; Precise
                 root; Real numbers; Square rooting algorithms",
  summary =      "An algorithm for evaluating the square root of
                 integers and real numbers is developed. The procedure
                 consists of two parts: one to obtain a close estimate
                 of the square root and the other to modify the initial
                 value, iteratively, until a precise \ldots{}",
  thesaurus =    "Digital arithmetic; Iterative methods; Number theory",
}


bibtype: mastersthesis
filename: elefunt.bib
label: Holton:1990:IJE
author: P. G. W. Holton
title: An Introduction to the Jacobian Elliptic Functions with some Applications
type: Thesis (M.Sc.)
school: University of Newcastle upon Tyne
address: Newcastle upon Tyne, UK
pages: 117
year: 1990
bibdate: Wed Mar 15 06:50:49 MDT 2017
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.15 06:50:49 MDT
acknowledgement: ack-nhfb
rawauthor: P. G. W. Holton
rawtitle: An Introduction to the {Jacobian} Elliptic Functions with some Applications
entry:
@MastersThesis{Holton:1990:IJE,
  author =       "P. G. W. Holton",
  title =        "An Introduction to the {Jacobian} Elliptic Functions
                 with some Applications",
  type =         "Thesis (M.Sc.)",
  school =       "University of Newcastle upon Tyne",
  address =      "Newcastle upon Tyne, UK",
  pages =        "117",
  year =         "1990",
  LCCN =         "????",
  bibdate =      "Wed Mar 15 06:50:49 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Ifantis:1990:DIP
author: E. K. Ifantis and P. D. Siafarikas
title: Differential inequalities for the positive zeros of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 30
number: 2
pages: 139--143
day: 28
month: may
monthnumber: 5
year: 1990
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:20:45 MST 2017
bibtimestamp: 2017.02.25 12:20:45 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279090022R
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: E. K. Ifantis and P. D. Siafarikas
rawtitle: Differential inequalities for the positive zeros of {Bessel} functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib

entry:
@Article{Ifantis:1990:DIP,
  author =       "E. K. Ifantis and P. D. Siafarikas",
  title =        "Differential inequalities for the positive zeros of
                 {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "30",
  number =       "2",
  pages =        "139--143",
  day =          "28",
  month =        may,
  year =         "1990",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:45 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279090022R",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Kiernan:1990:FAE
author: J. M. Kiernan and T. B. Blachowiak
title: Fast, Accurate Elementary Functions For the Cray Y-MP Computer
crossref: Cray:1990:PCU
pages: 243--252
year: 1990
bibdate: Thu Sep 1 10:15:30 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 10:15:30 ???
acknowledgement: ack-nj
rawauthor: J. M. Kiernan and T. B. Blachowiak
rawtitle: Fast, Accurate Elementary Functions For the {Cray Y-MP} Computer
entry:
@InProceedings{Kiernan:1990:FAE,
  author =       "J. M. Kiernan and T. B. Blachowiak",
  title =        "Fast, Accurate Elementary Functions For the {Cray
                 Y-MP} Computer",
  crossref =     "Cray:1990:PCU",
  pages =        "243--252",
  year =         "1990",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Kolbig:1990:BRC
author: K. S. Kolbig
journal: j-MATH-COMPUT
volume: 55
number: 191
pages: 395--397
month: jul
monthnumber: 7
year: 1990
CODEN: MCMPAF
DOI: https://doi.org/10.2307/2008818
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Jan 24 08:35:37 2017
bibtimestamp: 2017.01.24 08:35:37 ???
URL: http://www.jstor.org/stable/2008818
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: K. S. K{\"o}lbig
title:
Book Review: booktitle Computation of Functions on Electronic Computers --- Handbook (in Russian). Naukova Dumka, Kiev, 194, 599pp, by B. A. Popov, G. S. Tesler

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib

rawtitle:
Book Review: {{\booktitle{Computation of Functions on Electronic Computers --- Handbook}} (in Russian). Naukova Dumka, Kiev, 194, 599pp, by B. A. Popov, G. S. Tesler}

entry:
@Article{Kolbig:1990:BRC,
  author =       "K. S. K{\"o}lbig",
  title =        "Book Review: {{\booktitle{Computation of Functions on
                 Electronic Computers --- Handbook}} (in Russian).
                 Naukova Dumka, Kiev, 194, 599pp, by B. A. Popov, G. S.
                 Tesler}",
  journal =      j-MATH-COMPUT,
  volume =       "55",
  number =       "191",
  pages =        "395--397",
  month =        jul,
  year =         "1990",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2008818",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Jan 24 08:35:37 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  URL =          "http://www.jstor.org/stable/2008818",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Koren:1990:EEF
author: Israel Koren and Ofra Zinaty
title: Evaluating Elementary Functions in a Numerical Coprocessor Based on Rational Approximations
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 8
pages: 1030--1037
month: aug
monthnumber: 8
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.57042
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 1 10:15:30 1994
bibtimestamp: 1994.09.01 10:15:30 ???
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57042
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Israel Koren and Ofra Zinaty
rawtitle: Evaluating Elementary Functions in a Numerical Coprocessor Based on Rational Approximations
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

remark:
Contains coefficients of rational polynomial fits for sine (81.35 bits), cosine (75.84 bits), tangent (77.93 bits), log (80.26 bits), exp2 (71.72 bits), and asin (68.3 bits).

entry:
@Article{Koren:1990:EEF,
  author =       "Israel Koren and Ofra Zinaty",
  title =        "Evaluating Elementary Functions in a Numerical
                 Coprocessor Based on Rational Approximations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1030--1037",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57042",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57042",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Contains coefficients of rational polynomial fits for
                 sine (81.35 bits), cosine (75.84 bits), tangent (77.93
                 bits), log (80.26 bits), exp2 (71.72 bits), and asin
                 (68.3 bits).",
}


bibtype: article
filename: elefunt.bib
label: Lentz:1990:CFC
author: William J. Lentz
title: Continued fraction calculation of spherical Bessel functions
journal: j-COMPUT-PHYS
volume: 4
number: 4
pages: 403--407
month: jul
monthnumber: 7
year: 1990
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.168382
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
MRnumber: 33C10 30B70 65-04
bibdate: Wed Mar 22 14:36:46 2017
bibtimestamp: 2017.03.22 14:36:46 ???
URL: https://aip.scitation.org/doi/10.1063/1.168382
fjournal: Computers in Physics
ZMnumber: 0703.33001
acknowledgement: ack-nhfb
ajournal: Comput. Phys.
journalURL: https://aip.scitation.org/journal/cip
rawauthor: William J. Lentz
rawtitle: Continued fraction calculation of spherical {Bessel} functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/computphys.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
An efficient new method of calculating spherical Bessel functions of complex argument based on continued fractions is developed. The method does not depend on recurrence relations, and it allows accurate calculations on computers with differing word lengths. The method may be easily extended to other types of Bessel functions and to complex orders.

rawabstract:
An efficient new method of calculating spherical Bessel functions of complex argument based on continued fractions is developed. The method does not depend on recurrence relations, and it allows accurate calculations on computers with differing word lengths. The method may be easily extended to other types of Bessel functions and to complex orders.

entry:
@Article{Lentz:1990:CFC,
  author =       "William J. Lentz",
  title =        "Continued fraction calculation of spherical {Bessel}
                 functions",
  journal =      j-COMPUT-PHYS,
  volume =       "4",
  number =       "4",
  pages =        "403--407",
  month =        jul,
  year =         "1990",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168382",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  MRnumber =     "33C10 30B70 65-04",
  bibdate =      "Wed Mar 22 14:36:46 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168382",
  ZMnumber =     "0703.33001",
  abstract =     "An efficient new method of calculating spherical
                 Bessel functions of complex argument based on continued
                 fractions is developed. The method does not depend on
                 recurrence relations, and it allows accurate
                 calculations on computers with differing word lengths.
                 The method may be easily extended to other types of
                 Bessel functions and to complex orders.",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys.",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}


bibtype: article
filename: elefunt.bib
label: Levrie:1990:CAN
author: Paul Levrie and Adhemar Bultheel
title: Convergence Acceleration for the Numerical Solution of Second-Order Linear Recurrence Relations
journal: j-SIAM-J-NUMER-ANAL
volume: 27
number: 1
pages: 166--177
month: feb
monthnumber: 2
year: 1990
CODEN: SJNAAM
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
MRclass: 65Q05 (40A15 65B99)
MRnumber: 91a:65244
bibdate: Fri Oct 16 06:57:22 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.16 06:57:22 MDT
fjournal: SIAM Journal on Numerical Analysis
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: Paul Levrie and Adhemar Bultheel
rawtitle: Convergence Acceleration for the Numerical Solution of Second-Order Linear Recurrence Relations
entry:
@Article{Levrie:1990:CAN,
  author =       "Paul Levrie and Adhemar Bultheel",
  title =        "Convergence Acceleration for the Numerical Solution of
                 Second-Order Linear Recurrence Relations",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "27",
  number =       "1",
  pages =        "166--177",
  month =        feb,
  year =         "1990",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65Q05 (40A15 65B99)",
  MRnumber =     "91a:65244",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Lin:1990:MSL
author: Jinn Tyan Lin
title: Miscellanea: a Simpler Logistic Approximation to the Normal Tail Probability and its Inverse
journal: j-APPL-STAT
volume: 39
number: 2
pages: 255--257
year: 1990
CODEN: APSTAG
ISSN: 0035-9254 (print), 1467-9876 (electronic) OR 00359254 (print), 14679876 (electronic)
ISSNL: 0035-9254 OR 00359254
MRclass: 62E15
MRnumber: 1 060 209
bibdate: Sat Apr 21 10:25:45 MDT 2001
bibtimestamp: 2001.04.21 10:25:45 MDT
fjournal: Applied Statistics
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues
rawauthor: Jinn Tyan Lin
rawtitle: Miscellanea: a Simpler Logistic Approximation to the Normal Tail Probability and its Inverse
bibsource:
https://www.math.utah.edu/pub/tex/bib/as1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database

entry:
@Article{Lin:1990:MSL,
  author =       "Jinn Tyan Lin",
  title =        "Miscellanea: a Simpler Logistic Approximation to the
                 Normal Tail Probability and its Inverse",
  journal =      j-APPL-STAT,
  volume =       "39",
  number =       "2",
  pages =        "255--257",
  year =         "1990",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  MRclass =      "62E15",
  MRnumber =     "1 060 209",
  bibdate =      "Sat Apr 21 10:25:45 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/as1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}


bibtype: article
filename: elefunt.bib
label: Magnus:1990:CFL
author: Arne Magnus and John McCabe
title: On a continued fraction for $ log ^2_e(1 + x) $
journal: j-J-COMPUT-APPL-MATH
volume: 30
number: 1
pages: 81--86
day: 10
month: apr
monthnumber: 4
year: 1990
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:20:45 MST 2017
bibtimestamp: 2017.02.25 12:20:45 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279090007M
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Arne Magnus and John McCabe
rawtitle: On a continued fraction for $ \log^2_e(1 + x) $
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib

entry:
@Article{Magnus:1990:CFL,
  author =       "Arne Magnus and John McCabe",
  title =        "On a continued fraction for $ \log^2_e(1 + x) $",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "30",
  number =       "1",
  pages =        "81--86",
  day =          "10",
  month =        apr,
  year =         "1990",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:45 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279090007M",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Markstein:1990:CEF
author: P. W. Markstein
title: Computation of elementary functions on the IBM RISC System / 6000 processor
journal: j-IBM-JRD
volume: 34
number: 1
pages: 111--119
month: jan
monthnumber: 1
year: 1990
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 65-04 (65D20)
MRnumber: 1 057 659
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
affiliation: IBM Res. Div., Austin, TX, USA
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
thesaurus: Digital arithmetic; IBM computers; Reduced instruction set computing
rawauthor: P. W. Markstein
rawtitle: Computation of elementary functions on the {IBM RISC System\slash 6000} processor
abstract:
The additional speed and precision of the IBM RISC System / 6000 floating-point unit have motivated reexamination of algorithms to perform division, square root, and the elementary functions. New results are obtained which avoid the necessity of doing special testing to get the last bit rounded correctly in accordance with all of the IEEE rounding modes in the case of division and square root. For the elementary function library, a technique is described for always getting the last bit rounded correctly in the selected IEEE rounding mode.

keywords:
Division; Elementary functions; Floating-point unit; IBM RISC System / 6000 processor; IEEE rounding modes; IEEE rounding modes, IBM RISC System/6000 processor; Square root

rawabstract:
The additional speed and precision of the IBM RISC System\slash 6000 floating-point unit have motivated reexamination of algorithms to perform division, square root, and the elementary functions. New results are obtained which avoid the necessity of doing special testing to get the last bit rounded correctly in accordance with all of the IEEE rounding modes in the case of division and square root. For the elementary function library, a technique is described for always getting the last bit rounded correctly in the selected IEEE rounding mode.

entry:
@Article{Markstein:1990:CEF,
  author =       "P. W. Markstein",
  title =        "Computation of elementary functions on the {IBM RISC
                 System\slash 6000} processor",
  journal =      j-IBM-JRD,
  volume =       "34",
  number =       "1",
  pages =        "111--119",
  month =        jan,
  year =         "1990",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "65-04 (65D20)",
  MRnumber =     "1 057 659",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The additional speed and precision of the IBM RISC
                 System\slash 6000 floating-point unit have motivated
                 reexamination of algorithms to perform division, square
                 root, and the elementary functions. New results are
                 obtained which avoid the necessity of doing special
                 testing to get the last bit rounded correctly in
                 accordance with all of the IEEE rounding modes in the
                 case of division and square root. For the elementary
                 function library, a technique is described for always
                 getting the last bit rounded correctly in the selected
                 IEEE rounding mode.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Res. Div., Austin, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "Division; Elementary functions; Floating-point unit;
                 IBM RISC System\slash 6000 processor; IEEE rounding
                 modes; IEEE rounding modes, IBM RISC System/6000
                 processor; Square root",
  thesaurus =    "Digital arithmetic; IBM computers; Reduced instruction
                 set computing",
}


bibtype: article
filename: elefunt.bib
label: Matos:1990:CAM
author: Ana C. Matos
title: A convergence acceleration method based on a good estimation of the absolute value of the error
journal: j-IMA-J-NUMER-ANAL
volume: 10
number: 2
pages: 243--251
year: 1990
CODEN: IJNADH
ISSN: 0272-4979 (print), 1464-3642 (electronic) OR 02724979 (print), 14643642 (electronic)
ISSNL: 0272-4979 OR 02724979
MRclass: 65B99
MRnumber: 91m:65010
MRreviewer: K. B{\"o}hmer
bibdate: Sat Dec 23 17:06:35 MST 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; MathSciNet database
bibtimestamp: 2000.12.23 17:06:35 MST
fjournal: IMA Journal of Numerical Analysis
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://imajna.oxfordjournals.org/content/by/year
rawauthor: Ana C. Matos
rawtitle: A convergence acceleration method based on a good estimation of the absolute value of the error
entry:
@Article{Matos:1990:CAM,
  author =       "Ana C. Matos",
  title =        "A convergence acceleration method based on a good
                 estimation of the absolute value of the error",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "10",
  number =       "2",
  pages =        "243--251",
  year =         "1990",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65B99",
  MRnumber =     "91m:65010",
  MRreviewer =   "K. B{\"o}hmer",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "convergence acceleration",
}


bibtype: inproceedings
filename: elefunt.bib
label: Matula:1990:HPD
author: D. Matula
title: Highly parallel divide and square root algorithms for a new generation floating point processor
crossref: Ullrich:1990:CCA
pages: ??--??
year: 1990
bibdate: Thu Apr 2 08:38:35 1998
bibtimestamp: 1998.04.02 08:38:35 ???
acknowledgement: ack-sfo
rawauthor: D. Matula
rawtitle: Highly parallel divide and square root algorithms for a new generation floating point processor
entry:
@InProceedings{Matula:1990:HPD,
  author =       "D. Matula",
  title =        "Highly parallel divide and square root algorithms for
                 a new generation floating point processor",
  crossref =     "Ullrich:1990:CCA",
  pages =        "??--??",
  year =         "1990",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: McConnell:1990:LEP
author: C. R. McConnell
title: Letter to the Editor: Pocket computer approximation for areas under the standard normal curve
journal: j-AMER-STAT
volume: 44
number: 1
pages: 63--63
month: feb
monthnumber: 2
year: 1990
CODEN: ASTAAJ
ISSN: 0003-1305 (print), 1537-2731 (electronic) OR 00031305 (print), 15372731 (electronic)
ISSNL: 0003-1305 OR 00031305
bibdate: Sat Dec 16 17:19:37 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 17:19:37 ???
URL: http://www.jstor.org/stable/2684963
fjournal: The American Statistician
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/utas20
rawauthor: C. R. McConnell
rawtitle: Letter to the {Editor}: Pocket computer approximation for areas under the standard normal curve
entry:
@Article{McConnell:1990:LEP,
  author =       "C. R. McConnell",
  title =        "Letter to the {Editor}: Pocket computer approximation
                 for areas under the standard normal curve",
  journal =      j-AMER-STAT,
  volume =       "44",
  number =       "1",
  pages =        "63--63",
  month =        feb,
  year =         "1990",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Sat Dec 16 17:19:37 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2684963",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}


bibtype: article
filename: elefunt.bib
label: Montuschi:1990:SSR
author: P. Montuschi and P. M. Mezzalama
title: Survey of square rooting algorithms
journal: j-IEE-PROC-COMPUT-DIGIT-TECH
volume: 137
number: 1
pages: 31--40
month: jan
monthnumber: 1
year: 1990
CODEN: ICDTEA
ISSN: 1350-2387 (print), 1359-7027 (electronic) OR 13502387 (print), 13597027 (electronic)
ISSNL: 1350-2387 OR 13502387
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEE Proceedings. Computers and Digital Techniques
acknowledgement: ack-nhfb
rawauthor: P. Montuschi and P. M. Mezzalama
rawtitle: Survey of square rooting algorithms
entry:
@Article{Montuschi:1990:SSR,
  author =       "P. Montuschi and P. M. Mezzalama",
  title =        "Survey of square rooting algorithms",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "137",
  number =       "1",
  pages =        "31--40",
  month =        jan,
  year =         "1990",
  CODEN =        "ICDTEA",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
  summary =      "The paper reviews the algorithms for the computation
                 of square roots for binary machines. After an initial
                 classification, the algorithms are analysed in detail
                 by considering their specific peculiarities and
                 properties. Finally, some comments are \ldots{}",
}


bibtype: incollection
filename: elefunt.bib
label: Mora:1990:EFI
author: Gerardo Mora and Edwin Castro and Ioan Muntean
booktitle: Mathematics in Costa Rica, Vol. 1 (Spanish) (San Jose, 1990)
title: Elementary functions. I. (Spanish)
publisher: Univ. Costa Rica
address: San Jose, Costa Rica
pages: 76--86
year: 1990
MRclass: 26A09
MRnumber: 1 111 714
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Spanish
acknowledgement: ack-nhfb
rawauthor: Gerardo Mora and Edwin Castro and Ioan Muntean
rawbooktitle: Mathematics in Costa Rica, Vol. 1 (Spanish) (San Jos{\'e}, 1990)
rawtitle: Elementary functions. {I}. ({Spanish})
entry:
@InCollection{Mora:1990:EFI,
  author =       "Gerardo Mora and Edwin Castro and Ioan Muntean",
  booktitle =    "Mathematics in Costa Rica, Vol. 1 (Spanish) (San
                 Jos{\'e}, 1990)",
  title =        "Elementary functions. {I}. ({Spanish})",
  publisher =    "Univ. Costa Rica",
  address =      "San Jos{\'e}, Costa Rica",
  pages =        "76--86",
  year =         "1990",
  MRclass =      "26A09",
  MRnumber =     "1 111 714",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Spanish",
}


bibtype: techreport
filename: elefunt.bib
label: Morris:1990:NLM
author: Alfred H. Morris, Jr.
title: NSWC Library of Mathematics Subroutines
type: Report
number: NSWC TR 90-21
institution: Naval Surface Warfare Center
address: Dahlgren, VA 22448-5000, USA; Silver Spring, MD 20903-5000, USA
pages: xii + 492 + 9
month: jan
monthnumber: 1
year: 1990
bibdate: Tue Jun 13 08:47:19 2023
bibtimestamp: 2023.06.13 08:47:19 ???
note: See also later edition cite Morris:1993:NLM.
acknowledgement: ack-nhfb
rawauthor: Alfred H. {Morris, Jr.}
rawnote: See also later edition \cite{Morris:1993:NLM}.
rawtitle: {NSWC} Library of Mathematics Subroutines
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran2.bib

URL:
https://apps.dtic.mil/sti/citations/ADA476840; https://apps.dtic.mil/sti/pdfs/ADA476840.pdf; https://people.math.sc.edu/Burkardt/f_src/nswc/nswc.f90; https://people.math.sc.edu/Burkardt/f_src/nswc/nswc.html

abstract:
The NSWC library is a library of general-purpose Fortran subroutines that provide a basic computational capability in a variety of mathematical activities and emphasis has been placed on the transportability of the codes. Subroutines are available in the following areas Elementary Operations, Geometry, Special Functions, Polynomials, Vectors, Matrices, Large Dense Systems of Linear Equations, Banded Matrices, Sparse Matrices, Eigenvalues and Eigenvectors, Solution of Linear Equations, Least-Squares Solution of Linear Equations, Optimization, Transforms, Approximation of Functions, Curve Fitting, Surface Fitting, Manifold Fitting, Numerical Integration, Integral Equations, Ordinary--Differential Equations, Partial Differential Equations, and Random Number Generation.

remark:
The single Fortran 90 file of 99,021 nonblank lines compiles into a library of 905 distinct functions and subroutines: the source code appears to contain 139 functions and 762 subroutines (901 total entry points). The tableofcontents values in this entry is derived from optical character recognition (OCR) of the 8-page listing from the PDF files, with editorial correction of spelling and OCR errors, and matching of uppercase software names against the entry points of the compiled library. There are about five names in the PDF table of contents that disagree with subroutine names in the source code: they have been edited here to reflect the correct code names. There are numerous routine names in the compiled library that are not mentioned in the table of contents.

TOC:
Introduction / 1 Elementary Operations Machine Constants --- SPMPAR, DPMPAR, IPMPAR / 3 Sorting Lists --- ISHELL, SHELL, AORD, RISORT, SHELL2, DSORT, DAORD, DISORT, DDSORT / 5 Cube Root --- CBRT, DCBRT / 7 Four Quadrant Arctangent --- ARTNQ, DARTNQ / 7 Length of a Two-Dimensional Vector --- CPABS, DCPABS / 7 Reciprocal of a Complex Number --- CREC, DCREC / 9 Square Root of a Double Precision Complex Number --- DCSQRT / 9 Conversion of Polar to Cartesian Coordinates --- POCA / 11 Conversion of Cartesian to Polar Coordinates --- CAPO / 11 Rotation of Axes --- ROTA / 11 Planar Givens Rotations --- SROTG, DROTG / 13 Three Dimensional Rotations --- ROT3 / 15 Rotation of a Point on the Unit Sphere to the North Pole --- CONSTR / 17 Hyperbolic Sine and Cosine Functions --- SNHCSH / 19 Exponentials --- REXP, DREXP / 21 Logarithms --- ALNREL, RLOG, RLOG1, DLNREL, DRLOG, DRLOG1 / 23 Geometry Determining if a Point is Inside or Outside a Polygon --- LOCPT / 25 The Convex Hull for a Finite Planar Set --- HULL / 27 Areas of Planar Polygons --- PAREA / 29 Hamiltonian Circuits --- HC / 31 Special Functions Error Function --- CERF, CERFC, ERF, ERFC, ERFC1, DCERF, DCERFC, DERF, DERFC, DERFC1 / 35 Inverse Error Function --- ERFINV / 41 Normal Probability Distribution Function --- PNDF / 43 Inverse Normal Probability Distribution Function --- PNINV / 45 Dawson's Integral --- DAWSON / 47 Complex Fresnel Integral --- CFRNLI / 49 Real Fresnel Integrals --- FRESNEL / 51 Exponential Integral Function --- CEXPLI, EXPLI, DEI, DEI1 / 53 Sine and Cosine Integral Functions --- SI, CIN / 57 Dilogarithm Function --- CLI, ALI / 59 Gamma Function --- CGAMMA, GAMMA, GAMLN, DCGAMA, DGAMMA, DGAMLN / 61 Diganma Function --- CPSI, PSI, DCPSI, DPSI / 65 Logarithm of the Beta Function --- BETALN, DBETLN / 67 Incomplete Gamma Ratio Functions --- GRATIO, RCOMP / 69 Inverse Incomplete Gamma Ratio Function --- GAMINV / 71 Incomplete Beta Function --- BRATIO, ISUBX, BRCOMP / 73 Bessel Function $J_nu (z)$ --- CBSSLJ, BSSLJ, BESJ / 75 Bessel Function $Y_nu (z)$ --- BSSLY / 77 Modified Bessel Function $I_nu (z)$ --- BSSLI, BESI / 79 Modified Bessel Function $K_nu (z)$ --- CBSSLK, BSSLK / 81 Airy functions --- CAI, CBI, AI, AIE, BI, BIE / 83 Complete Complex Elliptic Integrals of the First and Second Kinds --- CK, CKE / 87 Real Elliptic Integrals of the First and Second Kinds --- ELLPI, RFVAL, RDVAL, DELLPI, DRFVAL, DRDVAL / 91 Real Elliptic Integrals of the Third Kind --- EPI, RJVAL, DEPI, DRJVAL / 95 Jacobian Elliptic Functions --- ELLPF, ELPFC1 / 99 Weierstrass Elliptic Function for the Equianharmonic and Lemniscatic Cases --- PEQ, PEQ1, PLEM, PLEM1 / 103 Integral of the Bivariate Density Function over Arbitrary Polygons and Semi-infinite Angular Regions --- VALR2 / 107 Circular Coverage Function --- CIRCV / 109 Elliptical Coverage Function --- PKILL, PKILL3 / 111 Polynomials Copying Polynomials --- PLCOPY, DPCOPY / 113 Addition of Polynomials --- PADD, DPADD / 115 Subtraction of Polynomials --- PSUBT, DPSUBT / 117 Multiplication of Polynomials --- PMULT, DPMULT / 119 Division of Polynomials --- PDIV, DPDIV / 121 Real Powers of Polynomials --- PLPWR, DPLPWR / 123 Inverses of Power Series --- PINV, DPINV / 125 Derivatives and Integrals of Polynomials --- MPLNMV / 127 Evaluation of Chebyshev Expansions --- CSEVL, DCSEVL / 129 Lagrange Polynomials --- LGRNGN, LGRNGV, LGRNGX / 131 Orthogonal Polynomials on Finite Sets --- ORTHOS, ORTHOV, ORTHOX / 133 Solutions of Nonlinear Equations Zeros of Continuous Functions --- ZEROIN / 135 Solution, of Systems of Nonlinear Equations --- HBRD / 137 Solutions of Quadratic, Cubic, and Quartic Equations --- QDCRT, CBCRT, QTCRT, DQDCRT, DCBCRT, DQTCRT / 139 Double Precision Roots of Polynomials --- DRPOLY, DCPOLY / 141 Accuracy of the Roots of a Real Polynomial --- RBND / 143 Vectors Copying Vectors --- SCOPY, DCOPY, CCOPY / 145 Interchanging Vectors --- SSWAP, DSWAP, CSWAP / 147 Planar Rotation of Vectors --- SROT, DROT, CSROT / 149 Dot Products of Vectors --- SDOT, DDOT, CDOTC, CDOTU / 151 Scaling Vectors --- SSCAL, DSCAL, CSCAL, CSSCAL / 153 Vector Addition --- SAXPY, DAXPY, CAXPY / 155 $L_1$ Norm of a Vector-- SASUM, DASUM, SCASUM / 157 $L_2$ Norm of a Vector --- SNRM2, DNRM2, SCNRM2 / 159 $L_infty $ Norm of a Vector --- ISAMAX, IDAMAX, ICAMAX / 161 Matrices Packing and Unpacking Symmetric Matrices --- MCVFS, DMCVFS, MCVSF, DMCVSF / 163 Conversion of Real Matrices to and from Double Precision Form --- MCVRD, MCVDR / 165 Storage of Real Matrices in the Complex Matrix Format --- MCVRC / 167 The Real and Imaginary Parts of a Complex Matrix --- CMREAL, CMIMAG / 169 Copying Matrices --- MCOPY, SMCOPY, DMCOPY, CMCOPY / 171 Computation of the Conjugate of a Complex Matrix --- CMCONJ / 173 Transposing Matrices --- TPOSE, DTPOSE, CTPOSE, TIP, DTIP, CTIP / 175 Computing Adjoints of Complex Matrices --- CMADJ, CTRANS / 177 Matrix Addition --- MADD, SMADD, DMADD, CMADD / 179 Matrix Subtraction --- MSUBT, SMSUBT, DMSUBT, CMSUBT / 181 Matrix Multiplication-- MTMS, DMTMS, CMTMS, MPROD, DMPROD, CMPROD / 183 Product of a Packed Symmetric Matrix and a Vector --- SVPRD, DSVPRD / 185 Transpose Matrix Products --- TMPROD / 187 Symmetric Matrix Products --- SMPROD / 189 Kronecker Product of Matrices --- KPROD, DKPROD, CKPROD / 191 Inverting General Real Matrices and Solving General Systems of Real Linear Equations --- CROUT, KROUT, NPIVOT, MSLV, DSMSLV / 193 Solutions of Real Equations with Iterative Improvement --- SLVMP / 197 Solution of Almost Block Diagonal Systems of Linear Equations --- ARCECO, ARCESL / 199 Solution of Almost Block Tridiagonal Systems of Linear Equations --- BTSLV / 201 Inverting Symmetric Real Matrices and Solving Symmetric Systems of Real Linear Equations --- SMSLV, DSMSLV / 203 Inverting Positive Definite Symmetric Matrices and Solving Positive Definite Symmetric Systems of Linear Equations --- PCHOL, DPCHOL / 207 Solution of Toeplitz Systems of Linear Equations --- TOPLX, DTOPLX / 209 Inverting General Complex Matrices and Solving General Systems of Complex Linear Equations --- CMSLV, CMSLV1, DCMSLV / 211 Solution of Complex Equations with Iterative Improvement --- CSLVMP / 215 Singular Value Decomposition of a Matrix --- SSVDC, DSVDC, CSVDC / 217 Evaluation of the Characteristic Polynomial of a Matrix --- DET, DPDET, CDET / 219 Solution of the Matrix Equation $A X + X B = C$ --- ABSLV, DABSLV / 221 Solution of the Matrix Equation $A^t X + X B = C$ when $C$ is Symmetric --- TASLV, DTASLV / 223 Solution of the Matrix Equation $A X^2 + X B + C = 0$ --- SQUINT / 225 Exponential of a Real Matrix --- MEXP, DMEXP / 227 Large Dense Systems of Linear Equations Solving systems of 200--400 Linear Equations --- LE, DPLE, CLE / 229 Banded Matrices Band Matrix Storage / 231 Conversion of Banded Matrices to and from the Standard Format --- CVBR, CVBC, CVRB, CVCB, CVRB1, CVCB1 / 233 Conversion of Banded Matrices to and from Sparse Form --- MCVBS, CMCVBS, MCVSB, CMCVSB / 235 Transposing Banded Matrices --- BPOSE, CBPOSE / 237 Addition of Banded Matrices --- BADD, CBADD / 239 Subtraction of Banded Matrices --- BSUBT, CBSUBT / 241 Multiplication of Banded Matrices --- BPROD, CBPROD / 243 Product of a Real Banded Matrix and Vector --- BVPRD, BVPRD1, BTPRD, BTPRD1 / 245 Product of a Complex Banded Matrix and Vector --- CBVPD, CBVPD1, CBTPD, CBTPD1 / 247 Solution of Banded Systems of Real Linear Equations --- BSLV, BSLV1 / 249 Solution of Banded Systems of Complex Linear Equations --- CBSLV, CBSLV1 / 251 Sparse Matrices Storage of Sparse Matrices / 253 Conversion of Sparse Matrices to and from the Standard Format --- CVRS, CVDS, CVCS, CVSR, CVSD, CVSC / 255 Conversion of Sparse Real Matrices to and from Double Precision Form --- SCVRD, SCVDR / 257 The Real and Imaginary Parts of a Sparse Complex Matrix --- CSREAL, CSIMAG / 259 Computing $A + i D$ for Sparse Real Matrices $A$ and $B$ --- SCVRC / 261 Copying Sparse Matrices --- RSCOPY, DSCOPY, CSCOPY / 263 Computing Conjugates of Sparse Complex Matrices --- SCONJ / 265 Transposing Sparse Real Matrices --- RPOSE, RPOSE1 / 267 Transposing Sparse Double Precision Matrices --- DPOSE, DPOSE1 / 269 Transposing Sparse Complex Matrices --- CPOSE, CPOSE1 / 271 Addition of Sparse Matrices --- SADD, DSADD, CSADD / 273 Subtraction of Sparse Matrices --- SSUBT, DSSUBT, CSSUBT / 275 Multiplication of Sparse Matrices --- SPROD, DSPROD, CSPROD / 277 Product of a Real Sparse Matrix and Vector --- MVPRD, MVPRD1, MTPRD, MTPRD1 / 279 Product of a Double Precision Sparse Matrix and Vector --- DVPRD, DVPRD1, DTPRD, DTPRD1 / 281 Product of a Complex Sparse Matrix and Vector --- CVPRD, CVPRD1, CTPRD, CTPRD1 / 283 Ordering the Rows of a Sparse Matrix by Increasing Length --- SPORD / 285 Reordering Sparse Matrices into Block Triangular Form --- BLKORD / 287 Solution of Sparse Systems of Real Linear Equations --- SPSLV, RSLV, TSLV / 289 Double Precision Solution of Sparse Systems of Real Linear Equations --- DSPSLV, DSLV, DTSLV / 293 Solution of Sparse Systems of Complex Linear Equations --- CSPSLV, CSLV, CTSLV / 297 Eigenvalues and Eigenvectors Computation of Eigenvalues of General Real Matrices --- EIG, EIG1 / 301 Computation of Eigenvalues and Eigenvectors of General Real Matrices --- EIGV, EIGV1 / 303 Double Precision Computation of Eigenvalues of Real Matrices --- DEIG / 305 Double Precision Computation of Eigenvalues and Eigenvectors of Real Matrices --- DEIGV / 307 Computation of Eigenvalues of Symmetric Real Matrices --- SEIG, SEIG1 / 309 Computation of Eigenvalues and Eigenvectors of Symmetric Real Matrices --- SEIGV, SEIGV1 / 311 Computation of Eigenvalues of Complex Matrices --- CEIG / 313 Computation of Eigenvalues and Eigenvectors of Complex Matrices --- CEIGV / 315 Double Precision Computation of Eigenvalues of Complex Matrices --- DCEIG / 317 Double Precision Computation of Eigenvalues and Eigenvectors of Complex Matrices --- DCEIGV / 319 $ell _1$ Solution of Linear Equations $ell _1$ Solution of Systems of Linear Equations with Equality and Inequality Constraints --- CL1 / 321 Least Squares Solution of Linear Equations Least Squares Solution of Systems of Linear Equations --- LLSQ, HFTI, HFTI2 / 323 Least Squares Solution of Overdetermined Systems of Linear Equations with Iterative Improvement --- LLSQMP / 327 Double Precision Least Squares Solution of Systems of Linear Equations --- DLLSQ, DHFTI, DHFTI2 / 329 Least Squares Solution of Systems of Linear Equations with Equality and Inequality Constraints --- LSEI / 333 Least Squares Solution of Systems of Linear Equations with Equality and Nonnegativity Constraints --- WNNLS / 337 Least Squares Iterative Improvement Solution of Systems of Linear Equations with Equality Constraints --- L2SLV / 341 Iterative Least Squares Solution of Banded Linear Equations --- BLSQ / 345 Iterative Least Squares Solution of Sparse Linear Equations --- SPLSQ, STLSQ / 347 Optimization Minimization of Functions of a Single Variable --- FMIN / 349 Minimization of Functions of n Variables --- OPTF / 351 Unconstrained Minimum of the Sum of Squares of Nonlinear Functions --- LMDIFF / 353 Linear Programming --- SMPLX, SSPLX / 355 The Assignment Problem --- ASSGN / 359 $0$--$1$ Knapsack Problem --- MKP / 361 Transforms Inversion of the Laplace Transform --- LAINV / 363 Fast Fourier Transform --- FFT, FFT1 / 367 Multivariate Fast Fourier Transform --- MFFT, MFFT1 / 369 Discrete Cosine and Sine Transforms --- COSQI, COSQB, COSQF, SINQB, SINQF / 371 Approximation of Functions Rational Minimax Approximation of Functions --- CHEBY / 375 $L_p$ Approximation of Functions --- ADAPT / 377 Calculation of the Taylor Series of a Complex Analytic Function --- CPSC, DCPSC / 381 Curve Fitting Linear Interpolation --- TRP / 385 Lagrange Interpolation --- LTRP / 387 Hermite Interpolation --- HTRP / 389 Conversion of Real Polynomials from Newton to Taylor Series Form --- PCOEFF / 391 Least Squares Polynomial Fit --- PFIT / 393 Weighted Least Squares Polynomial Fit --- WPFIT / 395 Cubic Spline Interpolation --- CBSPL, SPLIFT / 397 Weighted Least Squares Cubic Spline Fitting --- SPFIT / 399 Cubic Spline Evaluation --- SCOMP, SCOMP1, SCOMP2 / 401 Cubic Spline Evaluation and Differentiation --- SEVAL, SEVAL1, SEVAL2 / 403 Integrals of Cubic Splines --- CSINT, CSINT1, CSINT2 / 405 N-Dimensional Cubic Spline Closed Curve Fitting --- CSLOOP, LOPCMP, LOPDF / 407 Spline under Tension Interpolation --- CURV1 / 409 Spline under Tension Evaluation --- CURV2 / 411 Differentiation and Integration of Splines under Tension --- CURVD, CURVI / 413 Two Dimensional Spline under Tension Curve Fitting --- KURV1, KURV2 / 415 Two Dimensional Spline under Tension Closed Curve Fitting --- KURVP1, KURVP2 / 417 Three Dimensional Spline under Tension Curve Fitting --- QURV1, QURV2 / 419 B-Splines / 421 Piecewise Polynomial Interpolation --- BSTRP / 423 Conversion of Piecewise Polynomials from B-Spline to Taylor Series Form --- BSPP / 425 Piecewise Polynomial Evaluation --- PPVAL / 427 Weighted Least Squares Piecewise Polynomial Fitting --- BSL2 / 429 Surface Fitting over Rectangular Grids Bi-Splines under Tension / 431 Bi-Spline under Tension Surface Interpolation --- SURF / 433 Bi-Spline under Tension Evaluation --- SURF2, NSURF2 / 435 Surface Fitting over Arbitrarily Positioned Data Points Surface Interpolation for Arbitrarily Positioned Data Points --- BVIP, BVIP2 / 437 Manifold Fitting Weighted Least Squares Fitting with Polynomials of $n$ Variables --- MFIT, DMFIT, MEVAL, DMEVAL / 441 Numerical Integration Evaluation of Integrals over Finite Intervals --- QAGS, QSUBA, DQAGS / 445 Evaluation of Integrals over Infinite Intervals --- QAGI, DQAGI / 449 Evaluation of Double Integrals over Triangles --- CUBTRI / 453 Integral Equations Solution of Fredholm Integral Equations of the Second Kind --- IESLV / 455 Ordinary Differential Equations/Initial Value Problems The Initial Value Solvers --- Introductory Comments / 459 Adaptive Adams Solution of Nonstiff Differential Equations --- ODE / 461 Adaptive RKF Solution of Nonstiff Differential Equations --- RKF45 / 465 Adaptive RKF Solution of Nonstiff Differential Equations with Global Error Estimation --- GERK / 469 Adaptive Solution of Stiff Differential Equations --- SFODE, SFODE1 / 473 Fourth-Order Runge-Kutta --- RK / 477 Eighth-Order Runge-Kutta --- RK8 / 479 Partial Differential Equations Separable Second-Order Elliptic Equations on Rectangular Domains --- SEPDE / 481 Random Number Generation Uniform Random Number Generator --- URNG / 485 Gaussian Random Number Generator using the Box--Muller Transformation --- NRNG / 487 Appendix. Installation of the NSWC Library / 489 Index / 491 Distribution

rawabstract:
The NSWC library is a library of general-purpose Fortran subroutines that provide a basic computational capability in a variety of mathematical activities and emphasis has been placed on the transportability of the codes. Subroutines are available in the following areas Elementary Operations, Geometry, Special Functions, Polynomials, Vectors, Matrices, Large Dense Systems of Linear Equations, Banded Matrices, Sparse Matrices, Eigenvalues and Eigenvectors, Solution of Linear Equations, Least-Squares Solution of Linear Equations, Optimization, Transforms, Approximation of Functions, Curve Fitting, Surface Fitting, Manifold Fitting, Numerical Integration, Integral Equations, Ordinary--Differential Equations, Partial Differential Equations, and Random Number Generation.

rawTOC:
Introduction / 1 \\ \\ Elementary Operations \\ \\ Machine Constants --- SPMPAR, DPMPAR, IPMPAR / 3 \\ Sorting Lists --- ISHELL, SHELL, AORD, RISORT, SHELL2, DSORT, DAORD, DISORT, DDSORT / 5 \\ Cube Root --- CBRT, DCBRT / 7 \\ Four Quadrant Arctangent --- ARTNQ, DARTNQ / 7 \\ Length of a Two-Dimensional Vector --- CPABS, DCPABS / 7 \\ Reciprocal of a Complex Number --- CREC, DCREC / 9 \\ Square Root of a Double Precision Complex Number --- DCSQRT / 9 \\ Conversion of Polar to Cartesian Coordinates --- POCA / 11 \\ Conversion of Cartesian to Polar Coordinates --- CAPO / 11 \\ Rotation of Axes --- ROTA / 11 \\ Planar Givens Rotations --- SROTG, DROTG / 13 \\ Three Dimensional Rotations --- ROT3 / 15 \\ Rotation of a Point on the Unit Sphere to the North Pole --- CONSTR / 17 \\ Hyperbolic Sine and Cosine Functions --- SNHCSH / 19 \\ Exponentials --- REXP, DREXP / 21 \\ Logarithms --- ALNREL, RLOG, RLOG1, DLNREL, DRLOG, DRLOG1 / 23 \\ \\ Geometry \\ \\ Determining if a Point is Inside or Outside a Polygon --- LOCPT / 25 \\ The Convex Hull for a Finite Planar Set --- HULL / 27 \\ Areas of Planar Polygons --- PAREA / 29 \\ Hamiltonian Circuits --- HC / 31 \\ \\ Special Functions \\ \\ Error Function --- CERF, CERFC, ERF, ERFC, ERFC1, DCERF, DCERFC, DERF, DERFC, DERFC1 / 35 \\ Inverse Error Function --- ERFINV / 41 \\ Normal Probability Distribution Function --- PNDF / 43 \\ Inverse Normal Probability Distribution Function --- PNINV / 45 \\ Dawson's Integral --- DAWSON / 47 \\ Complex Fresnel Integral --- CFRNLI / 49 \\ Real Fresnel Integrals --- FRESNEL / 51 \\ Exponential Integral Function --- CEXPLI, EXPLI, DEI, DEI1 / 53 \\ Sine and Cosine Integral Functions --- SI, CIN / 57 \\ Dilogarithm Function --- CLI, ALI / 59 \\ Gamma Function --- CGAMMA, GAMMA, GAMLN, DCGAMA, DGAMMA, DGAMLN / 61 \\ Diganma Function --- CPSI, PSI, DCPSI, DPSI / 65 \\ Logarithm of the Beta Function --- BETALN, DBETLN / 67 \\ Incomplete Gamma Ratio Functions --- GRATIO, RCOMP / 69 \\ Inverse Incomplete Gamma Ratio Function --- GAMINV / 71 \\ Incomplete Beta Function --- BRATIO, ISUBX, BRCOMP / 73 \\ Bessel Function $J_\nu(z)$ --- CBSSLJ, BSSLJ, BESJ / 75 \\ Bessel Function $Y_\nu(z)$ --- BSSLY / 77 \\ Modified Bessel Function $I_\nu(z)$ --- BSSLI, BESI / 79 \\ Modified Bessel Function $K_\nu(z)$ --- CBSSLK, BSSLK / 81 \\ Airy functions --- CAI, CBI, AI, AIE, BI, BIE / 83 \\ Complete Complex Elliptic Integrals of the First and Second Kinds --- CK, CKE / 87 \\ Real Elliptic Integrals of the First and Second Kinds --- ELLPI, RFVAL, RDVAL, DELLPI, DRFVAL, DRDVAL / 91 \\ Real Elliptic Integrals of the Third Kind --- EPI, RJVAL, DEPI, DRJVAL / 95 \\ Jacobian Elliptic Functions --- ELLPF, ELPFC1 / 99 \\ Weierstrass Elliptic Function for the Equianharmonic and Lemniscatic Cases --- PEQ, PEQ1, PLEM, PLEM1 / 103 \\ Integral of the Bivariate Density Function over Arbitrary Polygons and Semi-infinite Angular Regions --- VALR2 / 107 \\ Circular Coverage Function --- CIRCV / 109 \\ Elliptical Coverage Function --- PKILL, PKILL3 / 111 \\ \\ Polynomials \\ \\ Copying Polynomials --- PLCOPY, DPCOPY / 113 \\ Addition of Polynomials --- PADD, DPADD / 115 \\ Subtraction of Polynomials --- PSUBT, DPSUBT / 117 \\ Multiplication of Polynomials --- PMULT, DPMULT / 119 \\ Division of Polynomials --- PDIV, DPDIV / 121 \\ Real Powers of Polynomials --- PLPWR, DPLPWR / 123 \\ Inverses of Power Series --- PINV, DPINV / 125 \\ Derivatives and Integrals of Polynomials --- MPLNMV / 127 \\ Evaluation of Chebyshev Expansions --- CSEVL, DCSEVL / 129 \\ Lagrange Polynomials --- LGRNGN, LGRNGV, LGRNGX / 131 \\ Orthogonal Polynomials on Finite Sets --- ORTHOS, ORTHOV, ORTHOX / 133 \\ \\ Solutions of Nonlinear Equations \\ \\ Zeros of Continuous Functions --- ZEROIN / 135 \\ Solution, of Systems of Nonlinear Equations --- HBRD / 137 \\ Solutions of Quadratic, Cubic, and Quartic Equations --- QDCRT, CBCRT, QTCRT, DQDCRT, DCBCRT, DQTCRT / 139 \\ Double Precision Roots of Polynomials --- DRPOLY, DCPOLY / 141 \\ Accuracy of the Roots of a Real Polynomial --- RBND / 143 \\ \\ Vectors \\ \\ Copying Vectors --- SCOPY, DCOPY, CCOPY / 145 \\ Interchanging Vectors --- SSWAP, DSWAP, CSWAP / 147 \\ Planar Rotation of Vectors --- SROT, DROT, CSROT / 149 \\ Dot Products of Vectors --- SDOT, DDOT, CDOTC, CDOTU / 151 \\ Scaling Vectors --- SSCAL, DSCAL, CSCAL, CSSCAL / 153 \\ Vector Addition --- SAXPY, DAXPY, CAXPY / 155 \\ $L_1$ Norm of a Vector-- SASUM, DASUM, SCASUM / 157 \\ $L_2$ Norm of a Vector --- SNRM2, DNRM2, SCNRM2 / 159 \\ $L_\infty$ Norm of a Vector --- ISAMAX, IDAMAX, ICAMAX / 161 \\ \\ Matrices \\ \\ Packing and Unpacking Symmetric Matrices --- MCVFS, DMCVFS, MCVSF, DMCVSF / 163 \\ Conversion of Real Matrices to and from Double Precision Form --- MCVRD, MCVDR / 165 \\ Storage of Real Matrices in the Complex Matrix Format --- MCVRC / 167 \\ The Real and Imaginary Parts of a Complex Matrix --- CMREAL, CMIMAG / 169 \\ Copying Matrices --- MCOPY, SMCOPY, DMCOPY, CMCOPY / 171 \\ Computation of the Conjugate of a Complex Matrix --- CMCONJ / 173 \\ Transposing Matrices --- TPOSE, DTPOSE, CTPOSE, TIP, DTIP, CTIP / 175 \\ Computing Adjoints of Complex Matrices --- CMADJ, CTRANS / 177 \\ Matrix Addition --- MADD, SMADD, DMADD, CMADD / 179 \\ Matrix Subtraction --- MSUBT, SMSUBT, DMSUBT, CMSUBT / 181 \\ Matrix Multiplication-- MTMS, DMTMS, CMTMS, MPROD, DMPROD, CMPROD / 183 \\ Product of a Packed Symmetric Matrix and a Vector --- SVPRD, DSVPRD / 185 \\ Transpose Matrix Products --- TMPROD / 187 \\ Symmetric Matrix Products --- SMPROD / 189 \\ Kronecker Product of Matrices --- KPROD, DKPROD, CKPROD / 191 \\ Inverting General Real Matrices and Solving General Systems of Real Linear Equations --- CROUT, KROUT, NPIVOT, MSLV, DSMSLV / 193 \\ Solutions of Real Equations with Iterative Improvement --- SLVMP / 197 \\ Solution of Almost Block Diagonal Systems of Linear Equations --- ARCECO, ARCESL / 199 \\ Solution of Almost Block Tridiagonal Systems of Linear Equations --- BTSLV / 201 \\ Inverting Symmetric Real Matrices and Solving Symmetric Systems of Real Linear Equations --- SMSLV, DSMSLV / 203 \\ Inverting Positive Definite Symmetric Matrices and Solving Positive Definite Symmetric Systems of Linear Equations --- PCHOL, DPCHOL / 207 \\ Solution of Toeplitz Systems of Linear Equations --- TOPLX, DTOPLX / 209 \\ Inverting General Complex Matrices and Solving General Systems of Complex Linear Equations --- CMSLV, CMSLV1, DCMSLV / 211 \\ Solution of Complex Equations with Iterative Improvement --- CSLVMP / 215 \\ Singular Value Decomposition of a Matrix --- SSVDC, DSVDC, CSVDC / 217 \\ Evaluation of the Characteristic Polynomial of a Matrix --- DET, DPDET, CDET / 219 \\ Solution of the Matrix Equation $A X + X B = C$ --- ABSLV, DABSLV / 221 \\ Solution of the Matrix Equation $A^t X + X B = C$ when $C$ is Symmetric --- TASLV, DTASLV / 223 \\ Solution of the Matrix Equation $A X^2 + X B + C = 0$ --- SQUINT / 225 \\ Exponential of a Real Matrix --- MEXP, DMEXP / 227 \\ \\ Large Dense Systems of Linear Equations \\ \\ Solving systems of 200--400 Linear Equations --- LE, DPLE, CLE / 229 \\ \\ Banded Matrices \\ \\ Band Matrix Storage / 231 \\ Conversion of Banded Matrices to and from the Standard Format --- CVBR, CVBC, CVRB, CVCB, CVRB1, CVCB1 / 233 \\ Conversion of Banded Matrices to and from Sparse Form --- MCVBS, CMCVBS, MCVSB, CMCVSB / 235 \\ Transposing Banded Matrices --- BPOSE, CBPOSE / 237 \\ Addition of Banded Matrices --- BADD, CBADD / 239 \\ Subtraction of Banded Matrices --- BSUBT, CBSUBT / 241 \\ Multiplication of Banded Matrices --- BPROD, CBPROD / 243 \\ Product of a Real Banded Matrix and Vector --- BVPRD, BVPRD1, BTPRD, BTPRD1 / 245 \\ Product of a Complex Banded Matrix and Vector --- CBVPD, CBVPD1, CBTPD, CBTPD1 / 247 \\ Solution of Banded Systems of Real Linear Equations --- BSLV, BSLV1 / 249 \\ Solution of Banded Systems of Complex Linear Equations --- CBSLV, CBSLV1 / 251 \\ \\ Sparse Matrices \\ \\ Storage of Sparse Matrices / 253 \\ Conversion of Sparse Matrices to and from the Standard Format --- CVRS, CVDS, CVCS, CVSR, CVSD, CVSC / 255 \\ Conversion of Sparse Real Matrices to and from Double Precision Form --- SCVRD, SCVDR / 257 \\ The Real and Imaginary Parts of a Sparse Complex Matrix --- CSREAL, CSIMAG / 259 \\ \\ Computing $A + i D$ for Sparse Real Matrices $A$ and $B$ --- SCVRC / 261 \\ Copying Sparse Matrices --- RSCOPY, DSCOPY, CSCOPY / 263 \\ Computing Conjugates of Sparse Complex Matrices --- SCONJ / 265 \\ Transposing Sparse Real Matrices --- RPOSE, RPOSE1 / 267 \\ Transposing Sparse Double Precision Matrices --- DPOSE, DPOSE1 / 269 \\ Transposing Sparse Complex Matrices --- CPOSE, CPOSE1 / 271 \\ Addition of Sparse Matrices --- SADD, DSADD, CSADD / 273 \\ Subtraction of Sparse Matrices --- SSUBT, DSSUBT, CSSUBT / 275 \\ Multiplication of Sparse Matrices --- SPROD, DSPROD, CSPROD / 277 \\ Product of a Real Sparse Matrix and Vector --- MVPRD, MVPRD1, MTPRD, MTPRD1 / 279 \\ Product of a Double Precision Sparse Matrix and Vector --- DVPRD, DVPRD1, DTPRD, DTPRD1 / 281 \\ Product of a Complex Sparse Matrix and Vector --- CVPRD, CVPRD1, CTPRD, CTPRD1 / 283 \\ Ordering the Rows of a Sparse Matrix by Increasing Length --- SPORD / 285 \\ Reordering Sparse Matrices into Block Triangular Form --- BLKORD / 287 \\ Solution of Sparse Systems of Real Linear Equations --- SPSLV, RSLV, TSLV / 289 \\ Double Precision Solution of Sparse Systems of Real Linear Equations --- DSPSLV, DSLV, DTSLV / 293 \\ Solution of Sparse Systems of Complex Linear Equations --- CSPSLV, CSLV, CTSLV / 297 \\ \\ Eigenvalues and Eigenvectors \\ \\ Computation of Eigenvalues of General Real Matrices --- EIG, EIG1 / 301 \\ Computation of Eigenvalues and Eigenvectors of General Real Matrices --- EIGV, EIGV1 / 303 \\ Double Precision Computation of Eigenvalues of Real Matrices --- DEIG / 305 \\ Double Precision Computation of Eigenvalues and Eigenvectors of Real Matrices --- DEIGV / 307 \\ Computation of Eigenvalues of Symmetric Real Matrices --- SEIG, SEIG1 / 309 \\ Computation of Eigenvalues and Eigenvectors of Symmetric Real Matrices --- SEIGV, SEIGV1 / 311 \\ Computation of Eigenvalues of Complex Matrices --- CEIG / 313 \\ Computation of Eigenvalues and Eigenvectors of Complex Matrices --- CEIGV / 315 \\ Double Precision Computation of Eigenvalues of Complex Matrices --- DCEIG / 317 \\ Double Precision Computation of Eigenvalues and Eigenvectors of Complex Matrices --- DCEIGV / 319 \\ \\ $\ell_1$ Solution of Linear Equations \\ \\ $\ell_1$ Solution of Systems of Linear Equations with Equality and Inequality Constraints --- CL1 / 321 \\ \\ Least Squares Solution of Linear Equations \\ \\ Least Squares Solution of Systems of Linear Equations --- LLSQ, HFTI, HFTI2 / 323 \\ Least Squares Solution of Overdetermined Systems of Linear Equations with Iterative Improvement --- LLSQMP / 327 \\ Double Precision Least Squares Solution of Systems of Linear Equations --- DLLSQ, DHFTI, DHFTI2 / 329 \\ Least Squares Solution of Systems of Linear Equations with Equality and Inequality Constraints --- LSEI / 333 \\ Least Squares Solution of Systems of Linear Equations with Equality and Nonnegativity Constraints --- WNNLS / 337 \\ Least Squares Iterative Improvement Solution of Systems of Linear Equations with Equality Constraints --- L2SLV / 341 \\ Iterative Least Squares Solution of Banded Linear Equations --- BLSQ / 345 \\ Iterative Least Squares Solution of Sparse Linear Equations --- SPLSQ, STLSQ / 347 \\ \\ Optimization \\ \\ Minimization of Functions of a Single Variable --- FMIN / 349 \\ Minimization of Functions of n Variables --- OPTF / 351 \\ Unconstrained Minimum of the Sum of Squares of Nonlinear Functions --- LMDIFF / 353 \\ Linear Programming --- SMPLX, SSPLX / 355 \\ The Assignment Problem --- ASSGN / 359 \\ $0$--$1$ Knapsack Problem --- MKP / 361 \\ \\ Transforms \\ \\ Inversion of the Laplace Transform --- LAINV / 363 \\ Fast Fourier Transform --- FFT, FFT1 / 367 \\ Multivariate Fast Fourier Transform --- MFFT, MFFT1 / 369 \\ Discrete Cosine and Sine Transforms --- COSQI, COSQB, COSQF, SINQB, SINQF / 371 \\ \\ Approximation of Functions \\ \\ Rational Minimax Approximation of Functions --- CHEBY / 375 \\ $L_p$ Approximation of Functions --- ADAPT / 377 \\ Calculation of the Taylor Series of a Complex Analytic Function --- CPSC, DCPSC / 381 \\ \\ Curve Fitting \\ \\ Linear Interpolation --- TRP / 385 \\ Lagrange Interpolation --- LTRP / 387 \\ Hermite Interpolation --- HTRP / 389 \\ Conversion of Real Polynomials from Newton to Taylor Series Form --- PCOEFF / 391 \\ Least Squares Polynomial Fit --- PFIT / 393 \\ Weighted Least Squares Polynomial Fit --- WPFIT / 395 \\ Cubic Spline Interpolation --- CBSPL, SPLIFT / 397 \\ Weighted Least Squares Cubic Spline Fitting --- SPFIT / 399 \\ Cubic Spline Evaluation --- SCOMP, SCOMP1, SCOMP2 / 401 \\ Cubic Spline Evaluation and Differentiation --- SEVAL, SEVAL1, SEVAL2 / 403 \\ Integrals of Cubic Splines --- CSINT, CSINT1, CSINT2 / 405 \\ N-Dimensional Cubic Spline Closed Curve Fitting --- CSLOOP, LOPCMP, LOPDF / 407 \\ Spline under Tension Interpolation --- CURV1 / 409 \\ Spline under Tension Evaluation --- CURV2 / 411 \\ Differentiation and Integration of Splines under Tension --- CURVD, CURVI / 413 \\ Two Dimensional Spline under Tension Curve Fitting --- KURV1, KURV2 / 415 \\ Two Dimensional Spline under Tension Closed Curve Fitting --- KURVP1, KURVP2 / 417 \\ Three Dimensional Spline under Tension Curve Fitting --- QURV1, QURV2 / 419 \\ B-Splines / 421 \\ Piecewise Polynomial Interpolation --- BSTRP / 423 \\ Conversion of Piecewise Polynomials from B-Spline to Taylor Series Form --- BSPP / 425 \\ Piecewise Polynomial Evaluation --- PPVAL / 427 \\ Weighted Least Squares Piecewise Polynomial Fitting --- BSL2 / 429 \\ \\ Surface Fitting over Rectangular Grids \\ \\ Bi-Splines under Tension / 431 \\ Bi-Spline under Tension Surface Interpolation --- SURF / 433 \\ Bi-Spline under Tension Evaluation --- SURF2, NSURF2 / 435 \\ \\ Surface Fitting over Arbitrarily Positioned Data Points \\ \\ Surface Interpolation for Arbitrarily Positioned Data Points --- BVIP, BVIP2 / 437 \\ \\ Manifold Fitting \\ \\ Weighted Least Squares Fitting with Polynomials of $n$ Variables --- MFIT, DMFIT, MEVAL, DMEVAL / 441 \\ \\ Numerical Integration \\ \\ Evaluation of Integrals over Finite Intervals --- QAGS, QSUBA, DQAGS / 445 \\ \\ Evaluation of Integrals over Infinite Intervals --- QAGI, DQAGI / 449 \\ Evaluation of Double Integrals over Triangles --- CUBTRI / 453 \\ \\ Integral Equations \\ \\ Solution of Fredholm Integral Equations of the Second Kind --- IESLV / 455 \\ \\ Ordinary Differential Equations/Initial Value Problems \\ \\ The Initial Value Solvers --- Introductory Comments / 459 \\ Adaptive Adams Solution of Nonstiff Differential Equations --- ODE / 461 \\ Adaptive RKF Solution of Nonstiff Differential Equations --- RKF45 / 465 \\ Adaptive RKF Solution of Nonstiff Differential Equations with Global Error Estimation --- GERK / 469 \\ Adaptive Solution of Stiff Differential Equations --- SFODE, SFODE1 / 473 \\ Fourth-Order Runge-Kutta --- RK / 477 \\ Eighth-Order Runge-Kutta --- RK8 / 479 \\ \\ Partial Differential Equations \\ \\ Separable Second-Order Elliptic Equations on Rectangular Domains --- SEPDE / 481 \\ \\ Random Number Generation \\ \\ Uniform Random Number Generator --- URNG / 485 \\ Gaussian Random Number Generator using the Box--M{\"u}ller Transformation --- NRNG / 487 \\ \\ Appendix. Installation of the NSWC Library / 489 \\ \\ Index / 491 \\ \\ Distribution

entry:
@TechReport{Morris:1990:NLM,
  author =       "Alfred H. {Morris, Jr.}",
  title =        "{NSWC} Library of Mathematics Subroutines",
  type =         "Report",
  number =       "NSWC TR 90-21",
  institution =  "Naval Surface Warfare Center",
  address =      "Dahlgren, VA 22448-5000, USA; Silver Spring, MD
                 20903-5000, USA",
  pages =        "xii + 492 + 9",
  month =        jan,
  year =         "1990",
  bibdate =      "Tue Jun 13 08:47:19 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran2.bib",
  note =         "See also later edition \cite{Morris:1993:NLM}.",
  URL =          "https://apps.dtic.mil/sti/citations/ADA476840;
                 https://apps.dtic.mil/sti/pdfs/ADA476840.pdf;
                 https://people.math.sc.edu/Burkardt/f_src/nswc/nswc.f90;
                 https://people.math.sc.edu/Burkardt/f_src/nswc/nswc.html",
  abstract =     "The NSWC library is a library of general-purpose
                 Fortran subroutines that provide a basic computational
                 capability in a variety of mathematical activities and
                 emphasis has been placed on the transportability of the
                 codes. Subroutines are available in the following areas
                 Elementary Operations, Geometry, Special Functions,
                 Polynomials, Vectors, Matrices, Large Dense Systems of
                 Linear Equations, Banded Matrices, Sparse Matrices,
                 Eigenvalues and Eigenvectors, Solution of Linear
                 Equations, Least-Squares Solution of Linear Equations,
                 Optimization, Transforms, Approximation of Functions,
                 Curve Fitting, Surface Fitting, Manifold Fitting,
                 Numerical Integration, Integral Equations,
                 Ordinary--Differential Equations, Partial Differential
                 Equations, and Random Number Generation.",
  acknowledgement = ack-nhfb,
  remark =       "The single Fortran 90 file of 99,021 nonblank lines
                 compiles into a library of 905 distinct functions and
                 subroutines: the source code appears to contain 139
                 functions and 762 subroutines (901 total entry
                 points).

                 The tableofcontents values in this entry is derived
                 from optical character recognition (OCR) of the 8-page
                 listing from the PDF files, with editorial correction
                 of spelling and OCR errors, and matching of uppercase
                 software names against the entry points of the compiled
                 library. There are about five names in the PDF table of
                 contents that disagree with subroutine names in the
                 source code: they have been edited here to reflect the
                 correct code names. There are numerous routine names in
                 the compiled library that are not mentioned in the
                 table of contents.",
  tableofcontents = "Introduction / 1 \\
                 \\
                 Elementary Operations \\
                 \\
                 Machine Constants --- SPMPAR, DPMPAR, IPMPAR / 3 \\
                 Sorting Lists --- ISHELL, SHELL, AORD, RISORT, SHELL2,
                 DSORT, DAORD, DISORT, DDSORT / 5 \\
                 Cube Root --- CBRT, DCBRT / 7 \\
                 Four Quadrant Arctangent --- ARTNQ, DARTNQ / 7 \\
                 Length of a Two-Dimensional Vector --- CPABS, DCPABS /
                 7 \\
                 Reciprocal of a Complex Number --- CREC, DCREC / 9 \\
                 Square Root of a Double Precision Complex Number ---
                 DCSQRT / 9 \\
                 Conversion of Polar to Cartesian Coordinates --- POCA /
                 11 \\
                 Conversion of Cartesian to Polar Coordinates --- CAPO /
                 11 \\
                 Rotation of Axes --- ROTA / 11 \\
                 Planar Givens Rotations --- SROTG, DROTG / 13 \\
                 Three Dimensional Rotations --- ROT3 / 15 \\
                 Rotation of a Point on the Unit Sphere to the North
                 Pole --- CONSTR / 17 \\
                 Hyperbolic Sine and Cosine Functions --- SNHCSH / 19
                 \\
                 Exponentials --- REXP, DREXP / 21 \\
                 Logarithms --- ALNREL, RLOG, RLOG1, DLNREL, DRLOG,
                 DRLOG1 / 23 \\
                 \\
                 Geometry \\
                 \\
                 Determining if a Point is Inside or Outside a Polygon
                 --- LOCPT / 25 \\
                 The Convex Hull for a Finite Planar Set --- HULL / 27
                 \\
                 Areas of Planar Polygons --- PAREA / 29 \\
                 Hamiltonian Circuits --- HC / 31 \\
                 \\
                 Special Functions \\
                 \\
                 Error Function --- CERF, CERFC, ERF, ERFC, ERFC1,
                 DCERF, DCERFC, DERF, DERFC, DERFC1 / 35 \\
                 Inverse Error Function --- ERFINV / 41 \\
                 Normal Probability Distribution Function --- PNDF / 43
                 \\
                 Inverse Normal Probability Distribution Function ---
                 PNINV / 45 \\
                 Dawson's Integral --- DAWSON / 47 \\
                 Complex Fresnel Integral --- CFRNLI / 49 \\
                 Real Fresnel Integrals --- FRESNEL / 51 \\
                 Exponential Integral Function --- CEXPLI, EXPLI, DEI,
                 DEI1 / 53 \\
                 Sine and Cosine Integral Functions --- SI, CIN / 57 \\
                 Dilogarithm Function --- CLI, ALI / 59 \\
                 Gamma Function --- CGAMMA, GAMMA, GAMLN, DCGAMA,
                 DGAMMA, DGAMLN / 61 \\
                 Diganma Function --- CPSI, PSI, DCPSI, DPSI / 65 \\
                 Logarithm of the Beta Function --- BETALN, DBETLN / 67
                 \\
                 Incomplete Gamma Ratio Functions --- GRATIO, RCOMP / 69
                 \\
                 Inverse Incomplete Gamma Ratio Function --- GAMINV / 71
                 \\
                 Incomplete Beta Function --- BRATIO, ISUBX, BRCOMP / 73
                 \\
                 Bessel Function $J_\nu(z)$ --- CBSSLJ, BSSLJ, BESJ / 75
                 \\
                 Bessel Function $Y_\nu(z)$ --- BSSLY / 77 \\
                 Modified Bessel Function $I_\nu(z)$ --- BSSLI, BESI /
                 79 \\
                 Modified Bessel Function $K_\nu(z)$ --- CBSSLK, BSSLK /
                 81 \\
                 Airy functions --- CAI, CBI, AI, AIE, BI, BIE / 83 \\
                 Complete Complex Elliptic Integrals of the First and
                 Second Kinds --- CK, CKE / 87 \\
                 Real Elliptic Integrals of the First and Second Kinds
                 --- ELLPI, RFVAL, RDVAL, DELLPI, DRFVAL, DRDVAL / 91
                 \\
                 Real Elliptic Integrals of the Third Kind --- EPI,
                 RJVAL, DEPI, DRJVAL / 95 \\
                 Jacobian Elliptic Functions --- ELLPF, ELPFC1 / 99 \\
                 Weierstrass Elliptic Function for the Equianharmonic
                 and Lemniscatic Cases --- PEQ, PEQ1, PLEM, PLEM1 / 103
                 \\
                 Integral of the Bivariate Density Function over
                 Arbitrary Polygons and Semi-infinite Angular Regions
                 --- VALR2 / 107 \\
                 Circular Coverage Function --- CIRCV / 109 \\
                 Elliptical Coverage Function --- PKILL, PKILL3 / 111
                 \\
                 \\
                 Polynomials \\
                 \\
                 Copying Polynomials --- PLCOPY, DPCOPY / 113 \\
                 Addition of Polynomials --- PADD, DPADD / 115 \\
                 Subtraction of Polynomials --- PSUBT, DPSUBT / 117 \\
                 Multiplication of Polynomials --- PMULT, DPMULT / 119
                 \\
                 Division of Polynomials --- PDIV, DPDIV / 121 \\
                 Real Powers of Polynomials --- PLPWR, DPLPWR / 123 \\
                 Inverses of Power Series --- PINV, DPINV / 125 \\
                 Derivatives and Integrals of Polynomials --- MPLNMV /
                 127 \\
                 Evaluation of Chebyshev Expansions --- CSEVL, DCSEVL /
                 129 \\
                 Lagrange Polynomials --- LGRNGN, LGRNGV, LGRNGX / 131
                 \\
                 Orthogonal Polynomials on Finite Sets --- ORTHOS,
                 ORTHOV, ORTHOX / 133 \\
                 \\
                 Solutions of Nonlinear Equations \\
                 \\
                 Zeros of Continuous Functions --- ZEROIN / 135 \\
                 Solution, of Systems of Nonlinear Equations --- HBRD /
                 137 \\
                 Solutions of Quadratic, Cubic, and Quartic Equations
                 --- QDCRT, CBCRT, QTCRT, DQDCRT, DCBCRT, DQTCRT / 139
                 \\
                 Double Precision Roots of Polynomials --- DRPOLY,
                 DCPOLY / 141 \\
                 Accuracy of the Roots of a Real Polynomial --- RBND /
                 143 \\
                 \\
                 Vectors \\
                 \\
                 Copying Vectors --- SCOPY, DCOPY, CCOPY / 145 \\
                 Interchanging Vectors --- SSWAP, DSWAP, CSWAP / 147 \\
                 Planar Rotation of Vectors --- SROT, DROT, CSROT / 149
                 \\
                 Dot Products of Vectors --- SDOT, DDOT, CDOTC, CDOTU /
                 151 \\
                 Scaling Vectors --- SSCAL, DSCAL, CSCAL, CSSCAL / 153
                 \\
                 Vector Addition --- SAXPY, DAXPY, CAXPY / 155 \\
                 $L_1$ Norm of a Vector-- SASUM, DASUM, SCASUM / 157 \\
                 $L_2$ Norm of a Vector --- SNRM2, DNRM2, SCNRM2 / 159
                 \\
                 $L_\infty$ Norm of a Vector --- ISAMAX, IDAMAX, ICAMAX
                 / 161 \\
                 \\
                 Matrices \\
                 \\
                 Packing and Unpacking Symmetric Matrices --- MCVFS,
                 DMCVFS, MCVSF, DMCVSF / 163 \\
                 Conversion of Real Matrices to and from Double
                 Precision Form --- MCVRD, MCVDR / 165 \\
                 Storage of Real Matrices in the Complex Matrix Format
                 --- MCVRC / 167 \\
                 The Real and Imaginary Parts of a Complex Matrix ---
                 CMREAL, CMIMAG / 169 \\
                 Copying Matrices --- MCOPY, SMCOPY, DMCOPY, CMCOPY /
                 171 \\
                 Computation of the Conjugate of a Complex Matrix ---
                 CMCONJ / 173 \\
                 Transposing Matrices --- TPOSE, DTPOSE, CTPOSE, TIP,
                 DTIP, CTIP / 175 \\
                 Computing Adjoints of Complex Matrices --- CMADJ,
                 CTRANS / 177 \\
                 Matrix Addition --- MADD, SMADD, DMADD, CMADD / 179 \\
                 Matrix Subtraction --- MSUBT, SMSUBT, DMSUBT, CMSUBT /
                 181 \\
                 Matrix Multiplication-- MTMS, DMTMS, CMTMS, MPROD,
                 DMPROD, CMPROD / 183 \\
                 Product of a Packed Symmetric Matrix and a Vector ---
                 SVPRD, DSVPRD / 185 \\
                 Transpose Matrix Products --- TMPROD / 187 \\
                 Symmetric Matrix Products --- SMPROD / 189 \\
                 Kronecker Product of Matrices --- KPROD, DKPROD, CKPROD
                 / 191 \\
                 Inverting General Real Matrices and Solving General
                 Systems of Real Linear Equations --- CROUT, KROUT,
                 NPIVOT, MSLV, DSMSLV / 193 \\
                 Solutions of Real Equations with Iterative Improvement
                 --- SLVMP / 197 \\
                 Solution of Almost Block Diagonal Systems of Linear
                 Equations --- ARCECO, ARCESL / 199 \\
                 Solution of Almost Block Tridiagonal Systems of Linear
                 Equations --- BTSLV / 201 \\
                 Inverting Symmetric Real Matrices and Solving Symmetric
                 Systems of Real Linear Equations --- SMSLV, DSMSLV /
                 203 \\
                 Inverting Positive Definite Symmetric Matrices and
                 Solving Positive Definite Symmetric Systems of Linear
                 Equations --- PCHOL, DPCHOL / 207 \\
                 Solution of Toeplitz Systems of Linear Equations ---
                 TOPLX, DTOPLX / 209 \\
                 Inverting General Complex Matrices and Solving General
                 Systems of Complex Linear Equations --- CMSLV, CMSLV1,
                 DCMSLV / 211 \\
                 Solution of Complex Equations with Iterative
                 Improvement --- CSLVMP / 215 \\
                 Singular Value Decomposition of a Matrix --- SSVDC,
                 DSVDC, CSVDC / 217 \\
                 Evaluation of the Characteristic Polynomial of a Matrix
                 --- DET, DPDET, CDET / 219 \\
                 Solution of the Matrix Equation $A X + X B = C$ ---
                 ABSLV, DABSLV / 221 \\
                 Solution of the Matrix Equation $A^t X + X B = C$ when
                 $C$ is Symmetric --- TASLV, DTASLV / 223 \\
                 Solution of the Matrix Equation $A X^2 + X B + C = 0$
                 --- SQUINT / 225 \\
                 Exponential of a Real Matrix --- MEXP, DMEXP / 227 \\
                 \\
                 Large Dense Systems of Linear Equations \\
                 \\
                 Solving systems of 200--400 Linear Equations --- LE,
                 DPLE, CLE / 229 \\
                 \\
                 Banded Matrices \\
                 \\
                 Band Matrix Storage / 231 \\
                 Conversion of Banded Matrices to and from the Standard
                 Format --- CVBR, CVBC, CVRB, CVCB, CVRB1, CVCB1 / 233
                 \\
                 Conversion of Banded Matrices to and from Sparse Form
                 --- MCVBS, CMCVBS, MCVSB, CMCVSB / 235 \\
                 Transposing Banded Matrices --- BPOSE, CBPOSE / 237 \\
                 Addition of Banded Matrices --- BADD, CBADD / 239 \\
                 Subtraction of Banded Matrices --- BSUBT, CBSUBT / 241
                 \\
                 Multiplication of Banded Matrices --- BPROD, CBPROD /
                 243 \\
                 Product of a Real Banded Matrix and Vector --- BVPRD,
                 BVPRD1, BTPRD, BTPRD1 / 245 \\
                 Product of a Complex Banded Matrix and Vector ---
                 CBVPD, CBVPD1, CBTPD, CBTPD1 / 247 \\
                 Solution of Banded Systems of Real Linear Equations ---
                 BSLV, BSLV1 / 249 \\
                 Solution of Banded Systems of Complex Linear Equations
                 --- CBSLV, CBSLV1 / 251 \\
                 \\
                 Sparse Matrices \\
                 \\
                 Storage of Sparse Matrices / 253 \\
                 Conversion of Sparse Matrices to and from the Standard
                 Format --- CVRS, CVDS, CVCS, CVSR, CVSD, CVSC / 255 \\
                 Conversion of Sparse Real Matrices to and from Double
                 Precision Form --- SCVRD, SCVDR / 257 \\
                 The Real and Imaginary Parts of a Sparse Complex Matrix
                 --- CSREAL, CSIMAG / 259 \\
                 \\
                 Computing $A + i D$ for Sparse Real Matrices $A$ and
                 $B$ --- SCVRC / 261 \\
                 Copying Sparse Matrices --- RSCOPY, DSCOPY, CSCOPY /
                 263 \\
                 Computing Conjugates of Sparse Complex Matrices ---
                 SCONJ / 265 \\
                 Transposing Sparse Real Matrices --- RPOSE, RPOSE1 /
                 267 \\
                 Transposing Sparse Double Precision Matrices --- DPOSE,
                 DPOSE1 / 269 \\
                 Transposing Sparse Complex Matrices --- CPOSE, CPOSE1 /
                 271 \\
                 Addition of Sparse Matrices --- SADD, DSADD, CSADD /
                 273 \\
                 Subtraction of Sparse Matrices --- SSUBT, DSSUBT,
                 CSSUBT / 275 \\
                 Multiplication of Sparse Matrices --- SPROD, DSPROD,
                 CSPROD / 277 \\
                 Product of a Real Sparse Matrix and Vector --- MVPRD,
                 MVPRD1, MTPRD, MTPRD1 / 279 \\
                 Product of a Double Precision Sparse Matrix and Vector
                 --- DVPRD, DVPRD1, DTPRD, DTPRD1 / 281 \\
                 Product of a Complex Sparse Matrix and Vector ---
                 CVPRD, CVPRD1, CTPRD, CTPRD1 / 283 \\
                 Ordering the Rows of a Sparse Matrix by Increasing
                 Length --- SPORD / 285 \\
                 Reordering Sparse Matrices into Block Triangular Form
                 --- BLKORD / 287 \\
                 Solution of Sparse Systems of Real Linear Equations ---
                 SPSLV, RSLV, TSLV / 289 \\
                 Double Precision Solution of Sparse Systems of Real
                 Linear Equations --- DSPSLV, DSLV, DTSLV / 293 \\
                 Solution of Sparse Systems of Complex Linear Equations
                 --- CSPSLV, CSLV, CTSLV / 297 \\
                 \\
                 Eigenvalues and Eigenvectors \\
                 \\
                 Computation of Eigenvalues of General Real Matrices ---
                 EIG, EIG1 / 301 \\
                 Computation of Eigenvalues and Eigenvectors of General
                 Real Matrices --- EIGV, EIGV1 / 303 \\
                 Double Precision Computation of Eigenvalues of Real
                 Matrices --- DEIG / 305 \\
                 Double Precision Computation of Eigenvalues and
                 Eigenvectors of Real Matrices --- DEIGV / 307 \\
                 Computation of Eigenvalues of Symmetric Real Matrices
                 --- SEIG, SEIG1 / 309 \\
                 Computation of Eigenvalues and Eigenvectors of
                 Symmetric Real Matrices --- SEIGV, SEIGV1 / 311 \\
                 Computation of Eigenvalues of Complex Matrices --- CEIG
                 / 313 \\
                 Computation of Eigenvalues and Eigenvectors of Complex
                 Matrices --- CEIGV / 315 \\
                 Double Precision Computation of Eigenvalues of Complex
                 Matrices --- DCEIG / 317 \\
                 Double Precision Computation of Eigenvalues and
                 Eigenvectors of Complex Matrices --- DCEIGV / 319 \\
                 \\
                 $\ell_1$ Solution of Linear Equations \\
                 \\
                 $\ell_1$ Solution of Systems of Linear Equations with
                 Equality and Inequality Constraints --- CL1 / 321 \\
                 \\
                 Least Squares Solution of Linear Equations \\
                 \\
                 Least Squares Solution of Systems of Linear Equations
                 --- LLSQ, HFTI, HFTI2 / 323 \\
                 Least Squares Solution of Overdetermined Systems of
                 Linear Equations with Iterative Improvement --- LLSQMP
                 / 327 \\
                 Double Precision Least Squares Solution of Systems of
                 Linear Equations --- DLLSQ, DHFTI, DHFTI2 / 329 \\
                 Least Squares Solution of Systems of Linear Equations
                 with Equality and Inequality Constraints --- LSEI / 333
                 \\
                 Least Squares Solution of Systems of Linear Equations
                 with Equality and Nonnegativity Constraints --- WNNLS /
                 337 \\
                 Least Squares Iterative Improvement Solution of Systems
                 of Linear Equations with Equality Constraints --- L2SLV
                 / 341 \\
                 Iterative Least Squares Solution of Banded Linear
                 Equations --- BLSQ / 345 \\
                 Iterative Least Squares Solution of Sparse Linear
                 Equations --- SPLSQ, STLSQ / 347 \\
                 \\
                 Optimization \\
                 \\
                 Minimization of Functions of a Single Variable --- FMIN
                 / 349 \\
                 Minimization of Functions of n Variables --- OPTF / 351
                 \\
                 Unconstrained Minimum of the Sum of Squares of
                 Nonlinear Functions --- LMDIFF / 353 \\
                 Linear Programming --- SMPLX, SSPLX / 355 \\
                 The Assignment Problem --- ASSGN / 359 \\
                 $0$--$1$ Knapsack Problem --- MKP / 361 \\
                 \\
                 Transforms \\
                 \\
                 Inversion of the Laplace Transform --- LAINV / 363 \\
                 Fast Fourier Transform --- FFT, FFT1 / 367 \\
                 Multivariate Fast Fourier Transform --- MFFT, MFFT1 /
                 369 \\
                 Discrete Cosine and Sine Transforms --- COSQI, COSQB,
                 COSQF, SINQB, SINQF / 371 \\
                 \\
                 Approximation of Functions \\
                 \\
                 Rational Minimax Approximation of Functions --- CHEBY /
                 375 \\
                 $L_p$ Approximation of Functions --- ADAPT / 377 \\
                 Calculation of the Taylor Series of a Complex Analytic
                 Function --- CPSC, DCPSC / 381 \\
                 \\
                 Curve Fitting \\
                 \\
                 Linear Interpolation --- TRP / 385 \\
                 Lagrange Interpolation --- LTRP / 387 \\
                 Hermite Interpolation --- HTRP / 389 \\
                 Conversion of Real Polynomials from Newton to Taylor
                 Series Form --- PCOEFF / 391 \\
                 Least Squares Polynomial Fit --- PFIT / 393 \\
                 Weighted Least Squares Polynomial Fit --- WPFIT / 395
                 \\
                 Cubic Spline Interpolation --- CBSPL, SPLIFT / 397 \\
                 Weighted Least Squares Cubic Spline Fitting --- SPFIT /
                 399 \\
                 Cubic Spline Evaluation --- SCOMP, SCOMP1, SCOMP2 / 401
                 \\
                 Cubic Spline Evaluation and Differentiation --- SEVAL,
                 SEVAL1, SEVAL2 / 403 \\
                 Integrals of Cubic Splines --- CSINT, CSINT1, CSINT2 /
                 405 \\
                 N-Dimensional Cubic Spline Closed Curve Fitting ---
                 CSLOOP, LOPCMP, LOPDF / 407 \\
                 Spline under Tension Interpolation --- CURV1 / 409 \\
                 Spline under Tension Evaluation --- CURV2 / 411 \\
                 Differentiation and Integration of Splines under
                 Tension --- CURVD, CURVI / 413 \\
                 Two Dimensional Spline under Tension Curve Fitting ---
                 KURV1, KURV2 / 415 \\
                 Two Dimensional Spline under Tension Closed Curve
                 Fitting --- KURVP1, KURVP2 / 417 \\
                 Three Dimensional Spline under Tension Curve Fitting
                 --- QURV1, QURV2 / 419 \\
                 B-Splines / 421 \\
                 Piecewise Polynomial Interpolation --- BSTRP / 423 \\
                 Conversion of Piecewise Polynomials from B-Spline to
                 Taylor Series Form --- BSPP / 425 \\
                 Piecewise Polynomial Evaluation --- PPVAL / 427 \\
                 Weighted Least Squares Piecewise Polynomial Fitting ---
                 BSL2 / 429 \\
                 \\
                 Surface Fitting over Rectangular Grids \\
                 \\
                 Bi-Splines under Tension / 431 \\
                 Bi-Spline under Tension Surface Interpolation --- SURF
                 / 433 \\
                 Bi-Spline under Tension Evaluation --- SURF2, NSURF2 /
                 435 \\
                 \\
                 Surface Fitting over Arbitrarily Positioned Data Points
                 \\
                 \\
                 Surface Interpolation for Arbitrarily Positioned Data
                 Points --- BVIP, BVIP2 / 437 \\
                 \\
                 Manifold Fitting \\
                 \\
                 Weighted Least Squares Fitting with Polynomials of $n$
                 Variables --- MFIT, DMFIT, MEVAL, DMEVAL / 441 \\
                 \\
                 Numerical Integration \\
                 \\
                 Evaluation of Integrals over Finite Intervals --- QAGS,
                 QSUBA, DQAGS / 445 \\
                 \\
                 Evaluation of Integrals over Infinite Intervals ---
                 QAGI, DQAGI / 449 \\
                 Evaluation of Double Integrals over Triangles ---
                 CUBTRI / 453 \\
                 \\
                 Integral Equations \\
                 \\
                 Solution of Fredholm Integral Equations of the Second
                 Kind --- IESLV / 455 \\
                 \\
                 Ordinary Differential Equations/Initial Value Problems
                 \\
                 \\
                 The Initial Value Solvers --- Introductory Comments /
                 459 \\
                 Adaptive Adams Solution of Nonstiff Differential
                 Equations --- ODE / 461 \\
                 Adaptive RKF Solution of Nonstiff Differential
                 Equations --- RKF45 / 465 \\
                 Adaptive RKF Solution of Nonstiff Differential
                 Equations with Global Error Estimation --- GERK / 469
                 \\
                 Adaptive Solution of Stiff Differential Equations ---
                 SFODE, SFODE1 / 473 \\
                 Fourth-Order Runge-Kutta --- RK / 477 \\
                 Eighth-Order Runge-Kutta --- RK8 / 479 \\
                 \\
                 Partial Differential Equations \\
                 \\
                 Separable Second-Order Elliptic Equations on
                 Rectangular Domains --- SEPDE / 481 \\
                 \\
                 Random Number Generation \\
                 \\
                 Uniform Random Number Generator --- URNG / 485 \\
                 Gaussian Random Number Generator using the
                 Box--M{\"u}ller Transformation --- NRNG / 487 \\
                 \\
                 Appendix. Installation of the NSWC Library / 489 \\
                 \\
                 Index / 491 \\
                 \\
                 Distribution",
}


bibtype: mastersthesis
filename: elefunt.bib
label: Muller:1990:HCA
author: Volker Muller
type: Diplomarbeit
school: Institut fur angewandte Mathematik, Universitat Karlsruhe
address: Karlsruhe, Germany
month: dec
monthnumber: 12
year: 1990
bibdate: Fri Sep 16 16:30:40 1994
bibtimestamp: 1994.09.16 16:30:40 ???
language: German
acknowledgement: ack-nj
rawauthor: Volker M{\"u}ller
title:
Hochgenaue CORDIC-Algorithmen fur reelle Standardfunktionen mittels dynamischer Defektberechnung. (German) [High-accuracy CORDIC Algorithms for Real Elementary Functions by Means of Dynamic Error Computation]

bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
{Hochgenaue CORDIC-Algorithmen f{\"u}r reelle Standardfunktionen mittels dynamischer Defektberechnung}. ({German}) [{High}-accuracy {CORDIC} Algorithms for Real Elementary Functions by Means of Dynamic Error Computation]

entry:
@MastersThesis{Muller:1990:HCA,
  author =       "Volker M{\"u}ller",
  title =        "{Hochgenaue CORDIC-Algorithmen f{\"u}r reelle
                 Standardfunktionen mittels dynamischer
                 Defektberechnung}. ({German}) [{High}-accuracy {CORDIC}
                 Algorithms for Real Elementary Functions by Means of
                 Dynamic Error Computation]",
  type =         "{Diplomarbeit}",
  school =       "Institut f{\"u}r angewandte Mathematik,
                 Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  month =        dec,
  year =         "1990",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: Osada:1990:CAM
author: Naoki Osada
title: A Convergence Acceleration Method for Some Logarithmically Convergent Sequences
journal: j-SIAM-J-NUMER-ANAL
volume: 27
number: 1
pages: 178--189
month: feb
monthnumber: 2
year: 1990
CODEN: SJNAAM
DOI: https://doi.org/10.1137/0727012
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
MRclass: 65B05
MRnumber: 1034928 (91b:65002)
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 2011.12.01 17:36:45 ???
fjournal: SIAM Journal on Numerical Analysis
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: Naoki Osada
rawtitle: A Convergence Acceleration Method for Some Logarithmically Convergent Sequences
entry:
@Article{Osada:1990:CAM,
  author =       "Naoki Osada",
  title =        "A Convergence Acceleration Method for Some
                 Logarithmically Convergent Sequences",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "27",
  number =       "1",
  pages =        "178--189",
  month =        feb,
  year =         "1990",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0727012",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65B05",
  MRnumber =     "1034928 (91b:65002)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Palmore:1990:CAC
author: J. Palmore and C. Herring
title: Computer arithmetic, chaos and fractals
journal: j-PHYSICA-D
volume: 42
number: 1--3
pages: 99--110
month: jun
monthnumber: 6
year: 1990
CODEN: PDNPDT
DOI: https://doi.org/10.1016/0167-2789(90)90069-2
ISSN: 0167-2789 (print), 1872-8022 (electronic) OR 01672789 (print), 18728022 (electronic)
ISSNL: 0167-2789 OR 01672789
bibdate: Tue Dec 12 09:17:24 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.12 09:17:24 MST
fjournal: Physica. D, Nonlinear phenomena
acknowledgement: ack-nhfb
affiliation: Dept. of Math., Illinois Univ., Urbana, IL, USA
journalURL: http://www.sciencedirect.com/science/journal/01672789
thesaurus: Chaos; Digital arithmetic; Fractals; Random number generation; Roundoff errors
rawauthor: J. Palmore and C. Herring
rawtitle: Computer arithmetic, chaos and fractals
note:
Ninth Annual International Conference of the Center for Nonlinear Studies on Self-Organizing, Collective and Cooperative Phenomena in Natural and Artificial Networks

abstract:
The authors explore aspects of computer arithmetic from the viewpoint of dynamical systems. They demonstrate the effects of finite precision arithmetic in three uniformly hyperbolic chaotic dynamical systems: Bernoulli shifts, cat maps, and pseudorandom number generators. They show that elementary floating-point operations in binary computer arithmetic possess an inherently fractal structure. Each of these dynamical systems allows us to compare the exact results in integer arithmetic with those obtained by using floating-point arithmetic.

keywords:
Bernoulli shifts; Binary computer arithmetic; Cat maps; Chaos; Computer arithmetic; Dynamical systems; Elementary floating-point operations; Finite precision arithmetic; Floating-point arithmetic; Fractal structure; Integer arithmetic; Pseudorandom number generators; Self-similar structure; Uniformly hyperbolic chaotic dynamical systems

rawabstract:
The authors explore aspects of computer arithmetic from the viewpoint of dynamical systems. They demonstrate the effects of finite precision arithmetic in three uniformly hyperbolic chaotic dynamical systems: Bernoulli shifts, cat maps, and pseudorandom number generators. They show that elementary floating-point operations in binary computer arithmetic possess an inherently fractal structure. Each of these dynamical systems allows us to compare the exact results in integer arithmetic with those obtained by using floating-point arithmetic.

rawnote:
Ninth Annual International Conference of the Center for Nonlinear Studies on Self-Organizing, Collective and Cooperative Phenomena in Natural and Artificial Networks

entry:
@Article{Palmore:1990:CAC,
  author =       "J. Palmore and C. Herring",
  title =        "Computer arithmetic, chaos and fractals",
  journal =      j-PHYSICA-D,
  volume =       "42",
  number =       "1--3",
  pages =        "99--110",
  month =        jun,
  year =         "1990",
  CODEN =        "PDNPDT",
  DOI =          "https://doi.org/10.1016/0167-2789(90)90069-2",
  ISSN =         "0167-2789 (print), 1872-8022 (electronic)",
  ISSN-L =       "0167-2789",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Ninth Annual International Conference of the Center
                 for Nonlinear Studies on Self-Organizing, Collective
                 and Cooperative Phenomena in Natural and Artificial
                 Networks",
  abstract =     "The authors explore aspects of computer arithmetic
                 from the viewpoint of dynamical systems. They
                 demonstrate the effects of finite precision arithmetic
                 in three uniformly hyperbolic chaotic dynamical
                 systems: Bernoulli shifts, cat maps, and pseudorandom
                 number generators. They show that elementary
                 floating-point operations in binary computer arithmetic
                 possess an inherently fractal structure. Each of these
                 dynamical systems allows us to compare the exact
                 results in integer arithmetic with those obtained by
                 using floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Illinois Univ., Urbana, IL, USA",
  classification = "C1160 (Combinatorial mathematics); C5230 (Digital
                 arithmetic methods)",
  confdate =     "22-26 May 1989",
  conflocation = "Los Alamos, NM, USA",
  fjournal =     "Physica. D, Nonlinear phenomena",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01672789",
  keywords =     "Bernoulli shifts; Binary computer arithmetic; Cat
                 maps; Chaos; Computer arithmetic; Dynamical systems;
                 Elementary floating-point operations; Finite precision
                 arithmetic; Floating-point arithmetic; Fractal
                 structure; Integer arithmetic; Pseudorandom number
                 generators; Self-similar structure; Uniformly
                 hyperbolic chaotic dynamical systems",
  pubcountry =   "Netherlands",
  thesaurus =    "Chaos; Digital arithmetic; Fractals; Random number
                 generation; Roundoff errors",
}


bibtype: article
filename: elefunt.bib
label: Poppe:1990:AEC
author: G. P. M. Poppe and C. M. J. Wijers
title: Algorithm 680: Evaluation of the Complex Error Function
journal: j-TOMS
volume: 16
number: 1
pages: 47--47
month: mar
monthnumber: 3
year: 1990
CODEN: ACMSCU
DOI: https://doi.org/10.1145/77626.77630
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 47. 65G05 (65-04)
MRnumber: 91h:65068b
bibdate: Sun Sep 04 23:03:20 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 1994.09.04 23:03:20 ???
note: See remark cite Zaghloul:2019:RO.
URL: http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p47-poppe/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
subject: bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: G. P. M. Poppe and C. M. J. Wijers
rawnote: See remark \cite{Zaghloul:2019:RO}.
rawtitle: {Algorithm 680}: Evaluation of the Complex Error Function
entry:
@Article{Poppe:1990:AEC,
  author =       "G. P. M. Poppe and C. M. J. Wijers",
  title =        "{Algorithm 680}: Evaluation of the Complex Error
                 Function",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "47--47",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.77630",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "47. 65G05 (65-04)",
  MRnumber =     "91h:65068b",
  bibdate =      "Sun Sep 04 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Zaghloul:2019:RO}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p47-poppe/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Rational approximation.",
}


bibtype: article
filename: elefunt.bib
label: Poppe:1990:MEC
author: G. P. M. Poppe and C. M. J. Wijers
title: More Efficient Computation of the Complex Error Function
journal: j-TOMS
volume: 16
number: 1
pages: 38--46
month: mar
monthnumber: 3
year: 1990
CODEN: ACMSCU
DOI: https://doi.org/10.1145/77626.77629
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65G05 (65D20)
MRnumber: 91h:65068a
bibdate: Sun Sep 04 23:03:20 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 1994.09.04 23:03:20 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p38-poppe/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: G. P. M. Poppe and C. M. J. Wijers
rawtitle: More Efficient Computation of the Complex Error Function
subject:
bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation.

entry:
@Article{Poppe:1990:MEC,
  author =       "G. P. M. Poppe and C. M. J. Wijers",
  title =        "More Efficient Computation of the Complex Error
                 Function",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "38--46",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.77629",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G05 (65D20)",
  MRnumber =     "91h:65068a",
  bibdate =      "Sun Sep 04 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p38-poppe/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Algorithm analysis. {\bf G.1.2}: Mathematics
                 of Computing, NUMERICAL ANALYSIS, Approximation,
                 Rational approximation.",
}


bibtype: article
filename: elefunt.bib
label: Press:1990:EI
author: William H. Press and Saul A. Teukolsky
title: Elliptic Integrals
journal: j-COMPUT-PHYS
volume: 4
number: 1
pages: 92--??
month: jan
monthnumber: 1
year: 1990
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.4822893
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Wed Apr 10 08:45:21 MDT 2019
bibtimestamp: 2019.04.10 08:45:21 MDT
URL: https://aip.scitation.org/doi/10.1063/1.4822893
fjournal: Computers in Physics
acknowledgement: ack-nhfb
ajournal: Comput. Phys
journalURL: https://aip.scitation.org/journal/cip
rawauthor: William H. Press and Saul A. Teukolsky
rawtitle: Elliptic Integrals
entry:
@Article{Press:1990:EI,
  author =       "William H. Press and Saul A. Teukolsky",
  title =        "Elliptic Integrals",
  journal =      j-COMPUT-PHYS,
  volume =       "4",
  number =       "1",
  pages =        "92--??",
  month =        jan,
  year =         "1990",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.4822893",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:45:21 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.4822893",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}


bibtype: article
filename: elefunt.bib
label: Reemtsen:1990:MFR
author: Rembert Reemtsen
title: Modifications of the First Remez Algorithm
journal: j-SIAM-J-NUMER-ANAL
volume: 27
number: 2
pages: 507--518
month: apr
monthnumber: 4
year: 1990
CODEN: SJNAAM
DOI: https://doi.org/10.1137/0727031
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
MRclass: 65D15
MRnumber: 91a:65039
bibdate: Fri Oct 16 06:57:22 MDT 1998
bibtimestamp: 1998.10.16 06:57:22 MDT
fjournal: SIAM Journal on Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: Rembert Reemtsen
rawtitle: Modifications of the First {Remez} Algorithm
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database

entry:
@Article{Reemtsen:1990:MFR,
  author =       "Rembert Reemtsen",
  title =        "Modifications of the First {Remez} Algorithm",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "27",
  number =       "2",
  pages =        "507--518",
  month =        apr,
  year =         "1990",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0727031",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65D15",
  MRnumber =     "91a:65039",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}


bibtype: article
filename: elefunt.bib
label: Revfeim:1990:LEM
author: K. J. A. Revfeim
title: Letter to the Editor: More approximations for the cumulative and inverse normal distribution
journal: j-AMER-STAT
volume: 44
number: 1
pages: 63--63
month: feb
monthnumber: 2
year: 1990
CODEN: ASTAAJ
ISSN: 0003-1305 (print), 1537-2731 (electronic) OR 00031305 (print), 15372731 (electronic)
ISSNL: 0003-1305 OR 00031305
bibdate: Fri Jan 27 14:51:19 MST 2012
bibtimestamp: 2012.01.27 14:51:19 MST
URL: http://www.jstor.org/stable/2684963
fjournal: The American Statistician
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/utas20
rawauthor: K. J. A. Revfeim
rawtitle: Letter to the {Editor}: More approximations for the cumulative and inverse normal distribution
bibsource:
http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326447; https://www.math.utah.edu/pub/tex/bib/amstat1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Revfeim:1990:LEM,
  author =       "K. J. A. Revfeim",
  title =        "Letter to the {Editor}: More approximations for the
                 cumulative and inverse normal distribution",
  journal =      j-AMER-STAT,
  volume =       "44",
  number =       "1",
  pages =        "63--63",
  month =        feb,
  year =         "1990",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Jan 27 14:51:19 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326447;
                 https://www.math.utah.edu/pub/tex/bib/amstat1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2684963",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}


bibtype: article
filename: elefunt.bib
label: Sedogbo:1990:CAS
author: Guy Antoine Sedogbo
title: Convergence acceleration of some logarithmic sequences
journal: j-J-COMPUT-APPL-MATH
volume: 32
number: 1--2
pages: 253--260
day: 26
month: nov
monthnumber: 11
year: 1990
CODEN: JCAMDI
DOI: https://doi.org/10.1016/0377-0427(90)90435-3
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 65B10 (40A25 65B99)
MRnumber: 1091794 (91m:65009)
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
note: Extrapolation and rational approximation (Luminy, 1989)
fjournal: Journal of Computational and Applied Mathematics
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Guy Antoine Sedogbo
rawnote: Extrapolation and rational approximation (Luminy, 1989)
rawtitle: Convergence acceleration of some logarithmic sequences
entry:
@Article{Sedogbo:1990:CAS,
  author =       "Guy Antoine Sedogbo",
  title =        "Convergence acceleration of some logarithmic
                 sequences",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "32",
  number =       "1--2",
  pages =        "253--260",
  day =          "26",
  month =        nov,
  year =         "1990",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(90)90435-3",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65B10 (40A25 65B99)",
  MRnumber =     "1091794 (91m:65009)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Extrapolation and rational approximation (Luminy,
                 1989)",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "convergence acceleration",
}


bibtype: book
filename: elefunt.bib
label: Swartzlander:1990:CA
author: Earl E. Swartzlander
title: Computer arithmetic
publisher: pub-IEEE
address: pub-IEEE:adr
pages: various
year: 1990
LCCN: QA76.6.C633 1990
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.02.24 15:01:45 MST
note: Two volumes.
series: IEEE Computer Society Press tutorial
keywords: Computer arithmetic.; Electronic digital computers --- Programming.; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: Earl E. Swartzlander
rawnote: Two volumes.
rawtitle: Computer arithmetic
ISBN:
0-8186-8931-5 (v. 1), 0-8186-5931-9 (v. 1 microfiche) OR 0818689315 (v. 1), 0818659319 (v. 1 microfiche)

ISBN13:
978-0-8186-8931-4 (v. 1), 978-0-8186-5931-7 (v. 1 microfiche) OR 9780818689314 (v. 1), 9780818659317 (v. 1 microfiche)

TOC:
Arithmetic operations in a binary computer / R. F. Shaw High-speed arithmetic in binary computers / O. L. MacSorley Fast carry logic for digital computers / B. Gilchrist, J. H. Pomerene, and S. Y. Wong A logic for high-speed addition / A. Weinberger and J. L. Smith Conditional-sum addition logic / J. Sklansky An evaluation of several two-summand binary adders / J. Sklansky Adder with distributed control / A. Svoboda Multiple addition by residue threshold functions and their representation by array logic / I. T. Ho and T. C. Chen Counting responders in an associative memory / C. C. Foster and F. D. Stockton Parallel counters / E. E. Swartzlander, Jr. A signed binary multiplication technique / A. D. Booth Multiplying made easy for digital assemblies / C. Ghest. A binary multiplication scheme based on squaring / T. C. Chen A suggestion for a fast multiplier / C. S. Wallace Some schemes for parallel multipliers / L. Dadda On parallel digital multipliers / L. Dadda A compact high-speed parallel multiplication scheme / W. J. Stenzel, W. J. Kubitz, and G. H. Garcia A two's complement parallel array multiplication algorithm / C. R. Baugh and B. A. Wooley Comments on ``A two's complement parallel array multiplication algorithm'' / P. E. Blankenship The quasi-serial multiplier / E. E. Swartzlander, Jr. The two's complement quasi-serial multiplier / T. G. McDaneld and R. K. Guha A new class of digital division methods / J. E Robertson An algorithm for rapid binary division / J. B. Wilson and R. S. Ledley. Digit-by-digit transcendental-function computation / R. J. Linhardt and H. S. Miller A unified algorithm for elementary functions / J. S. Walther Some properties of iterative square-rooting methods using high-speed multiplication /C. V. Ramamoorthy, J. R. Goodman, and K. H. Kim Radix-16 evaluation of certain elementary functions / M. D. Ercegovac On the distribution of numbers / R. W. Hamming An analysis of floating-point addition / D. W. Sweeney The IBMldots Model 91: floating-point execution unit / S. F. Anderson ldots [et al.] Design of large high-speed floating-point-arithmetic units / J. B. Gosling Analysis of rounding methods in floating-point arithmetic / D. J. Kuck,D. S. Parker, Jr., and A. H. Sameh. cos x, tan-p1s x, and cot-p1s x / W. H. Specker.

annote:
Vol. 1 is a reprint. Originally published: Stroudsburg, Pa.: Dowden, Hutchinson and Ross, c1980. Originally published in series: Benchmark papers in electrical engineering and computer science; 21. Vol 2 is a sequel to the earlier collection. Vol. 1: 2nd ed.

rawTOC:
Arithmetic operations in a binary computer / R. F. Shaw \\ High-speed arithmetic in binary computers / O. L. MacSorley \\ Fast carry logic for digital computers / B. Gilchrist, J. H. Pomerene, and S. Y. Wong \\ A logic for high-speed addition / A. Weinberger and J. L. Smith \\ Conditional-sum addition logic / J. Sklansky \\ An evaluation of several two-summand binary adders / J. Sklansky \\ Adder with distributed control / A. Svoboda \\ Multiple addition by residue threshold functions and their representation by array logic / I. T. Ho and T. C. Chen \\ Counting responders in an associative memory / C. C. Foster and F. D. Stockton \\ Parallel counters / E. E. Swartzlander, Jr. \\ A signed binary multiplication technique / A. D. Booth \\ Multiplying made easy for digital assemblies / C. Ghest. A binary multiplication scheme based on squaring / T. C. Chen \\ A suggestion for a fast multiplier / C. S. Wallace \\ Some schemes for parallel multipliers / L. Dadda \\ On parallel digital multipliers / L. Dadda \\ A compact high-speed parallel multiplication scheme / W. J. Stenzel, W. J. Kubitz, and G. H. Garcia \\ A two's complement parallel array multiplication algorithm / C. R. Baugh and B. A. Wooley \\ Comments on ``A two's complement parallel array multiplication algorithm'' / P. E. Blankenship \\ The quasi-serial multiplier / E. E. Swartzlander, Jr. \\ The two's complement quasi-serial multiplier / T. G. McDaneld and R. K. Guha \\ A new class of digital division methods / J. E Robertson \\ An algorithm for rapid binary division / J. B. Wilson and R. S. Ledley. Digit-by-digit transcendental-function computation / R. J. Linhardt and H. S. Miller \\ A unified algorithm for elementary functions / J. S. Walther \\ Some properties of iterative square-rooting methods using high-speed multiplication /C. V. Ramamoorthy, J. R. Goodman, and K. H. Kim \\ Radix-16 evaluation of certain elementary functions / M. D. Ercegovac \\ On the distribution of numbers / R. W. Hamming \\ An analysis of floating-point addition / D. W. Sweeney \\ The IBM\ldots{}Model 91: floating-point execution unit / S. F. Anderson \ldots{} [et al.] \\ Design of large high-speed floating-point-arithmetic units / J. B. Gosling \\ Analysis of rounding methods in floating-point arithmetic / D. J. Kuck,D. S. Parker, Jr., and A. H. Sameh. \\ cos x, tan-p1s x, and cot-p1s x / W. H. Specker.

entry:
@Book{Swartzlander:1990:CA,
  author =       "Earl E. Swartzlander",
  title =        "Computer arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "various",
  year =         "1990",
  ISBN =         "0-8186-8931-5 (v. 1), 0-8186-5931-9 (v. 1
                 microfiche)",
  ISBN-13 =      "978-0-8186-8931-4 (v. 1), 978-0-8186-5931-7 (v. 1
                 microfiche)",
  LCCN =         "QA76.6.C633 1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Two volumes.",
  series =       "IEEE Computer Society Press tutorial",
  acknowledgement = ack-nhfb,
  annote =       "Vol. 1 is a reprint. Originally published:
                 Stroudsburg, Pa.: Dowden, Hutchinson and Ross, c1980.
                 Originally published in series: Benchmark papers in
                 electrical engineering and computer science; 21. Vol 2
                 is a sequel to the earlier collection. Vol. 1: 2nd
                 ed.",
  keywords =     "Computer arithmetic.; Electronic digital computers ---
                 Programming.; Floating-point arithmetic.",
  tableofcontents = "Arithmetic operations in a binary computer / R. F.
                 Shaw \\
                 High-speed arithmetic in binary computers / O. L.
                 MacSorley \\
                 Fast carry logic for digital computers / B. Gilchrist,
                 J. H. Pomerene, and S. Y. Wong \\
                 A logic for high-speed addition / A. Weinberger and J.
                 L. Smith \\
                 Conditional-sum addition logic / J. Sklansky \\
                 An evaluation of several two-summand binary adders / J.
                 Sklansky \\
                 Adder with distributed control / A. Svoboda \\
                 Multiple addition by residue threshold functions and
                 their representation by array logic / I. T. Ho and T.
                 C. Chen \\
                 Counting responders in an associative memory / C. C.
                 Foster and F. D. Stockton \\
                 Parallel counters / E. E. Swartzlander, Jr. \\
                 A signed binary multiplication technique / A. D. Booth
                 \\
                 Multiplying made easy for digital assemblies / C.
                 Ghest. A binary multiplication scheme based on squaring
                 / T. C. Chen \\
                 A suggestion for a fast multiplier / C. S. Wallace \\
                 Some schemes for parallel multipliers / L. Dadda \\
                 On parallel digital multipliers / L. Dadda \\
                 A compact high-speed parallel multiplication scheme /
                 W. J. Stenzel, W. J. Kubitz, and G. H. Garcia \\
                 A two's complement parallel array multiplication
                 algorithm / C. R. Baugh and B. A. Wooley \\
                 Comments on ``A two's complement parallel array
                 multiplication algorithm'' / P. E. Blankenship \\
                 The quasi-serial multiplier / E. E. Swartzlander, Jr.
                 \\
                 The two's complement quasi-serial multiplier / T. G.
                 McDaneld and R. K. Guha \\
                 A new class of digital division methods / J. E
                 Robertson \\
                 An algorithm for rapid binary division / J. B. Wilson
                 and R. S. Ledley. Digit-by-digit
                 transcendental-function computation / R. J. Linhardt
                 and H. S. Miller \\
                 A unified algorithm for elementary functions / J. S.
                 Walther \\
                 Some properties of iterative square-rooting methods
                 using high-speed multiplication /C. V. Ramamoorthy, J.
                 R. Goodman, and K. H. Kim \\
                 Radix-16 evaluation of certain elementary functions /
                 M. D. Ercegovac \\
                 On the distribution of numbers / R. W. Hamming \\
                 An analysis of floating-point addition / D. W. Sweeney
                 \\
                 The IBM\ldots{}Model 91: floating-point execution unit
                 / S. F. Anderson \ldots{} [et al.] \\
                 Design of large high-speed floating-point-arithmetic
                 units / J. B. Gosling \\
                 Analysis of rounding methods in floating-point
                 arithmetic / D. J. Kuck,D. S. Parker, Jr., and A. H.
                 Sameh. \\
                 cos x, tan-p1s x, and cot-p1s x / W. H. Specker.",
}


bibtype: article
filename: elefunt.bib
label: Tang:1990:AET
author: Ping Tak Peter Tang
title: Accurate and Efficient Testing of the Exponential and Logarithm Functions
journal: j-TOMS
volume: 16
number: 3
pages: 185--200
month: sep
monthnumber: 9
year: 1990
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65-04 (65G99)
MRnumber: 1 070 797
bibdate: Sun Sep 04 23:14:59 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.04 23:14:59 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; languages; verification
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Ping Tak Peter Tang
rawtitle: Accurate and Efficient Testing of the Exponential and Logarithm Functions
URL:
http://doi.acm.org/10.1145/79505.79506; http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p185-tang/

abstract:
Table-driven techniques can be used to test highly accurate implementation of EXP LOG. The largest error observed in EXP and LOG accurately to within 1/500 unit in the last place are reported in our tests. Methods to verify the tests' reliability are discussed. Results of applying the tests to our own as well as to a number of other implementations of EXP and LOG are presented.

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability.

rawabstract:
Table-driven techniques can be used to test highly accurate implementation of EXP LOG. The largest error observed in EXP and LOG accurately to within 1/500 unit in the last place are reported in our tests. Methods to verify the tests' reliability are discussed. Results of applying the tests to our own as well as to a number of other implementations of EXP and LOG are presented.

entry:
@Article{Tang:1990:AET,
  author =       "Ping Tak Peter Tang",
  title =        "Accurate and Efficient Testing of the Exponential and
                 Logarithm Functions",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "185--200",
  month =        sep,
  year =         "1990",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65G99)",
  MRnumber =     "1 070 797",
  bibdate =      "Sun Sep 04 23:14:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://doi.acm.org/10.1145/79505.79506;
                 http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p185-tang/",
  abstract =     "Table-driven techniques can be used to test highly
                 accurate implementation of EXP LOG. The largest error
                 observed in EXP and LOG accurately to within 1/500 unit
                 in the last place are reported in our tests. Methods to
                 verify the tests' reliability are discussed. Results of
                 applying the tests to our own as well as to a number of
                 other implementations of EXP and LOG are presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; languages; verification",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Portability.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Tang:1990:FAL
author: Ping Tak Peter Tang
title: A fast algorithm for linear complex Chebyshev approximation
crossref: Mason:1990:AAI
pages: 265--274
year: 1990
bibdate: Wed Nov 29 14:12:06 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.11.29 14:12:06 ???
acknowledgement: ack-nhfb
rawauthor: Ping Tak Peter Tang
rawtitle: A fast algorithm for linear complex {Chebyshev} approximation
entry:
@InProceedings{Tang:1990:FAL,
  author =       "Ping Tak Peter Tang",
  title =        "A fast algorithm for linear complex {Chebyshev}
                 approximation",
  crossref =     "Mason:1990:AAI",
  pages =        "265--274",
  year =         "1990",
  bibdate =      "Wed Nov 29 14:12:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: elefunt.bib
label: Tang:1990:PGE
author: Ping Tak Peter Tang
title: A Portable Generic Elementary Function Package in Ada and an Accurate Test Suite
type: Technical report
number: ANL-90/35
institution: inst-ANL
address: inst-ANL:adr
pages: iii + 35
month: nov
monthnumber: 11
year: 1990
bibdate: Fri Dec 28 11:36:25 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.12.28 11:36:25 ???
URL: http://www.osti.gov/bridge/servlets/purl/6310184-4n5sOR/6310184.PDF
acknowledgement: ack-nhfb
rawauthor: Ping Tak Peter Tang
rawtitle: A Portable Generic Elementary Function Package in {Ada} and an Accurate Test Suite
abstract:
A comprehensive set of elementary functions has been implemented portably in Ada. The high accuracy of the implementation has been confirmed by rigorous analysis. Moreover, we present new test methods that are efficient and offer a high resolution of 0.005 unit in the last place, Tbese test methods have been implemented portably here and confirm the accuracy of our implemented functions. Reports on the accuracy of other function libraries obtained by our test programs are also presented.

rawabstract:
A comprehensive set of elementary functions has been implemented portably in Ada. The high accuracy of the implementation has been confirmed by rigorous analysis. Moreover, we present new test methods that are efficient and offer a high resolution of 0.005 unit in the last place, Tbese test methods have been implemented portably here and confirm the accuracy of our implemented functions. Reports on the accuracy of other function libraries obtained by our test programs are also presented.

entry:
@TechReport{Tang:1990:PGE,
  author =       "Ping Tak Peter Tang",
  title =        "A Portable Generic Elementary Function Package in
                 {Ada} and an Accurate Test Suite",
  type =         "Technical report",
  number =       "ANL-90/35",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  pages =        "iii + 35",
  month =        nov,
  year =         "1990",
  bibdate =      "Fri Dec 28 11:36:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.osti.gov/bridge/servlets/purl/6310184-4n5sOR/6310184.PDF",
  abstract =     "A comprehensive set of elementary functions has been
                 implemented portably in Ada. The high accuracy of the
                 implementation has been confirmed by rigorous analysis.
                 Moreover, we present new test methods that are
                 efficient and offer a high resolution of 0.005 unit in
                 the last place, Tbese test methods have been
                 implemented portably here and confirm the accuracy of
                 our implemented functions. Reports on the accuracy of
                 other function libraries obtained by our test programs
                 are also presented.",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: elefunt.bib
label: Tang:1990:SSI
author: Ping Tak Peter Tang
title: Some Software Implementations of the Functions Sine and Cosine
type: Technical report
number: ANL-90/3
institution: inst-ANL
address: inst-ANL:adr
pages: iii + 35
month: apr
monthnumber: 4
year: 1990
bibdate: Fri Dec 28 11:21:38 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.12.28 11:21:38 ???
URL: http://www-fp.mcs.anl.gov/division/publications/abstracts/abstracts90.htm
acknowledgement: ack-nhfb
rawauthor: Ping Tak Peter Tang
rawtitle: Some Software Implementations of the Functions Sine and Cosine
abstract:
This document presents several software implementations of the elementary functions sin and cos designed to fit a large class of machines. Implementation details are provided. Also provided is a detailed error analysis that bounds the errors of these implementations, over the full range of input arguments, from 0.721 to 0.912 units in the last place. Tests performed on these codes give results that are consistent with the error bounds.

rawabstract:
This document presents several software implementations of the elementary functions sin and cos designed to fit a large class of machines. Implementation details are provided. Also provided is a detailed error analysis that bounds the errors of these implementations, over the full range of input arguments, from 0.721 to 0.912 units in the last place. Tests performed on these codes give results that are consistent with the error bounds.

entry:
@TechReport{Tang:1990:SSI,
  author =       "Ping Tak Peter Tang",
  title =        "Some Software Implementations of the Functions Sine
                 and Cosine",
  type =         "Technical report",
  number =       "ANL-90/3",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  month =        apr,
  year =         "1990",
  bibdate =      "Fri Dec 28 11:21:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www-fp.mcs.anl.gov/division/publications/abstracts/abstracts90.htm",
  abstract =     "This document presents several software
                 implementations of the elementary functions sin and cos
                 designed to fit a large class of machines.
                 Implementation details are provided. Also provided is a
                 detailed error analysis that bounds the errors of these
                 implementations, over the full range of input
                 arguments, from 0.721 to 0.912 units in the last place.
                 Tests performed on these codes give results that are
                 consistent with the error bounds.",
  acknowledgement = ack-nhfb,
  xxnote =       "Where is this? I can find no electronic version
                 online, other than the abstract at the given URL.",
}


bibtype: article
filename: elefunt.bib
label: Tang:1990:TDI
author: Ping Tak Peter Tang
title: Table-Driven Implementation of the Logarithm Function in IEEE Floating-Point Arithmetic
journal: j-TOMS
volume: 16
number: 4
pages: 378--400
month: dec
monthnumber: 12
year: 1990
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sun Sep 04 23:26:09 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.04 23:26:09 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; design; performance; reliability; standardization; theory; verification
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/toms
rawauthor: Ping Tak Peter Tang
rawtitle: Table-Driven Implementation of the Logarithm Function in {IEEE} Floating-Point Arithmetic
URL:
http://doi.acm.org/10.1145/98267.98294; http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p378-tang/

abstract:
Algorithms and implementation details for the logarithm functions in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementation need only working- precision arithmetic and are provably accurate to within 0.57 ulp.

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.

rawabstract:
Algorithms and implementation details for the logarithm functions in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementation need only working- precision arithmetic and are provably accurate to within 0.57 ulp.

entry:
@Article{Tang:1990:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Logarithm Function
                 in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "378--400",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:26:09 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://doi.acm.org/10.1145/98267.98294;
                 http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p378-tang/",
  abstract =     "Algorithms and implementation details for the
                 logarithm functions in both single and double precision
                 of IEEE 754 arithmetic are presented here. With a table
                 of moderate size, the implementation need only working-
                 precision arithmetic and are provably accurate to
                 within 0.57 ulp.",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; performance; reliability;
                 standardization; theory; verification",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}


bibtype: article
filename: elefunt.bib
label: Todd:1990:WMP
author: John Todd
title: The Weierstrass mean. I. The periods of $ wp (z vert e_1, e_2, e_3) $
journal: j-NUM-MATH
volume: 57
number: 8
pages: 737--746
month: aug
monthnumber: 8
year: 1990
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65D20 (33E05)
MRnumber: 91m:65057
MRreviewer: Syvert P. N{\o}rsett
bibdate: Mon May 26 11:49:34 MDT 1997
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
keywords: convergence; elliptic objects; limits; numerical methods; Weierstrass mean
acknowledgement: ack-nhfb
corpsource: California Inst. of Technol., Pasadena, CA, USA
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: John Todd
rawtitle: The {Weierstrass} mean. {I}. The periods of $ \wp (z \vert e_1, e_2, e_3) $
entry:
@Article{Todd:1990:WMP,
  author =       "John Todd",
  title =        "The {Weierstrass} mean. {I}. The periods of $ \wp (z
                 \vert e_1, e_2, e_3) $",
  journal =      j-NUM-MATH,
  volume =       "57",
  number =       "8",
  pages =        "737--746",
  month =        aug,
  year =         "1990",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65D20 (33E05)",
  MRnumber =     "91m:65057",
  MRreviewer =   "Syvert P. N{\o}rsett",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290 (Numerical analysis); C4100 (Numerical
                 analysis)",
  corpsource =   "California Inst. of Technol., Pasadena, CA, USA",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "convergence; elliptic objects; limits; numerical
                 methods; Weierstrass mean",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Watson:1990:NMC
author: G. Alistair Watson
title: Numerical methods for Chebyshev approximation of complex-valued functions
crossref: Mason:1990:AAI
pages: 246--264
year: 1990
bibdate: Wed Nov 29 14:09:32 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.11.29 14:09:32 ???
acknowledgement: ack-nhfb
rawauthor: G. Alistair Watson
rawtitle: Numerical methods for {Chebyshev} approximation of complex-valued functions
entry:
@InProceedings{Watson:1990:NMC,
  author =       "G. Alistair Watson",
  title =        "Numerical methods for {Chebyshev} approximation of
                 complex-valued functions",
  crossref =     "Mason:1990:AAI",
  pages =        "246--264",
  year =         "1990",
  bibdate =      "Wed Nov 29 14:09:32 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Wells:1990:LE
title: Letters to the Editor
journal: j-AMER-STAT
volume: 44
number: 1
pages: 56--65
month: feb
monthnumber: 2
year: 1990
CODEN: ASTAAJ
ISSN: 0003-1305 (print), 1537-2731 (electronic) OR 00031305 (print), 15372731 (electronic)
ISSNL: 0003-1305 OR 00031305
bibdate: Fri Jan 27 14:51:19 MST 2012
bibtimestamp: 2012.01.27 14:51:19 MST
URL: http://www.jstor.org/stable/2684963
fjournal: The American Statistician
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/utas20
rawtitle: Letters to the Editor
author:
Martin T. Wells and Ram C. Tiwari and I. Arizono and H. Ohta and James W. Mergerson and Gabriella M. Belli and Christopher Cox and Murray A. Jorgensen and Jacques Benichou and Mitchell H. Gail and Warren F. Kuhfeld and Brian Dawkins and Walter B. Studdiford and Colin Goodall and W. D. Kaigh and Stephen W. Looney and Robert Kinnison and James A. Gibbons and Joel R. Levin and Ronald C. Serlin and K. J. A. Revfeim and Charles R. McConnell and Robert M. Norton and R. W. Farebrother and I. J. Good and Stanley Lebergott and Vedula N. Murty

bibsource:
http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326447; https://www.math.utah.edu/pub/tex/bib/amstat1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawauthor:
Martin T. Wells and Ram C. Tiwari and I. Arizono and H. Ohta and James W. Mergerson and Gabriella M. Belli and Christopher Cox and Murray A. Jorgensen and Jacques Benichou and Mitchell H. Gail and Warren F. Kuhfeld and Brian Dawkins and Walter B. Studdiford and Colin Goodall and W. D. Kaigh and Stephen W. Looney and Robert Kinnison and James A. Gibbons and Joel R. Levin and Ronald C. Serlin and K. J. A. Revfeim and Charles R. McConnell and Robert M. Norton and R. W. Farebrother and I. J. Good and Stanley Lebergott and Vedula N. Murty

entry:
@Article{Wells:1990:LE,
  author =       "Martin T. Wells and Ram C. Tiwari and I. Arizono and
                 H. Ohta and James W. Mergerson and Gabriella M. Belli
                 and Christopher Cox and Murray A. Jorgensen and Jacques
                 Benichou and Mitchell H. Gail and Warren F. Kuhfeld and
                 Brian Dawkins and Walter B. Studdiford and Colin
                 Goodall and W. D. Kaigh and Stephen W. Looney and
                 Robert Kinnison and James A. Gibbons and Joel R. Levin
                 and Ronald C. Serlin and K. J. A. Revfeim and Charles
                 R. McConnell and Robert M. Norton and R. W. Farebrother
                 and I. J. Good and Stanley Lebergott and Vedula N.
                 Murty",
  title =        "Letters to the Editor",
  journal =      j-AMER-STAT,
  volume =       "44",
  number =       "1",
  pages =        "56--65",
  month =        feb,
  year =         "1990",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Jan 27 14:51:19 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326447;
                 https://www.math.utah.edu/pub/tex/bib/amstat1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2684963",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}


bibtype: article
filename: elefunt.bib
label: Weniger:1990:RAM
author: Ernst Joachim Weniger and Jiri Cizek
title: Rational approximations for the modified Bessel function of the second kind
journal: j-COMP-PHYS-COMM
volume: 59
number: 3
pages: 471--493
month: jul
monthnumber: 7
year: 1990
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(90)90089-J
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:29:12 MST 2012
bibtimestamp: 2012.02.13 21:29:12 MST
URL: http://www.sciencedirect.com/science/article/pii/001046559090089J
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Ernst Joachim Weniger and Ji{\v{r}}i C{\'\i}{\v{z}}ek
rawtitle: Rational approximations for the modified {Bessel} function of the second kind
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
Various different rational approximations for the modified Bessel function $ K_nu (z) $ are compared with respect to their ability of computing $ K_nu (z) $ efficiently and reliably in the troublesome region of moderately large arguments $z$. The starting point for the construction of the rational approximations is the asymptotic series $_2 F_0$ for $ K_nu (z) $, which diverges for all finite arguments $z$ but is Borel summable and Stieltjes summable. The numerical tests showed that Pade approximants for $ K_nu (z) $ are significantly less efficient than the other rational approximations which were considered. The best results were produced by some recently derived sequence transformations (E. J. Weniger, Comput. Phys. Rep. bf 10 (1989) 189), which are closely related to Levin's sequence transformations (D. Levin, Int. J. Comput. Math. B bf 3 (1973) 371).

rawabstract:
Various different rational approximations for the modified Bessel function $ K_\nu (z) $ are compared with respect to their ability of computing $ K_\nu (z) $ efficiently and reliably in the troublesome region of moderately large arguments $z$. The starting point for the construction of the rational approximations is the asymptotic series $_2 F_0$ for $ K_\nu (z) $, which diverges for all finite arguments $z$ but is Borel summable and Stieltjes summable. The numerical tests showed that Pad{\'e} approximants for $ K_\nu (z) $ are significantly less efficient than the other rational approximations which were considered. The best results were produced by some recently derived sequence transformations (E. J. Weniger, Comput. Phys. Rep. {\bf 10} (1989) 189), which are closely related to Levin's sequence transformations (D. Levin, Int. J. Comput. Math. B {\bf 3} (1973) 371).

entry:
@Article{Weniger:1990:RAM,
  author =       "Ernst Joachim Weniger and Ji{\v{r}}i
                 C{\'\i}{\v{z}}ek",
  title =        "Rational approximations for the modified {Bessel}
                 function of the second kind",
  journal =      j-COMP-PHYS-COMM,
  volume =       "59",
  number =       "3",
  pages =        "471--493",
  month =        jul,
  year =         "1990",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(90)90089-J",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:29:12 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/001046559090089J",
  abstract =     "Various different rational approximations for the
                 modified Bessel function $ K_\nu (z) $ are compared
                 with respect to their ability of computing $ K_\nu (z)
                 $ efficiently and reliably in the troublesome region of
                 moderately large arguments $z$. The starting point for
                 the construction of the rational approximations is the
                 asymptotic series $_2 F_0$ for $ K_\nu (z) $, which
                 diverges for all finite arguments $z$ but is Borel
                 summable and Stieltjes summable. The numerical tests
                 showed that Pad{\'e} approximants for $ K_\nu (z) $ are
                 significantly less efficient than the other rational
                 approximations which were considered. The best results
                 were produced by some recently derived sequence
                 transformations (E. J. Weniger, Comput. Phys. Rep. {\bf
                 10} (1989) 189), which are closely related to Levin's
                 sequence transformations (D. Levin, Int. J. Comput.
                 Math. B {\bf 3} (1973) 371).",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Bartoloni:1991:MFU
title: MAD, a floating-point unit for massively-parallel processors
journal: Particle World
volume: 2
number: 3
pages: 65--73
year: 1991
CODEN: PARWEG
ISSN: 1043-6790 OR 10436790
bibdate: Tue Dec 12 09:26:54 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.12 09:26:54 MST
acknowledgement: ack-nhfb
affiliation: Roma Univ., Italy
thesaurus: Digital arithmetic; Microprocessor chips; Parallel architectures; Physics computing
rawtitle: {MAD}, a floating-point unit for massively-parallel processors
author:
A. Bartoloni and C. Battista and S. Cabasino and N. Cabibbo and F. Del Prete and F. Marzano and P. S. Paolucci and R. Sarno and G. Salina and G. M. Todesco and M. Torelli and R. Tripiccione and W. Tross and E. Zanetti

abstract:
The authors describe in detail the architecture and implementation of the MAD chip. It is a floating point unit, used as the elementary processing element of the APE100 array processor. The design has been accurately tailored to the requirements of a SIMD floating point intensive machine.

keywords:
APE100 array processor; Architecture; Elementary processing element; Floating-point unit; Massively-parallel processors; SIMD floating point intensive machine

rawabstract:
The authors describe in detail the architecture and implementation of the MAD chip. It is a floating point unit, used as the elementary processing element of the APE100 array processor. The design has been accurately tailored to the requirements of a SIMD floating point intensive machine.

rawauthor:
A. Bartoloni and C. Battista and S. Cabasino and N. Cabibbo and F. Del Prete and F. Marzano and P. S. Paolucci and R. Sarno and G. Salina and G. M. Todesco and M. Torelli and R. Tripiccione and W. Tross and E. Zanetti

entry:
@Article{Bartoloni:1991:MFU,
  author =       "A. Bartoloni and C. Battista and S. Cabasino and N.
                 Cabibbo and F. Del Prete and F. Marzano and P. S.
                 Paolucci and R. Sarno and G. Salina and G. M. Todesco
                 and M. Torelli and R. Tripiccione and W. Tross and E.
                 Zanetti",
  title =        "{MAD}, a floating-point unit for massively-parallel
                 processors",
  journal =      "Particle World",
  volume =       "2",
  number =       "3",
  pages =        "65--73",
  month =        "????",
  year =         "1991",
  CODEN =        "PARWEG",
  ISSN =         "1043-6790",
  bibdate =      "Tue Dec 12 09:26:54 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The authors describe in detail the architecture and
                 implementation of the MAD chip. It is a floating point
                 unit, used as the elementary processing element of the
                 APE100 array processor. The design has been accurately
                 tailored to the requirements of a SIMD floating point
                 intensive machine.",
  acknowledgement = ack-nhfb,
  affiliation =  "Roma Univ., Italy",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5220P (Parallel architecture);
                 C5230 (Digital arithmetic methods); C7320 (Physics and
                 Chemistry)",
  keywords =     "APE100 array processor; Architecture; Elementary
                 processing element; Floating-point unit;
                 Massively-parallel processors; SIMD floating point
                 intensive machine",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic; Microprocessor chips; Parallel
                 architectures; Physics computing",
}


bibtype: techreport
filename: elefunt.bib
label: Beebe:1991:ASR
author: Nelson H. F. Beebe
title: Accurate Square Root Computation
institution: inst-CSC
address: inst-CSC:adr
pages: 23
day: 4
month: feb
monthnumber: 2
year: 1991
bibdate: Sat Feb 8 10:28:55 2020
bibtimestamp: 2020.02.08 10:28:55 ???
note: Supplemental class notes prepared for Mathematics 118.
rawauthor: Nelson H. F. Beebe
rawnote: Supplemental class notes prepared for Mathematics 118.
rawtitle: Accurate Square Root Computation
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@TechReport{Beebe:1991:ASR,
  author =       "Nelson H. F. Beebe",
  title =        "Accurate Square Root Computation",
  institution =  inst-CSC,
  address =      inst-CSC:adr,
  pages =        "23",
  day =          "4",
  month =        feb,
  year =         "1991",
  bibdate =      "Sat Feb 8 10:28:55 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supplemental class notes prepared for Mathematics
                 118.",
}


bibtype: article
filename: elefunt.bib
label: Boersma:1991:UAB
author: J. Boersma
title: Uniform asymptotics of a Bessel-function series occurring in a transmission-line problem
journal: j-J-COMPUT-APPL-MATH
volume: 37
number: 1--3
pages: 143--159
day: 18
month: nov
monthnumber: 11
year: 1991
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:02:22 MST 2017
bibtimestamp: 2017.02.25 13:02:22 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279190113X
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: J. Boersma
rawtitle: Uniform asymptotics of a {Bessel}-function series occurring in a transmission-line problem
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib

entry:
@Article{Boersma:1991:UAB,
  author =       "J. Boersma",
  title =        "Uniform asymptotics of a {Bessel}-function series
                 occurring in a transmission-line problem",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "37",
  number =       "1--3",
  pages =        "143--159",
  day =          "18",
  month =        nov,
  year =         "1991",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:02:22 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279190113X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Bohlender:1991:SEF
author: G. Bohlender and W. Walter and P. Kornerup and D. W. Matula
title: Semantics for exact floating point operations
crossref: Kornerup:1991:PIS
pages: 22--26
year: 1991
bibdate: Wed Dec 13 13:13:34 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.13 13:13:34 MST
note: IEEE Catalog number 91CH3015-5.
acknowledgement: ack-nhfb
affiliation: Inst. fur Angewandte Math., Karlsruhe Univ., Germany
bookpages: xiii + 282
thesaurus: Digital arithmetic; Number theory
rawauthor: G. Bohlender and W. Walter and P. Kornerup and D. W. Matula
rawnote: IEEE Catalog number 91CH3015-5.
rawtitle: Semantics for exact floating point operations
abstract:
Semantics are given for the four elementary arithmetic operations and the square root, to characterize what are termed exact floating point operations. The operands of the arithmetic operations and the argument of the square root are all floating point numbers in one format. In every case, the result is a pair of floating point numbers in the same format with no accuracy lost in the computation. These semantics make it possible to realize the following principle: it shall be a user option to discard any information in the result of a floating point arithmetic operation. The reliability and portability previously associated with only mathematical software implementations in integer arithmetic can thus be attained exploiting the generally higher efficiency of floating point hardware.

keywords:
Argument; Elementary arithmetic operations; Exact floating point operations; Floating point arithmetic; Floating point hardware; Floating point numbers; Integer arithmetic; Mathematical software; Operands; Portability; Reliability; Semantics; Square root

rawabstract:
Semantics are given for the four elementary arithmetic operations and the square root, to characterize what are termed exact floating point operations. The operands of the arithmetic operations and the argument of the square root are all floating point numbers in one format. In every case, the result is a pair of floating point numbers in the same format with no accuracy lost in the computation. These semantics make it possible to realize the following principle: it shall be a user option to discard any information in the result of a floating point arithmetic operation. The reliability and portability previously associated with only mathematical software implementations in integer arithmetic can thus be attained exploiting the generally higher efficiency of floating point hardware.

entry:
@InProceedings{Bohlender:1991:SEF,
  author =       "G. Bohlender and W. Walter and P. Kornerup and D. W.
                 Matula",
  title =        "Semantics for exact floating point operations",
  crossref =     "Kornerup:1991:PIS",
  bookpages =    "xiii + 282",
  pages =        "22--26",
  year =         "1991",
  bibdate =      "Wed Dec 13 13:13:34 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "IEEE Catalog number 91CH3015-5.",
  abstract =     "Semantics are given for the four elementary arithmetic
                 operations and the square root, to characterize what
                 are termed exact floating point operations. The
                 operands of the arithmetic operations and the argument
                 of the square root are all floating point numbers in
                 one format. In every case, the result is a pair of
                 floating point numbers in the same format with no
                 accuracy lost in the computation. These semantics make
                 it possible to realize the following principle: it
                 shall be a user option to discard any information in
                 the result of a floating point arithmetic operation.
                 The reliability and portability previously associated
                 with only mathematical software implementations in
                 integer arithmetic can thus be attained exploiting the
                 generally higher efficiency of floating point
                 hardware.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe Univ., Germany",
  classification = "C1160 (Combinatorial mathematics); C5230 (Digital
                 arithmetic methods)",
  confdate =     "26-28 June 1991",
  conflocation = "Grenoble, France",
  confsponsor =  "IEEE; CNRS; IMAG",
  keywords =     "Argument; Elementary arithmetic operations; Exact
                 floating point operations; Floating point arithmetic;
                 Floating point hardware; Floating point numbers;
                 Integer arithmetic; Mathematical software; Operands;
                 Portability; Reliability; Semantics; Square root",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Number theory",
}


bibtype: book
filename: elefunt.bib
label: Brezinski:1991:EMT
author: Claude Brezinski and Michela Redivo Zaglia
title: Extrapolation Methods: Theory and Practice
volume: 2
publisher: pub-NORTH-HOLLAND
address: pub-NORTH-HOLLAND:adr
pages: ix + 464
year: 1991
ISBN: 0-444-88814-4 OR 0444888144
ISBN13: 978-0-444-88814-3 OR 9780444888143
LCCN: QA281 .B74 1991
bibdate: Mon May 24 09:18:52 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; melvyl.cdlib.org:210/CDL90
bibtimestamp: 2010.05.24 09:18:52 MDT
series: Studies in computational mathematics
subject: extrapolation; data processing
acknowledgement: ack-nhfb
rawauthor: Claude Brezinski and Michela {Redivo Zaglia}
rawtitle: Extrapolation Methods: Theory and Practice
TOC:
Preface / v 1 INTRODUCTION TO THE THEORY / 1 1.1 First steps / 1 1.2 What is an extrapolation method? / 5 1.3 What is an extrapolation algorithm? / 8 1.4 Quasi-linear sequence transformations / 11 1.5 Sequence transformations as ratios of determinants / 18 1.6 Triangular recursive schemes / 21 1.7 Normal forms of the algorithms / 26 1.8 Progressive forms of the algorithms / 28 1.9 Particular rules of the algorithms / 34 1.10 Accelerability and non-accelerability / 39 1.11 Optimality / 42 1.12 Asymptotic behaviour of sequences / 47 2 SCALAR EXTRAPOLATION ALGORITHMS / 55 2.1 The $E$-algorithm / 55 2.2 Richardson extrapolation process T2 2.3 The $epsilon $-algorithm / 78 2.4 The $G$-transformation / 95 2.5 Rational extrapolation / 101 2.6 Generalizations of the $epsilon $-algorithm / 108 2.7 Levin's transforms / 113 2.8 Overholt's process / 119 2.9 $Theta $-type algorithms / 121 2.10 The iterated $Delta ^2$ process / 128 2.11 Miscellaneous algorithms / 131 3 SPECIAL DEVICES / 145 3.1 Error estimates and acceleration / 145 3.2 Convergence tests and acceleration 151 3.3 Construction of asymptotic expansions / 159 3.4 Construction of extrapolation processes / 165 3.5 Extraction procedures / 171 3.6 Automatic selection / 178 3.7 Composite sequence transformations / 185 3.8 Error control / 193 3.9 Contractive sequence transformations / 201 3.10 Least squares extrapolation / 210 4 VECTOR EXTRAPOLATION ALGORITHMS / 213 4.1 The vector $epsilon $-algorithm / 216 4.2 The topological $epsilon $-algorithm / 220 4.3 The vector $E$-algorithm / 228 4.4 The recursive projection algorithm / 233 4.5 The H-algorithm / 238 4.6 The Ford--Sidi algorithms / 244 4.7 Miscellaneous algorithms / 247 5 CONTINUOUS PREDICTION ALGORITHMS / 253 5.1 The Taylor expansion / 254 5.2 Confluent Overholt's process / 255 5.3 Confluent $epsilon $-algorithms / 256 5.4 Confluent $rho $-algorithm / 262 5.5 Confluent $G$-transform / 265 5.6 Confluent $E$-algorithm / 266 5.7 $Theta $-type confluent algorithms / 267 6 APPLICATIONS / 269 6.1 Sequences and series / 270 6.1.1 Simple sequences / 270 6.1.2 Double sequences / 278 6.1.3 Chebyshev and Fourier series / 282 6.1.4 Continued fractions / 284 6.1.5 Vector sequences / 208 6.2 Systems of equations / 302 6.2.1 Linear systems / 303 6.2.2 Projection methods / 2307 6.2.3 Regularization and penalty techniques / 309 6.2.4 Nonlinear equations / 315 6.2.5 Continuation methods / 330 6.3 Eigenelements / 332 6.3.1 Eigenvalues and eigenvectors / 333 6.3.2 Derivatives of eigensystems / 336 6.4 Integral and differential equations / 338 6.4.1 Implicit Runge--Kutta methods / 339 6.4.2 Boundary value problems / 340 6.4.3 Nonlinear methods / 346 6.4.4 Laplace transform inversion / 348 6.4.5 Partial differential equations / 352 6.5 Interpolation and approximation / 354 6.6 Statistics / 357 6.6.1 The jackknife / 358 6.6.2 ARMA models / 359 6.6.3 Monte--Carlo methods / 361 6.7 Integration and differentiation / 365 6.7.1 Acceleration of quadrature formulae / 366 6.7.2 Nonlinear quadrature formulae / 372 6.7.3 Cauchy's principal values / 373 6.7.4 Infinite integrals / 378 6.7.5 Multiple integrals / 387 6.7.6 Numerical differentiation / 389 6.8 Prediction / 5389 7 SOFTWARE / 397 7.1 Programming the algorithms / 397 7.2 Computer arithmetic / 400 73 Programs / 403 Bibliography / 413 Index / 455

rawTOC:
Preface / v \\ 1 INTRODUCTION TO THE THEORY / 1 \\ 1.1 First steps / 1 \\ 1.2 What is an extrapolation method? / 5 \\ 1.3 What is an extrapolation algorithm? / 8 \\ 1.4 Quasi-linear sequence transformations / 11 \\ 1.5 Sequence transformations as ratios of determinants / 18 \\ 1.6 Triangular recursive schemes / 21 \\ 1.7 Normal forms of the algorithms / 26 \\ 1.8 Progressive forms of the algorithms / 28 \\ 1.9 Particular rules of the algorithms / 34 \\ 1.10 Accelerability and non-accelerability / 39 \\ 1.11 Optimality / 42 \\ 1.12 Asymptotic behaviour of sequences / 47 \\ \\ 2 SCALAR EXTRAPOLATION ALGORITHMS / 55 \\ 2.1 The $E$-algorithm / 55 \\ 2.2 Richardson extrapolation process T2 \\ 2.3 The $\epsilon$-algorithm / 78 \\ 2.4 The $G$-transformation / 95 \\ 2.5 Rational extrapolation / 101 \\ 2.6 Generalizations of the $\epsilon$-algorithm / 108 \\ 2.7 Levin's transforms / 113 \\ 2.8 Overholt's process / 119 \\ 2.9 $\Theta$-type algorithms / 121 \\ 2.10 The iterated $\Delta^2$ process / 128 \\ 2.11 Miscellaneous algorithms / 131 \\ \\ 3 SPECIAL DEVICES / 145 \\ 3.1 Error estimates and acceleration / 145 \\ 3.2 Convergence tests and acceleration 151 \\ 3.3 Construction of asymptotic expansions / 159 \\ 3.4 Construction of extrapolation processes / 165 \\ 3.5 Extraction procedures / 171 \\ 3.6 Automatic selection / 178 \\ 3.7 Composite sequence transformations / 185 \\ 3.8 Error control / 193 \\ 3.9 Contractive sequence transformations / 201 \\ 3.10 Least squares extrapolation / 210 \\ \\ 4 VECTOR EXTRAPOLATION ALGORITHMS / 213 \\ 4.1 The vector $\epsilon$-algorithm / 216 \\ 4.2 The topological $\epsilon$-algorithm / 220 \\ 4.3 The vector $E$-algorithm / 228 \\ 4.4 The recursive projection algorithm / 233 \\ 4.5 The H-algorithm / 238 \\ 4.6 The Ford--Sidi algorithms / 244 \\ 4.7 Miscellaneous algorithms / 247 \\ \\ 5 CONTINUOUS PREDICTION ALGORITHMS / 253 \\ 5.1 The Taylor expansion / 254 \\ 5.2 Confluent Overholt's process / 255 \\ 5.3 Confluent $\epsilon$-algorithms / 256 \\ 5.4 Confluent $\rho$-algorithm / 262 \\ 5.5 Confluent $G$-transform / 265 \\ 5.6 Confluent $E$-algorithm / 266 \\ 5.7 $\Theta$-type confluent algorithms / 267 \\ \\ 6 APPLICATIONS / 269 \\ 6.1 Sequences and series / 270 \\ 6.1.1 Simple sequences / 270 \\ 6.1.2 Double sequences / 278 \\ 6.1.3 Chebyshev and Fourier series / 282 \\ 6.1.4 Continued fractions / 284 \\ 6.1.5 Vector sequences / 208 \\ 6.2 Systems of equations / 302 \\ 6.2.1 Linear systems / 303 \\ 6.2.2 Projection methods / 2307 \\ 6.2.3 Regularization and penalty techniques / 309 \\ 6.2.4 Nonlinear equations / 315 \\ 6.2.5 Continuation methods / 330 \\ 6.3 Eigenelements / 332 \\ 6.3.1 Eigenvalues and eigenvectors / 333 \\ 6.3.2 Derivatives of eigensystems / 336 \\ 6.4 Integral and differential equations / 338 \\ 6.4.1 Implicit Runge--Kutta methods / 339 \\ 6.4.2 Boundary value problems / 340 \\ 6.4.3 Nonlinear methods / 346 \\ 6.4.4 Laplace transform inversion / 348 \\ 6.4.5 Partial differential equations / 352 \\ 6.5 Interpolation and approximation / 354 \\ 6.6 Statistics / 357 \\ 6.6.1 The jackknife / 358 \\ 6.6.2 ARMA models / 359 \\ 6.6.3 Monte--Carlo methods / 361 \\ 6.7 Integration and differentiation / 365 \\ 6.7.1 Acceleration of quadrature formulae / 366 \\ 6.7.2 Nonlinear quadrature formulae / 372 \\ 6.7.3 Cauchy's principal values / 373 \\ 6.7.4 Infinite integrals / 378 \\ 6.7.5 Multiple integrals / 387 \\ 6.7.6 Numerical differentiation / 389 \\ 6.8 Prediction / 5389 \\ \\ 7 SOFTWARE / 397 \\ 7.1 Programming the algorithms / 397 \\ 7.2 Computer arithmetic / 400 \\ 73 Programs / 403 \\ \\ Bibliography / 413 \\ \\ Index / 455

entry:
@Book{Brezinski:1991:EMT,
  author =       "Claude Brezinski and Michela {Redivo Zaglia}",
  title =        "Extrapolation Methods: Theory and Practice",
  volume =       "2",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "ix + 464",
  year =         "1991",
  ISBN =         "0-444-88814-4",
  ISBN-13 =      "978-0-444-88814-3",
  LCCN =         "QA281 .B74 1991",
  bibdate =      "Mon May 24 09:18:52 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "Studies in computational mathematics",
  acknowledgement = ack-nhfb,
  subject =      "extrapolation; data processing",
  tableofcontents = "Preface / v \\
                 1 INTRODUCTION TO THE THEORY / 1 \\
                 1.1 First steps / 1 \\
                 1.2 What is an extrapolation method? / 5 \\
                 1.3 What is an extrapolation algorithm? / 8 \\
                 1.4 Quasi-linear sequence transformations / 11 \\
                 1.5 Sequence transformations as ratios of determinants
                 / 18 \\
                 1.6 Triangular recursive schemes / 21 \\
                 1.7 Normal forms of the algorithms / 26 \\
                 1.8 Progressive forms of the algorithms / 28 \\
                 1.9 Particular rules of the algorithms / 34 \\
                 1.10 Accelerability and non-accelerability / 39 \\
                 1.11 Optimality / 42 \\
                 1.12 Asymptotic behaviour of sequences / 47 \\
                 \\
                 2 SCALAR EXTRAPOLATION ALGORITHMS / 55 \\
                 2.1 The $E$-algorithm / 55 \\
                 2.2 Richardson extrapolation process T2 \\
                 2.3 The $\epsilon$-algorithm / 78 \\
                 2.4 The $G$-transformation / 95 \\
                 2.5 Rational extrapolation / 101 \\
                 2.6 Generalizations of the $\epsilon$-algorithm / 108
                 \\
                 2.7 Levin's transforms / 113 \\
                 2.8 Overholt's process / 119 \\
                 2.9 $\Theta$-type algorithms / 121 \\
                 2.10 The iterated $\Delta^2$ process / 128 \\
                 2.11 Miscellaneous algorithms / 131 \\
                 \\
                 3 SPECIAL DEVICES / 145 \\
                 3.1 Error estimates and acceleration / 145 \\
                 3.2 Convergence tests and acceleration 151 \\
                 3.3 Construction of asymptotic expansions / 159 \\
                 3.4 Construction of extrapolation processes / 165 \\
                 3.5 Extraction procedures / 171 \\
                 3.6 Automatic selection / 178 \\
                 3.7 Composite sequence transformations / 185 \\
                 3.8 Error control / 193 \\
                 3.9 Contractive sequence transformations / 201 \\
                 3.10 Least squares extrapolation / 210 \\
                 \\
                 4 VECTOR EXTRAPOLATION ALGORITHMS / 213 \\
                 4.1 The vector $\epsilon$-algorithm / 216 \\
                 4.2 The topological $\epsilon$-algorithm / 220 \\
                 4.3 The vector $E$-algorithm / 228 \\
                 4.4 The recursive projection algorithm / 233 \\
                 4.5 The H-algorithm / 238 \\
                 4.6 The Ford--Sidi algorithms / 244 \\
                 4.7 Miscellaneous algorithms / 247 \\
                 \\
                 5 CONTINUOUS PREDICTION ALGORITHMS / 253 \\
                 5.1 The Taylor expansion / 254 \\
                 5.2 Confluent Overholt's process / 255 \\
                 5.3 Confluent $\epsilon$-algorithms / 256 \\
                 5.4 Confluent $\rho$-algorithm / 262 \\
                 5.5 Confluent $G$-transform / 265 \\
                 5.6 Confluent $E$-algorithm / 266 \\
                 5.7 $\Theta$-type confluent algorithms / 267 \\
                 \\
                 6 APPLICATIONS / 269 \\
                 6.1 Sequences and series / 270 \\
                 6.1.1 Simple sequences / 270 \\
                 6.1.2 Double sequences / 278 \\
                 6.1.3 Chebyshev and Fourier series / 282 \\
                 6.1.4 Continued fractions / 284 \\
                 6.1.5 Vector sequences / 208 \\
                 6.2 Systems of equations / 302 \\
                 6.2.1 Linear systems / 303 \\
                 6.2.2 Projection methods / 2307 \\
                 6.2.3 Regularization and penalty techniques / 309 \\
                 6.2.4 Nonlinear equations / 315 \\
                 6.2.5 Continuation methods / 330 \\
                 6.3 Eigenelements / 332 \\
                 6.3.1 Eigenvalues and eigenvectors / 333 \\
                 6.3.2 Derivatives of eigensystems / 336 \\
                 6.4 Integral and differential equations / 338 \\
                 6.4.1 Implicit Runge--Kutta methods / 339 \\
                 6.4.2 Boundary value problems / 340 \\
                 6.4.3 Nonlinear methods / 346 \\
                 6.4.4 Laplace transform inversion / 348 \\
                 6.4.5 Partial differential equations / 352 \\
                 6.5 Interpolation and approximation / 354 \\
                 6.6 Statistics / 357 \\
                 6.6.1 The jackknife / 358 \\
                 6.6.2 ARMA models / 359 \\
                 6.6.3 Monte--Carlo methods / 361 \\
                 6.7 Integration and differentiation / 365 \\
                 6.7.1 Acceleration of quadrature formulae / 366 \\
                 6.7.2 Nonlinear quadrature formulae / 372 \\
                 6.7.3 Cauchy's principal values / 373 \\
                 6.7.4 Infinite integrals / 378 \\
                 6.7.5 Multiple integrals / 387 \\
                 6.7.6 Numerical differentiation / 389 \\
                 6.8 Prediction / 5389 \\
                 \\
                 7 SOFTWARE / 397 \\
                 7.1 Programming the algorithms / 397 \\
                 7.2 Computer arithmetic / 400 \\
                 73 Programs / 403 \\
                 \\
                 Bibliography / 413 \\
                 \\
                 Index / 455",
}


bibtype: article
filename: elefunt.bib
label: Bunch:1991:DFA
author: K. J. Bunch and W. N. Cain and R. W. Grow
title: A data fitting approach to series convergence acceleration
journal: j-APPL-MATH-COMP
volume: 42
number: 2 (part II)
pages: 189--195
year: 1991
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/0096-3003(91)90050-W
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
MRclass: 65B10 (65D10)
MRnumber: 1094414 (91k:65015)
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
fjournal: Applied Mathematics and Computation
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: K. J. Bunch and W. N. Cain and R. W. Grow
rawtitle: A data fitting approach to series convergence acceleration
entry:
@Article{Bunch:1991:DFA,
  author =       "K. J. Bunch and W. N. Cain and R. W. Grow",
  title =        "A data fitting approach to series convergence
                 acceleration",
  journal =      j-APPL-MATH-COMP,
  volume =       "42",
  number =       "2 (part II)",
  pages =        "189--195",
  month =        "????",
  year =         "1991",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/0096-3003(91)90050-W",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  MRclass =      "65B10 (65D10)",
  MRnumber =     "1094414 (91k:65015)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1991:TEI
author: B. C. Carlson
title: A table of elliptic integrals: One quadratic factor
journal: j-MATH-COMPUT
volume: 56
number: 193
pages: 267--280
month: jan
monthnumber: 1
year: 1991
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33E05 (65A05)
MRnumber: 92b:33056
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
corpsource: Dept. of Math., Iowa State Univ., Ames, IA, USA
journalURL: http://www.ams.org/mcom/
treatment: P Practical
rawauthor: B. C. Carlson
rawtitle: A table of elliptic integrals: {One} quadratic factor
keywords:
conjugate complex zeros; elliptic integrals; Fortran programs; integral equations; integration; polynomial; R-functions; square root

classcodes:
B0290R (Integral equations); B0290M (Numerical integration and differentiation); C4180 (Integral equations); C4160 (Numerical integration and differentiation)

entry:
@Article{Carlson:1991:TEI,
  author =       "B. C. Carlson",
  title =        "A table of elliptic integrals: {One} quadratic
                 factor",
  journal =      j-MATH-COMPUT,
  volume =       "56",
  number =       "193",
  pages =        "267--280",
  month =        jan,
  year =         "1991",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33E05 (65A05)",
  MRnumber =     "92b:33056",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290R (Integral equations); B0290M (Numerical
                 integration and differentiation); C4180 (Integral
                 equations); C4160 (Numerical integration and
                 differentiation)",
  corpsource =   "Dept. of Math., Iowa State Univ., Ames, IA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "conjugate complex zeros; elliptic integrals; Fortran
                 programs; integral equations; integration; polynomial;
                 R-functions; square root",
  treatment =    "P Practical",
}


bibtype: techreport
filename: elefunt.bib
label: Cody:1991:CPT
author: W. J. Cody
title: CELEFUNT: a Portable Test Package for Complex Elementary Functions
type: Technical Report
number: ANL-91/1
institution: inst-ANL
address: inst-ANL:adr
pages: iii + 21
month: jan
monthnumber: 1
year: 1991
bibdate: Fri Sep 23 23:39:07 1994
bibtimestamp: 1994.09.23 23:39:07 ???
acknowledgement: ack-nhfb
rawauthor: W. J. Cody
rawtitle: {CELEFUNT}: a Portable Test Package for Complex Elementary Functions
entry:
@TechReport{Cody:1991:CPT,
  author =       "W. J. Cody",
  title =        "{CELEFUNT}: a Portable Test Package for Complex
                 Elementary Functions",
  type =         "Technical Report",
  number =       "ANL-91/1",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  pages =        "iii + 21",
  month =        jan,
  year =         "1991",
  bibdate =      "Fri Sep 23 23:39:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Corless:1991:NEA
author: R. M. Corless and D. J. Jeffrey and H. Rasmussen
title: Numerical evaluation of Airy functions with complex arguments
journal: j-J-COMPUT-PHYS
volume: 93
number: 1
pages: 252--253
month: mar
monthnumber: 3
year: 1991
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(91)90089-4
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Mon Jan 2 07:55:47 MST 2012
bibtimestamp: 2012.01.02 07:55:47 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999191900894
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: R. M. Corless and D. J. Jeffrey and H. Rasmussen
rawtitle: Numerical evaluation of {Airy} functions with complex arguments
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib

entry:
@Article{Corless:1991:NEA,
  author =       "R. M. Corless and D. J. Jeffrey and H. Rasmussen",
  title =        "Numerical evaluation of {Airy} functions with complex
                 arguments",
  journal =      j-J-COMPUT-PHYS,
  volume =       "93",
  number =       "1",
  pages =        "252--253",
  month =        mar,
  year =         "1991",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(91)90089-4",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:55:47 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999191900894",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Crenshaw:1991:SRS
author: J. W. Crenshaw
title: Square roots are simple?
journal: j-EMBED-SYS-PROG
volume: 4
number: 11
pages: 30--52
month: nov
monthnumber: 11
year: 1991
CODEN: EYPRE4
ISSN: 1040-3272 OR 10403272
bibdate: Wed Sep 14 19:14:52 1994
bibtimestamp: 1994.09.14 19:14:52 ???
fjournal: Embedded Systems Programming
acknowledgement: ack-nj
rawauthor: J. W. Crenshaw
rawtitle: Square roots are simple?
entry:
@Article{Crenshaw:1991:SRS,
  author =       "J. W. Crenshaw",
  title =        "Square roots are simple?",
  journal =      j-EMBED-SYS-PROG,
  volume =       "4",
  number =       "11",
  pages =        "30--52",
  month =        nov,
  year =         "1991",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Wed Sep 14 19:14:52 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Embedded Systems Programming",
}


bibtype: article
filename: elefunt.bib
label: DeDoelder:1991:SSC
author: P. J. De Doelder
journal: j-J-COMPUT-APPL-MATH
volume: 37
number: 1--3
pages: 125--141
day: 18
month: nov
monthnumber: 11
year: 1991
CODEN: JCAMDI
DOI: https://doi.org/10.1016/0377-0427(91)90112-W
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:02:22 MST 2017
bibtimestamp: 2017.02.25 13:02:22 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279190112W
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: P. J. {De Doelder}
title:
On some series containing $ psi (x) - psi (y >) $ and $ (psi (x) - psi (y >))^2 $ for certain values of $x$ and $y$

rawtitle:
On some series containing $ \psi (x) - \psi (y >) $ and $ (\psi (x) - \psi (y >))^2 $ for certain values of $x$ and $y$

entry:
@Article{DeDoelder:1991:SSC,
  author =       "P. J. {De Doelder}",
  title =        "On some series containing $ \psi (x) - \psi (y >) $
                 and $ (\psi (x) - \psi (y >))^2 $ for certain values of
                 $x$ and $y$",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "37",
  number =       "1--3",
  pages =        "125--141",
  day =          "18",
  month =        nov,
  year =         "1991",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(91)90112-W",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:02:22 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279190112W",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Dritz:1991:IPS
author: Kenneth W. Dritz
title: Introduction to the proposed standard for the elementary functions in Ada
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 3--8
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Mar 20 07:41:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.20 07:41:09 MST
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
classcodes: C6140D (High level languages); C7310 (Mathematics)
corpsource: Dept. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: Kenneth W. Dritz
rawtitle: Introduction to the proposed standard for the elementary functions in {Ada}
keywords:
Ada; committees; elementary functions; generic package; ISO standard; mathematics computing; secondary; standards

entry:
@Article{Dritz:1991:IPS,
  author =       "Kenneth W. Dritz",
  title =        "Introduction to the proposed standard for the
                 elementary functions in {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "3--8",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics)",
  corpsource =   "Dept. of Math. and Comput. Sci., Argonne Nat. Lab.,
                 IL, USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; committees; elementary functions; generic
                 package; ISO standard; mathematics computing;
                 secondary; standards",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Dritz:1991:PSGa
author: K. W. Dritz
title: Proposed standard for a generic package of elementary functions for Ada
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 9--46
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Mar 20 07:41:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.20 07:41:09 MST
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
classcodes: C6140D (High level languages); C6110B (Software engineering techniques); C7310 (Mathematics)
corpsource: Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: K. W. Dritz
rawtitle: Proposed standard for a generic package of elementary functions for {Ada}
keywords:
ACM SIGAda Numerics Working; Ada; Ada-Europe Numerics Working Group; basic; elementary functions; ELEMENTARY-FUNCTIONS-; EXCEPTIONS; generic package; GENERIC-ELEMENTARY-FUNCTIONS; Group; international standard; joint proposal; mathematical routines; mathematics computing; NRG; Rapporteur Group; reusable applications; SC22; software reusability; specification; standards; WG9 Numerics

entry:
@Article{Dritz:1991:PSGa,
  author =       "K. W. Dritz",
  title =        "Proposed standard for a generic package of elementary
                 functions for {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "9--46",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C6110B (Software
                 engineering techniques); C7310 (Mathematics)",
  corpsource =   "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "ACM SIGAda Numerics Working; Ada; Ada-Europe Numerics
                 Working Group; basic; elementary functions;
                 ELEMENTARY-FUNCTIONS-; EXCEPTIONS; generic package;
                 GENERIC-ELEMENTARY-FUNCTIONS; Group; international
                 standard; joint proposal; mathematical routines;
                 mathematics computing; NRG; Rapporteur Group; reusable
                 applications; SC22; software reusability;
                 specification; standards; WG9 Numerics",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Dritz:1991:PSGb
author: K. W. Dritz
title: Proposed standard for a generic package of primitive functions for Ada
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 66--82
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Mar 20 07:41:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.20 07:41:09 MST
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
classcodes: C6140D (High level languages); C7310 (Mathematics)
corpsource: Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: K. W. Dritz
rawtitle: Proposed standard for a generic package of primitive functions for {Ada}
keywords:
Ada; compliable Ada; elementary functions; generic package; GENERIC-; mathematical; mathematics computing; primitive functions; primitive operations; PRIMITIVE-FUNCTIONS; software; specification; standards

entry:
@Article{Dritz:1991:PSGb,
  author =       "K. W. Dritz",
  title =        "Proposed standard for a generic package of primitive
                 functions for {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "66--82",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics)",
  corpsource =   "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; compliable Ada; elementary functions; generic
                 package; GENERIC-; mathematical; mathematics computing;
                 primitive functions; primitive operations;
                 PRIMITIVE-FUNCTIONS; software; specification;
                 standards",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Dritz:1991:RPS
author: K. W. Dritz
title: Rationale for the proposed standard for a generic package of elementary functions for Ada
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 47--65
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Mar 20 07:41:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.20 07:41:09 MST
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
classcodes: C6140D (High level languages); C7310 (Mathematics); C6110 (Systems analysis and programming)
corpsource: Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: K. W. Dritz
rawtitle: Rationale for the proposed standard for a generic package of elementary functions for {Ada}
keywords:
ACM SIGAda Numerics Working Group; Ada; Ada-Europe Numerics; collateral; elementary functions standard; mathematics computing; numerical software; portability; programming; robustness; standards; Working Group

entry:
@Article{Dritz:1991:RPS,
  author =       "K. W. Dritz",
  title =        "Rationale for the proposed standard for a generic
                 package of elementary functions for {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "47--65",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics);
                 C6110 (Systems analysis and programming)",
  corpsource =   "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "ACM SIGAda Numerics Working Group; Ada; Ada-Europe
                 Numerics; collateral; elementary functions standard;
                 mathematics computing; numerical software; portability;
                 programming; robustness; standards; Working Group",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Duprat:1991:WND
author: J. Duprat and J.-M. Muller
title: Writing numbers differently for faster calculation
journal: j-TECHNIQUE-SCI-INFORMATIQUES
volume: 10
number: 3
pages: 211--224
year: 1991
CODEN: TTSIDJ
ISSN: 0752-4072, 0264-7419 OR 07524072, 02647419
ISSNL: 0752-4072 OR 07524072
bibdate: Tue Dec 12 09:20:21 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.12 09:20:21 MST
fjournal: Technique et science informatiques : TSI
language: French
acknowledgement: ack-nhfb
affiliation: Ecole Normale Superieure de Lyon, France
thesaurus: Digital arithmetic
rawauthor: J. Duprat and J.-M. Muller
rawtitle: Writing numbers differently for faster calculation
abstract:
Instead of Avizienis' or the carry save methods a borrow save (BS) notation is proposed. Examples are given of BS addition, subtraction, shifting and multiplication with the necessary elementary cells being proposed and circuits for testing zero and sign being described. Floating point arithmetic is explained, involving pseudo normalisation and applications are covered including the Cordic algorithm.

keywords:
Addition; Borrow save; Carry save methods; Cordic algorithm; Floating point arithmetic; Multiplication; Pseudo normalisation; Shifting; Subtraction; Zero

rawabstract:
Instead of Avizienis' or the carry save methods a borrow save (BS) notation is proposed. Examples are given of BS addition, subtraction, shifting and multiplication with the necessary elementary cells being proposed and circuits for testing zero and sign being described. Floating point arithmetic is explained, involving pseudo normalisation and applications are covered including the Cordic algorithm.

entry:
@Article{Duprat:1991:WND,
  author =       "J. Duprat and J.-M. Muller",
  title =        "Writing numbers differently for faster calculation",
  journal =      j-TECHNIQUE-SCI-INFORMATIQUES,
  volume =       "10",
  number =       "3",
  pages =        "211--224",
  month =        "????",
  year =         "1991",
  CODEN =        "TTSIDJ",
  ISSN =         "0752-4072, 0264-7419",
  ISSN-L =       "0752-4072",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Instead of Avizienis' or the carry save methods a
                 borrow save (BS) notation is proposed. Examples are
                 given of BS addition, subtraction, shifting and
                 multiplication with the necessary elementary cells
                 being proposed and circuits for testing zero and sign
                 being described. Floating point arithmetic is
                 explained, involving pseudo normalisation and
                 applications are covered including the Cordic
                 algorithm.",
  acknowledgement = ack-nhfb,
  affiliation =  "Ecole Normale Superieure de Lyon, France",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Technique et science informatiques : TSI",
  keywords =     "Addition; Borrow save; Carry save methods; Cordic
                 algorithm; Floating point arithmetic; Multiplication;
                 Pseudo normalisation; Shifting; Subtraction; Zero",
  language =     "French",
  pubcountry =   "France",
  thesaurus =    "Digital arithmetic",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ferguson:1991:AMA
author: Warren E. Ferguson, Jr. and Tom Brightman
title: Accurate and Monotone Approximations of Some Transcendental Functions
crossref: Kornerup:1991:PIS
pages: 237--244
year: 1991
DOI: https://doi.org/10.1109/ARITH.1991.145566
bibdate: Sat Nov 27 12:40:58 MST 2004
bibtimestamp: 2004.11.27 12:40:58 MST
URL: https://ieeexplore.ieee.org/document/145566
keywords: CORDIC algorithms
acknowledgement: ack-nj
rawauthor: Warren E. {Ferguson, Jr.} and Tom Brightman
rawtitle: Accurate and Monotone Approximations of Some Transcendental Functions
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

remark:
From page. 237: ``For example, an approximation of the sine function on $ [ - pi / 4, pi / 4] $ that is accurate to 66 bits of precision will necessarily be monotonic when rounded to 64 bits of precision. We have used this technique to establish the monotonicity of a Cyrix FasMath coprocessor's polynomial based approximations of transcendental functions [2]. Since this technique does not depend on how the approximation is determined, then it also can be applied to approximations derived by other means, e.g.,, CORDIC based approximations.''

entry:
@InProceedings{Ferguson:1991:AMA,
  author =       "Warren E. {Ferguson, Jr.} and Tom Brightman",
  title =        "Accurate and Monotone Approximations of Some
                 Transcendental Functions",
  crossref =     "Kornerup:1991:PIS",
  pages =        "237--244",
  year =         "1991",
  DOI =          "https://doi.org/10.1109/ARITH.1991.145566",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://ieeexplore.ieee.org/document/145566",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "CORDIC algorithms",
  remark =       "From page. 237: ``For example, an approximation of the
                 sine function on $ [ - \pi / 4, \pi / 4] $ that is
                 accurate to 66 bits of precision will necessarily be
                 monotonic when rounded to 64 bits of precision. We have
                 used this technique to establish the monotonicity of a
                 Cyrix FasMath coprocessor's polynomial based
                 approximations of transcendental functions [2]. Since
                 this technique does not depend on how the approximation
                 is determined, then it also can be applied to
                 approximations derived by other means, e.g.,, CORDIC
                 based approximations.''",
}


bibtype: article
filename: elefunt.bib
label: Gal:1991:AEM
author: Shmuel Gal and Boris Bachelis
title: An Accurate Elementary Mathematical Library for the IEEE Floating Point Standard
journal: j-TOMS
volume: 17
number: 1
pages: 26--45
month: mar
monthnumber: 3
year: 1991
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D20 (65-04 65D15)
MRnumber: 92a:65069
bibdate: Sun Sep 04 23:33:02 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.04 23:33:02 ???
URL: http://www.acm.org/pubs/toc/Abstracts/toms/103151.html
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; theory
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Shmuel Gal and Boris Bachelis
rawtitle: An Accurate Elementary Mathematical Library for the {IEEE} Floating Point Standard
abstract:
The algorithms used by the IBM Israel Scientific Center for the elementary mathematical library using the IEEE standard for binary floating point arithmetic are described. The algorithms are based on the ``accurate tables method.'' This methodology achieves high performance and produces very accurate results. It overcomes one of the main problems encountered in elementary mathematical functions computations: achieving last bit accuracy. The results obtained are correctly rounded for almost all argument values. par Our main idea in the accurate tables method is to use ``nonstandard tables,'' which are different from the natural tables of equally spaced points in which the rounding error prevents obtaining last bit accuracy. In order to achieve a small error we use the following idea: Perturb the original, equally spaced, points in such a way that the table value (or tables values in case we need several tables) will be very close to numbers which can be exactly represented by the computer (much closer than the usual double precision representation). Thus we were able to control the error introduced by the computer representation of real numbers and extended the accuracy without actually using extended precision arithmetic.

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation.

rawabstract:
The algorithms used by the IBM Israel Scientific Center for the elementary mathematical library using the IEEE standard for binary floating point arithmetic are described. The algorithms are based on the ``accurate tables method.'' This methodology achieves high performance and produces very accurate results. It overcomes one of the main problems encountered in elementary mathematical functions computations: achieving last bit accuracy. The results obtained are correctly rounded for almost all argument values. \par Our main idea in the accurate tables method is to use ``nonstandard tables,'' which are different from the natural tables of equally spaced points in which the rounding error prevents obtaining last bit accuracy. In order to achieve a small error we use the following idea: Perturb the original, equally spaced, points in such a way that the table value (or tables values in case we need several tables) will be very close to numbers which can be exactly represented by the computer (much closer than the usual double precision representation). Thus we were able to control the error introduced by the computer representation of real numbers and extended the accuracy without actually using extended precision arithmetic.

entry:
@Article{Gal:1991:AEM,
  author =       "Shmuel Gal and Boris Bachelis",
  title =        "An Accurate Elementary Mathematical Library for the
                 {IEEE} Floating Point Standard",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "26--45",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65-04 65D15)",
  MRnumber =     "92a:65069",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/toms/103151.html",
  abstract =     "The algorithms used by the IBM Israel Scientific
                 Center for the elementary mathematical library using
                 the IEEE standard for binary floating point arithmetic
                 are described. The algorithms are based on the
                 ``accurate tables method.'' This methodology achieves
                 high performance and produces very accurate results. It
                 overcomes one of the main problems encountered in
                 elementary mathematical functions computations:
                 achieving last bit accuracy. The results obtained are
                 correctly rounded for almost all argument values.
                 \par

                 Our main idea in the accurate tables method is to use
                 ``nonstandard tables,'' which are different from the
                 natural tables of equally spaced points in which the
                 rounding error prevents obtaining last bit accuracy. In
                 order to achieve a small error we use the following
                 idea: Perturb the original, equally spaced, points in
                 such a way that the table value (or tables values in
                 case we need several tables) will be very close to
                 numbers which can be exactly represented by the
                 computer (much closer than the usual double precision
                 representation). Thus we were able to control the error
                 introduced by the computer representation of real
                 numbers and extended the accuracy without actually
                 using extended precision arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation.",
}


bibtype: article
filename: elefunt.bib
label: Gray:1991:GMA
author: H. L. Gray and Suojin Wang
title: A General Method for Approximating Tail Probabilities
journal: j-J-AM-STAT-ASSOC
volume: 86
number: 413
pages: 159--166
month: mar
monthnumber: 3
year: 1991
CODEN: JSTNAL
ISSN: 0162-1459 (print), 1537-274X (electronic) OR 01621459 (print), 1537274X (electronic)
ISSNL: 0162-1459 OR 01621459
bibdate: Wed Jan 25 08:06:12 MST 2012
bibtimestamp: 2012.01.25 08:06:12 MST
URL: http://www.jstor.org/stable/2289726
fjournal: Journal of the American Statistical Association
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/uasa20
rawauthor: H. L. Gray and Suojin Wang
rawtitle: A General Method for Approximating Tail Probabilities
bibsource:
http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314297; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1990.bib

entry:
@Article{Gray:1991:GMA,
  author =       "H. L. Gray and Suojin Wang",
  title =        "A General Method for Approximating Tail
                 Probabilities",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "86",
  number =       "413",
  pages =        "159--166",
  month =        mar,
  year =         "1991",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:06:12 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314297;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1990.bib",
  URL =          "http://www.jstor.org/stable/2289726",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}


bibtype: inproceedings
filename: elefunt.bib
label: Gustafson:1991:CAA
author: Sven-AA ke Gustafson and Frank Stenger
crossref: Bowers:1991:CCI
pages: 161--171
year: 1991
MRclass: 41A30 (93B40)
MRnumber: MR1140021
bibdate: Thu May 10 16:31:10 2007
bibtimestamp: 2007.05.10 16:31:10 ???
keywords: Chebyshev acceleration; convergence acceleration
ZMnumber: 0746.41034
acknowledgement: ack-nhfb
reviewer: Zhang Ganglu (Dongying)
rawauthor: Sven-{\AA}ke Gustafson and Frank Stenger
title:
Convergence acceleration applied to Sinc approximation with application to approximation of $ |x|^alpha $

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

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 $.

rawabstract:
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 $.

rawtitle:
Convergence acceleration applied to {Sinc} approximation with application to approximation of $ |x|^\alpha $

entry:
@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",
  MRclass =      "41A30 (93B40)",
  MRnumber =     "MR1140021",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.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; convergence acceleration",
  reviewer =     "Zhang Ganglu (Dongying)",
}


bibtype: article
filename: elefunt.bib
label: Hamza:1991:MBD
author: K. M. Hamza and M. A. H. Abdul-Karim
title: Microprocessor Based Direct Square Root Extractor
journal: Modelling
volume: 34
number: 1
pages: 45--48
year: 1991
bibdate: Thu Sep 1 10:15:42 1994
bibtimestamp: 1994.09.01 10:15:42 ???
acknowledgement: ack-nj
rawauthor: K. M. Hamza and M. A. H. Abdul-Karim
rawtitle: Microprocessor Based Direct Square Root Extractor
entry:
@Article{Hamza:1991:MBD,
  author =       "K. M. Hamza and M. A. H. Abdul-Karim",
  title =        "Microprocessor Based Direct Square Root Extractor",
  journal =      "Modelling",
  volume =       "34",
  number =       "1",
  pages =        "45--48",
  month =        "????",
  year =         "1991",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Ifantis:1991:PZS
author: E. K. Ifantis and C. G. Kokologiannaki and C. B. Kouris
title: On the positive zeros of the second derivative of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 34
number: 1
pages: 21--31
day: 10
month: feb
monthnumber: 2
year: 1991
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:20:48 MST 2017
bibtimestamp: 2017.02.25 12:20:48 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042791901449
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: E. K. Ifantis and C. G. Kokologiannaki and C. B. Kouris
rawtitle: On the positive zeros of the second derivative of {Bessel} functions
entry:
@Article{Ifantis:1991:PZS,
  author =       "E. K. Ifantis and C. G. Kokologiannaki and C. B.
                 Kouris",
  title =        "On the positive zeros of the second derivative of
                 {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "34",
  number =       "1",
  pages =        "21--31",
  day =          "10",
  month =        feb,
  year =         "1991",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042791901449",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Ikebe:1991:CZO
author: Yasuhiko Ikebe and Yasushi Kikuchi and Issei Fujishiro
title: Computing zeros and orders of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 38
number: 1--3
pages: 169--184
day: 23
month: dec
monthnumber: 12
year: 1991
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:02:23 MST 2017
bibtimestamp: 2017.02.25 13:02:23 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279190169K
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Yasuhiko Ikebe and Yasushi Kikuchi and Issei Fujishiro
rawtitle: Computing zeros and orders of {Bessel} functions
entry:
@Article{Ikebe:1991:CZO,
  author =       "Yasuhiko Ikebe and Yasushi Kikuchi and Issei
                 Fujishiro",
  title =        "Computing zeros and orders of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "38",
  number =       "1--3",
  pages =        "169--184",
  day =          "23",
  month =        dec,
  year =         "1991",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:02:23 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279190169K",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Iserles:1991:CDC
author: A. Iserles
title: Complex dynamics of convergence acceleration
journal: j-IMA-J-NUMER-ANAL
volume: 11
number: 2
pages: 205--240
year: 1991
CODEN: IJNADH
ISSN: 0272-4979 (print), 1464-3642 (electronic) OR 02724979 (print), 14643642 (electronic)
ISSNL: 0272-4979 OR 02724979
MRclass: 65B05 (65E05)
MRnumber: 92h:65006
bibdate: Sat Dec 23 17:06:35 MST 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; MathSciNet database
bibtimestamp: 2000.12.23 17:06:35 MST
fjournal: IMA Journal of Numerical Analysis
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://imajna.oxfordjournals.org/content/by/year
rawauthor: A. Iserles
rawtitle: Complex dynamics of convergence acceleration
entry:
@Article{Iserles:1991:CDC,
  author =       "A. Iserles",
  title =        "Complex dynamics of convergence acceleration",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "11",
  number =       "2",
  pages =        "205--240",
  year =         "1991",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65B05 (65E05)",
  MRnumber =     "92h:65006",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Laforgia:1991:BMB
author: Andrea Laforgia
title: Bounds for modified Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 34
number: 3
pages: 263--267
day: 26
month: apr
monthnumber: 4
year: 1991
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:20:49 MST 2017
bibtimestamp: 2017.02.25 12:20:49 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279190087Z
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Andrea Laforgia
rawtitle: Bounds for modified {Bessel} functions
entry:
@Article{Laforgia:1991:BMB,
  author =       "Andrea Laforgia",
  title =        "Bounds for modified {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "34",
  number =       "3",
  pages =        "263--267",
  day =          "26",
  month =        apr,
  year =         "1991",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:49 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279190087Z",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Levrie:1991:CAF
author: Paul Levrie
title: Convergence acceleration for $n$-fractions
journal: j-APPL-NUM-MATH
volume: 7
number: 6
pages: 481--492
month: jun
monthnumber: 6
year: 1991
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
MRclass: 40A15 (65B05)
MRnumber: 92k:40001
MRreviewer: Claude Brezinski
bibdate: Sat Feb 8 10:09:54 MST 1997
bibtimestamp: 1997.02.08 10:09:54 MST
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: Paul Levrie
rawtitle: Convergence acceleration for $n$-fractions
bibsource:
https://www.math.utah.edu/pub/tex/bib/applnummath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Levrie:1991:CAF,
  author =       "Paul Levrie",
  title =        "Convergence acceleration for $n$-fractions",
  journal =      j-APPL-NUM-MATH,
  volume =       "7",
  number =       "6",
  pages =        "481--492",
  month =        jun,
  year =         "1991",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "40A15 (65B05)",
  MRnumber =     "92k:40001",
  MRreviewer =   "Claude Brezinski",
  bibdate =      "Sat Feb 8 10:09:54 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Levrie:1991:CFC
author: Paul Levrie
journal: j-APPL-NUM-MATH
volume: 8
number: 3
pages: 225--242
month: oct
monthnumber: 10
year: 1991
CODEN: ANMAEL
DOI: https://doi.org/10.1090/surv/037
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
MRclass: 65B99 (65Q05)
MRnumber: 92m:65012
MRreviewer: J. Albrycht
bibdate: Sat Feb 8 10:09:54 MST 1997
bibtimestamp: 1997.02.08 10:09:54 MST
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: Paul Levrie
title:
$ G $-continued fractions and convergence acceleration in the solution of third-order linear recurrence relations of Poincare type

rawtitle:
$ {G} $-continued fractions and convergence acceleration in the solution of third-order linear recurrence relations of {Poincar{\'e}} type

entry:
@Article{Levrie:1991:CFC,
  author =       "Paul Levrie",
  title =        "$ {G} $-continued fractions and convergence
                 acceleration in the solution of third-order linear
                 recurrence relations of {Poincar{\'e}} type",
  journal =      j-APPL-NUM-MATH,
  volume =       "8",
  number =       "3",
  pages =        "225--242",
  month =        oct,
  year =         "1991",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1090/surv/037",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65B99 (65Q05)",
  MRnumber =     "92m:65012",
  MRreviewer =   "J. Albrycht",
  bibdate =      "Sat Feb 8 10:09:54 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lyons:1991:FMF
author: Ken Lyons
title: A fast method for finding an integer square root
crossref: Koopman:1991:PST
pages: 27--30
year: 1991
bibdate: Tue May 4 05:57:50 MDT 1999
bibtimestamp: 1999.05.04 05:57:50 MDT
URL: http://www.acm.org:80/pubs/citations/proceedings/plan/259965/p27-lyons/
acknowledgement: ack-nhfb
rawauthor: Ken Lyons
rawtitle: A fast method for finding an integer square root
bibsource:
http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@InProceedings{Lyons:1991:FMF,
  author =       "Ken Lyons",
  title =        "A fast method for finding an integer square root",
  crossref =     "Koopman:1991:PST",
  pages =        "27--30",
  year =         "1991",
  bibdate =      "Tue May 4 05:57:50 MDT 1999",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/plan/259965/p27-lyons/",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Markstein:1991:WFF
author: V. Markstein and P. Markstein and T. Nguyen and S. Poole
title: Wide Format Floating-Point Math Libraries
crossref: IEEE:1991:PSA
pages: 130--138
year: 1991
bibdate: Wed Dec 13 18:34:51 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.13 18:34:51 ???
acknowledgement: ack-nhfb
affiliation: ISQUARE, Inc., Austin, TX, USA
thesaurus: Digital arithmetic; Mathematics computing; Parallel processing; Performance evaluation
rawauthor: V. Markstein and P. Markstein and T. Nguyen and S. Poole
rawtitle: Wide Format Floating-Point Math Libraries
abstract:
The authors present the performance and accuracy evaluations of eleven transcendental functions found in 64- and 128-bit floating-point formats in math libraries on the Cray Y-MP, the IBM 3090E/VF, the Convex C-240, the Hewlett--Packard 9000/720, and the IBM System/6000. Both architecture and algorithms are shown to impact the results.

keywords:
128 Bit; 64 Bit; Accuracy evaluations; Convex C-240; Cray Y-MP; Floating-point formats; Hewlett--Packard 9000/720; IBM 3090E/VF; IBM System/6000; Math libraries; Performance; Transcendental functions; Wide format floating point math libraries

rawabstract:
The authors present the performance and accuracy evaluations of eleven transcendental functions found in 64- and 128-bit floating-point formats in math libraries on the Cray Y-MP, the IBM 3090E/VF, the Convex C-240, the Hewlett--Packard 9000/720, and the IBM System/6000. Both architecture and algorithms are shown to impact the results.

entry:
@InProceedings{Markstein:1991:WFF,
  author =       "V. Markstein and P. Markstein and T. Nguyen and S.
                 Poole",
  title =        "Wide Format Floating-Point Math Libraries",
  crossref =     "IEEE:1991:PSA",
  pages =        "130--138",
  year =         "1991",
  bibdate =      "Wed Dec 13 18:34:51 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The authors present the performance and accuracy
                 evaluations of eleven transcendental functions found in
                 64- and 128-bit floating-point formats in math
                 libraries on the Cray Y-MP, the IBM 3090E/VF, the
                 Convex C-240, the Hewlett--Packard 9000/720, and the
                 IBM System/6000. Both architecture and algorithms are
                 shown to impact the results.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "ISQUARE, Inc., Austin, TX, USA",
  classification = "C5230 (Digital arithmetic methods); C5470
                 (Performance evaluation and testing); C7310
                 (Mathematics)",
  confdate =     "18-22 Nov. 1991",
  conflocation = "Albuquerque, NM, USA",
  confsponsor =  "IEEE; ACM",
  keywords =     "128 Bit; 64 Bit; Accuracy evaluations; Convex C-240;
                 Cray Y-MP; Floating-point formats; Hewlett--Packard
                 9000/720; IBM 3090E/VF; IBM System/6000; Math
                 libraries; Performance; Transcendental functions; Wide
                 format floating point math libraries",
  numericalindex = "Word length 6.4E+01 bit; Word length 1.28E+02 bit",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Mathematics computing; Parallel
                 processing; Performance evaluation",
}


bibtype: article
filename: elefunt.bib
label: Maximon:1991:EIP
author: Leonard C. Maximon
title: On the evaluation of the integral over the product of two spherical Bessel functions
journal: j-J-MATH-PHYS
volume: 32
number: 3
pages: 642--648
month: mar
monthnumber: 3
year: 1991
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.529405
ISSNL: 0022-2488 OR 00222488
MRclass: 33C55
MRnumber: 92f:33018
MRreviewer: S. K. Chatterjea
bibdate: Tue Nov 1 08:57:23 MDT 2011
bibtimestamp: 2011.11.01 08:57:23 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v32/i3/p642_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: Leonard C. Maximon
rawtitle: On the evaluation of the integral over the product of two spherical {Bessel} functions
bibsource:
http://jmp.aip.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib

entry:
@Article{Maximon:1991:EIP,
  author =       "Leonard C. Maximon",
  title =        "On the evaluation of the integral over the product of
                 two spherical {Bessel} functions",
  journal =      j-J-MATH-PHYS,
  volume =       "32",
  number =       "3",
  pages =        "642--648",
  month =        mar,
  year =         "1991",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.529405",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "33C55",
  MRnumber =     "92f:33018",
  MRreviewer =   "S. K. Chatterjea",
  bibdate =      "Tue Nov 1 08:57:23 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v32/i3/p642_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "7",
}


bibtype: article
filename: elefunt.bib
label: McQuillan:1991:HPV
author: S. E. McQuillan and J. V. McCanny and R. F. Woods
title: High performance VLSI architecture for division and square root
journal: j-ELECT-LETTERS
volume: 27
number: 1
pages: 19--21
day: 3
month: jan
monthnumber: 1
year: 1991
CODEN: ELLEAK
DOI: https://doi.org/10.1049/el:19910013
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: Electronics Letters
acknowledgement: ack-nhfb
rawauthor: S. E. McQuillan and J. V. McCanny and R. F. Woods
rawtitle: High performance {VLSI} architecture for division and square root
entry:
@Article{McQuillan:1991:HPV,
  author =       "S. E. McQuillan and J. V. McCanny and R. F. Woods",
  title =        "High performance {VLSI} architecture for division and
                 square root",
  journal =      j-ELECT-LETTERS,
  volume =       "27",
  number =       "1",
  pages =        "19--21",
  day =          "3",
  month =        jan,
  year =         "1991",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19910013",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220;
                 https://digital-library.theiet.org/journal/el",
  summary =      "A novel high performance bit parallel architecture to
                 perform square root and division is proposed. Relevant
                 VLSI design issues have been addressed. By employing
                 redundant arithmetic and a semisystolic schedule, the
                 throughput has been made independent of the size of the
                 array.",
}


bibtype: inproceedings
filename: elefunt.bib
label: McQuillan:1991:VAM
author: S. E. McQuillan and J. V. McCanny
title: A VLSI architecture for multiplication, division and square root
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1205--1208
year: 1991
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: S. E. McQuillan and J. V. McCanny
rawtitle: A {VLSI} architecture for multiplication, division and square root
booktitle:
1991 International Conference on Acoustics, Speech, and Signal Processing: ICASSP-91, 14--17 April 1991

rawbooktitle:
1991 International Conference on Acoustics, Speech, and Signal Processing: {ICASSP-91, 14--17} April 1991

entry:
@InProceedings{McQuillan:1991:VAM,
  author =       "S. E. McQuillan and J. V. McCanny",
  booktitle =    "1991 International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP-91, 14--17} April 1991",
  title =        "A {VLSI} architecture for multiplication, division and
                 square root",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1205--1208",
  year =         "1991",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "A high-performance VLSI architecture to perform
                 combined multiply-accumulate, divide, and square root
                 operations is proposed. The circuit is highly regular,
                 requires only minimal control, and can be reconfigured
                 for every cycle. The execution time \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Midy:1991:CSE
author: P. Midy and Y. Yakovlev
title: Computing some elementary functions of a complex variable
journal: j-MATH-COMPUT-SIMUL
volume: 33
number: 1
pages: 33--49
year: 1991
CODEN: MCSIDR
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
MRclass: 65Y10 (65D20)
MRnumber: MR1122989
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Mathematics and Computers in Simulation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03784754
rawauthor: P. Midy and Y. Yakovlev
rawtitle: Computing some elementary functions of a complex variable
entry:
@Article{Midy:1991:CSE,
  author =       "P. Midy and Y. Yakovlev",
  title =        "Computing some elementary functions of a complex
                 variable",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "33",
  number =       "1",
  pages =        "33--49",
  year =         "1991",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  MRclass =      "65Y10 (65D20)",
  MRnumber =     "MR1122989",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784754",
}


bibtype: article
filename: elefunt.bib
label: Montuschi:1991:OAE
author: P. Montuschi and M. Mezzalama
title: Optimal Absolute Error Starting Values for Newton--Raphson Calculation of Square Root
journal: j-COMPUTING
volume: 46
number: 1
pages: 67--86
month: mar
monthnumber: 3
year: 1991
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65H05 (65G99)
MRnumber: 92a:65161
bibdate: Tue Oct 12 16:33:42 MDT 1999
bibtimestamp: 1999.10.12 16:33:42 MDT
fjournal: Computing
acknowledgement: ack-nhfb
affiliation: Politecnico di Torino
affiliationaddress: Torino, Italy
journalURL: http://link.springer.com/journal/607
journalabr: Comput Vienna New York
rawauthor: P. Montuschi and M. Mezzalama
rawtitle: Optimal Absolute Error Starting Values for {Newton--Raphson} Calculation of Square Root
bibsource:
Compendex database; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/tex/bib/computing.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database; OCLC Contents1st database

keywords:
Absolute Error; Computer Programming --- Algorithms; Mathematical Techniques; Newton--Raphson Method; Optimization; Square Roots

entry:
@Article{Montuschi:1991:OAE,
  author =       "P. Montuschi and M. Mezzalama",
  title =        "Optimal Absolute Error Starting Values for
                 {Newton--Raphson} Calculation of Square Root",
  journal =      j-COMPUTING,
  volume =       "46",
  number =       "1",
  pages =        "67--86",
  month =        mar,
  year =         "1991",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65H05 (65G99)",
  MRnumber =     "92a:65161",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database; OCLC Contents1st database",
  acknowledgement = ack-nhfb,
  affiliation =  "Politecnico di Torino",
  affiliationaddress = "Torino, Italy",
  classification = "723; 921",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput Vienna New York",
  keywords =     "Absolute Error; Computer Programming --- Algorithms;
                 Mathematical Techniques; Newton--Raphson Method;
                 Optimization; Square Roots",
}


bibtype: inproceedings
filename: elefunt.bib
label: Montuschi:1991:SRD
author: Paolo Montuschi and Luigi Ciminiera
title: Simple radix 2 division and square root with skipping of some addition steps
crossref: Kornerup:1991:PIS
pages: 202--209
year: 1991
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibtimestamp: 2005.07.16 15:28:14 MDT
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Montuschi.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Paolo Montuschi and Luigi Ciminiera
rawtitle: Simple radix 2 division and square root with skipping of some addition steps
entry:
@InProceedings{Montuschi:1991:SRD,
  author =       "Paolo Montuschi and Luigi Ciminiera",
  title =        "Simple radix 2 division and square root with skipping
                 of some addition steps",
  crossref =     "Kornerup:1991:PIS",
  pages =        "202--209",
  year =         "1991",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Montuschi.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
  summary =      "The authors present a novel algorithm for shared radix
                 2 division and square root whose main characteristic is
                 the ability to avoid any addition when the digit 0 has
                 been selected. The solution presented uses a redundant
                 representation of the \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: OGrady:1991:HOA
author: E. Pearse O'Grady and Baek-Kyu Young
title: A hardware-oriented algorithm for floating-point function generation
journal: j-IEEE-TRANS-COMPUT
volume: 40
number: 2
pages: 237--241
month: feb
monthnumber: 2
year: 1991
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.73596
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. Pearse O'Grady and Baek-Kyu Young
rawtitle: A hardware-oriented algorithm for floating-point function generation
abstract:
An algorithm is presented for performing accurate, high-speed, floating-point function generation for univariate functions defined at arbitrary breakpoints. Rapid identification of the breakdown interval, which includes the input argument, is the key operation in the algorithm. A hardware implementation which makes extensive use of read/write memories illustrates the algorithm.

rawabstract:
An algorithm is presented for performing accurate, high-speed, floating-point function generation for univariate functions defined at arbitrary breakpoints. Rapid identification of the breakdown interval, which includes the input argument, is the key operation in the algorithm. A hardware implementation which makes extensive use of read/write memories illustrates the algorithm.

entry:
@Article{OGrady:1991:HOA,
  author =       "E. Pearse O'Grady and Baek-Kyu Young",
  title =        "A hardware-oriented algorithm for floating-point
                 function generation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "2",
  pages =        "237--241",
  month =        feb,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.73596",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "An algorithm is presented for performing accurate,
                 high-speed, floating-point function generation for
                 univariate functions defined at arbitrary breakpoints.
                 Rapid identification of the breakdown interval, which
                 includes the input argument, is the key operation in
                 the algorithm. A hardware implementation which makes
                 extensive use of read/write memories illustrates the
                 algorithm.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Okabe:1991:LDC
author: Y. Okabe and N. Takagi and S. Yaima
title: Log-Depth Circuits for Elementary Functions Using Residue Number System
journal: j-ELECTRON-COMMUN-JPN
volume: 74
number: 8
pages: 31--37
year: 1991
CODEN: ECOJAL
ISSN: 0424-8368 OR 04248368
bibdate: Mon May 19 15:16:09 1997
bibtimestamp: 1997.05.19 15:16:09 ???
note: Translated from Denshi Joho Tsushin Gakkai Ronbunshi, vol.21-DI, no.9, September 1990, pp.723-728
fjournal: Electronics and communications in Japan
acknowledgement: ack-nhfb
key: OTY91
rawauthor: Y. Okabe and N. Takagi and S. Yaima
rawtitle: Log-Depth Circuits for Elementary Functions Using Residue Number System
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawnote:
Translated from Denshi Joho Tsushin Gakkai Ronbunshi, vol.\ 21-DI, no.\ 9, September 1990, pp.\ 723-728

entry:
@Article{Okabe:1991:LDC,
  author =       "Y. Okabe and N. Takagi and S. Yaima",
  key =          "OTY91",
  title =        "Log-Depth Circuits for Elementary Functions Using
                 Residue Number System",
  journal =      j-ELECTRON-COMMUN-JPN,
  volume =       "74",
  number =       "8",
  pages =        "31--37",
  year =         "1991",
  CODEN =        "ECOJAL",
  ISSN =         "0424-8368",
  bibdate =      "Mon May 19 15:16:09 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Translated from Denshi Joho Tsushin Gakkai Ronbunshi,
                 vol.\ 21-DI, no.\ 9, September 1990, pp.\ 723-728",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics and communications in Japan",
}


bibtype: article
filename: elefunt.bib
label: Olver:1991:UEIb
author: F. W. J. Olver
journal: j-SIAM-J-MATH-ANA
volume: 22
number: 5
pages: 1475--1489
month: sep
monthnumber: 9
year: 1991
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 41A60 (33C15)
MRnumber: 92g:41035
MRreviewer: Hans-J{\"u}rgen Glaeske
bibdate: Sun Nov 28 19:25:21 MST 2010
bibtimestamp: 2010.11.28 19:25:21 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: F. W. J. Olver
title:
Uniform, Exponentially Improved, Asymptotic Expansions for the Confluent Hypergeometric Function and Other Integral Transforms

bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/SIMA/22/5; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib

rawtitle:
Uniform, Exponentially Improved, Asymptotic Expansions for the Confluent Hypergeometric Function and Other Integral Transforms

entry:
@Article{Olver:1991:UEIb,
  author =       "F. W. J. Olver",
  title =        "Uniform, Exponentially Improved, Asymptotic Expansions
                 for the Confluent Hypergeometric Function and Other
                 Integral Transforms",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "22",
  number =       "5",
  pages =        "1475--1489",
  month =        sep,
  year =         "1991",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "41A60 (33C15)",
  MRnumber =     "92g:41035",
  MRreviewer =   "Hans-J{\"u}rgen Glaeske",
  bibdate =      "Sun Nov 28 19:25:21 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/22/5;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: article
filename: elefunt.bib
label: Press:1991:BFF
author: William H. Press and Saul A. Teukolsky
title: Bessel Functions of Fractional Order
journal: j-COMPUT-PHYS
volume: 5
number: 2
pages: 244--??
month: mar
monthnumber: 3
year: 1991
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.4822982
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Wed Apr 10 08:45:28 MDT 2019
bibtimestamp: 2019.04.10 08:45:28 MDT
URL: https://aip.scitation.org/doi/10.1063/1.4822982
fjournal: Computers in Physics
acknowledgement: ack-nhfb
ajournal: Comput. Phys
journalURL: https://aip.scitation.org/journal/cip
rawauthor: William H. Press and Saul A. Teukolsky
rawtitle: {Bessel} Functions of Fractional Order
entry:
@Article{Press:1991:BFF,
  author =       "William H. Press and Saul A. Teukolsky",
  title =        "{Bessel} Functions of Fractional Order",
  journal =      j-COMPUT-PHYS,
  volume =       "5",
  number =       "2",
  pages =        "244--??",
  month =        mar,
  year =         "1991",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.4822982",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:45:28 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.4822982",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}


bibtype: article
filename: elefunt.bib
label: Press:1991:MBF
author: William H. Press and Saul A. Teukolsky
title: Modified Bessel Functions of Fractional Order
journal: j-COMPUT-PHYS
volume: 5
number: 3
pages: 330--??
month: may
monthnumber: 5
year: 1991
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.4822991
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Wed Apr 10 08:45:29 MDT 2019
bibtimestamp: 2019.04.10 08:45:29 MDT
URL: https://aip.scitation.org/doi/10.1063/1.4822991
fjournal: Computers in Physics
acknowledgement: ack-nhfb
ajournal: Comput. Phys
journalURL: https://aip.scitation.org/journal/cip
rawauthor: William H. Press and Saul A. Teukolsky
rawtitle: Modified {Bessel} Functions of Fractional Order
entry:
@Article{Press:1991:MBF,
  author =       "William H. Press and Saul A. Teukolsky",
  title =        "Modified {Bessel} Functions of Fractional Order",
  journal =      j-COMPUT-PHYS,
  volume =       "5",
  number =       "3",
  pages =        "330--??",
  month =        may,
  year =         "1991",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.4822991",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:45:29 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.4822991",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}


bibtype: book
filename: elefunt.bib
label: Saan:1991:VFP
author: T. Saan
publisher: Eston. Nauchno-Proizvod. Obcdprime ed. Vychisl. Tekhn. Inform., Tartu
pages: 139
year: 1991
MRclass: 65-04 (65D15)
MRnumber: 94f:65008
MRreviewer: W. Govaerts
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: T. Saan
title:
cyr Vychislenie elementarnykh funktsiui s pomoshch'yu drobno-ratsional'nykh priblizheniui . (Russian) [Calculation of elementary functions by means of rational approximations]

rawtitle:
{{\cyr Vychislenie {\`e}lementarnykh funktsi{\u\i}s pomoshch'yu drobno-ratsional'nykh priblizheni{\u\i}}}. ({Russian}) [Calculation of elementary functions by means of rational approximations]

entry:
@Book{Saan:1991:VFP,
  author =       "T. Saan",
  title =        "{{\cyr Vychislenie {\`e}lementarnykh funktsi{\u\i}s
                 pomoshch'yu drobno-ratsional'nykh priblizheni{\u\i}}}.
                 ({Russian}) [Calculation of elementary functions by
                 means of rational approximations]",
  publisher =    "{\`E}ston. Nauchno-Proizvod. Ob\cdprime ed. Vychisl.
                 Tekhn. Inform., Tartu",
  pages =        "139",
  year =         "1991",
  MRclass =      "65-04 (65D15)",
  MRnumber =     "94f:65008",
  MRreviewer =   "W. Govaerts",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: article
filename: elefunt.bib
label: Smith:1991:AFP
author: David M. Smith
title: Algorithm 693: A FORTRAN Package for Floating-Point Multiple-Precision Arithmetic
journal: j-TOMS
volume: 17
number: 2
pages: 273--283
month: jun
monthnumber: 6
year: 1991
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sun Sep 04 23:44:20 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.04 23:44:20 ???
URL: http://www.acm.org/pubs/toc/Abstracts/toms/108585.html
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
affiliation: Loyola Marymount Univ., Los Angeles, CA, USA
journalURL: https://dl.acm.org/loi/toms
thesaurus: Digital arithmetic; Function approximation; Mathematics computing; Software packages; Subroutines
rawauthor: David M. Smith
rawtitle: Algorithm 693: {A FORTRAN} Package for Floating-Point Multiple-Precision Arithmetic
abstract:
FM is a collection of FORTRAN-77 routines which performs floating-point multiple-precision arithmetic and elementary functions. Results are almost always correctly rounded, and due to improved algorithms used for elementary functions, reasonable efficiency is obtained.

keywords:
Accuracy; Algorithms; Elementary functions; Floating-point multiple-precision arithmetic; FM; FORTRAN-77 routines; Mathematical library; Portable software; Rounding off

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf D.3.2: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.

rawabstract:
FM is a collection of FORTRAN-77 routines which performs floating-point multiple-precision arithmetic and elementary functions. Results are almost always correctly rounded, and due to improved algorithms used for elementary functions, reasonable efficiency is obtained.

entry:
@Article{Smith:1991:AFP,
  author =       "David M. Smith",
  title =        "Algorithm 693: {A FORTRAN} Package for Floating-Point
                 Multiple-Precision Arithmetic",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "273--283",
  month =        jun,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:44:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/toms/108585.html",
  abstract =     "FM is a collection of FORTRAN-77 routines which
                 performs floating-point multiple-precision arithmetic
                 and elementary functions. Results are almost always
                 correctly rounded, and due to improved algorithms used
                 for elementary functions, reasonable efficiency is
                 obtained.",
  acknowledgement = ack-nhfb,
  affiliation =  "Loyola Marymount Univ., Los Angeles, CA, USA",
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods); C7310
                 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Accuracy; Algorithms; Elementary functions;
                 Floating-point multiple-precision arithmetic; FM;
                 FORTRAN-77 routines; Mathematical library; Portable
                 software; Rounding off",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf D.3.2}:
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77.",
  thesaurus =    "Digital arithmetic; Function approximation;
                 Mathematics computing; Software packages; Subroutines",
}


bibtype: article
filename: elefunt.bib
label: Squire:1991:ANS
author: Jon S. Squire
title: Ada numerics standardization and testing
journal: j-SIGADA-LETTERS
volume: 11
number: 7
address: New York, NY, USA
pages: 1--286
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: ACM SIGAda Ada Letters
keywords: Ada (Computer program language)
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/citation.cfm?id=J32
rawauthor: Jon S. Squire
rawtitle: {Ada} numerics standardization and testing
annote:
``A special edition from SIGAda ldots presented by SIGAda Numerics Working Group and Ada-Europe Numerics Working Group and ISO- IEC/JTC1/SC22/WG9 Numerics Rapporteur Group.''--Cover. Includes bibliographies. Introduction to the proposed standard for the elementary functions in Ada / Kenneth W. Dritz --- Proposed standard for a generic package of elementary functions for Ada / edited by Kenneth W. Dritz --- Rationale for the proposed standard for a generic package of elementary functions for Ada; Proposed standard for a generic package of primitive functions for Ada; Rationale for the proposed standard for a generic package of primitive functions for Ada / Kenneth W. Dritz --- Proposed standard for packages of real and complex type declarations and basic operations for Ada (including vector and matrix types) / edited by Graham S. Hodgson --- Rationale for the proposed standard for packages of real and complex type declarations and basic operations for Ada (including vector and matrix types) / Graham S. Hodgson. Proposed standard for a generic package of complex elementary functions / edited by Jon S. Squire --- Rationale for the proposed standard for a generic package of complex elementary functions / Jon S. Squire --- A portable generic elementary function package in Ada and an accurate test suite / Ping Tak Peter Tang --- Towards validation of generic elementary functions and other standard Ada numerics packages / Jon S. Squire --- Floating point attributes in Ada / Dik T. Winter --- An Ada math library for real-time avionics / Donald A. Celarier and Donald W. Sando --- Predifined floating point type names, uniformity rapporteur group UI-48 / edited by Jon S. Squire.

entry:
@Article{Squire:1991:ANS,
  author =       "Jon S. Squire",
  title =        "{Ada} numerics standardization and testing",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  address =      "New York, NY, USA",
  pages =        "1--286",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  annote =       "``A special edition from SIGAda \ldots{} presented by
                 SIGAda Numerics Working Group and Ada-Europe Numerics
                 Working Group and ISO- IEC/JTC1/SC22/WG9 Numerics
                 Rapporteur Group.''--Cover. Includes bibliographies.
                 Introduction to the proposed standard for the
                 elementary functions in Ada / Kenneth W. Dritz ---
                 Proposed standard for a generic package of elementary
                 functions for Ada / edited by Kenneth W. Dritz ---
                 Rationale for the proposed standard for a generic
                 package of elementary functions for Ada; Proposed
                 standard for a generic package of primitive functions
                 for Ada; Rationale for the proposed standard for a
                 generic package of primitive functions for Ada /
                 Kenneth W. Dritz --- Proposed standard for packages of
                 real and complex type declarations and basic operations
                 for Ada (including vector and matrix types) / edited by
                 Graham S. Hodgson --- Rationale for the proposed
                 standard for packages of real and complex type
                 declarations and basic operations for Ada (including
                 vector and matrix types) / Graham S. Hodgson. Proposed
                 standard for a generic package of complex elementary
                 functions / edited by Jon S. Squire --- Rationale for
                 the proposed standard for a generic package of complex
                 elementary functions / Jon S. Squire --- A portable
                 generic elementary function package in Ada and an
                 accurate test suite / Ping Tak Peter Tang --- Towards
                 validation of generic elementary functions and other
                 standard Ada numerics packages / Jon S. Squire ---
                 Floating point attributes in Ada / Dik T. Winter --- An
                 Ada math library for real-time avionics / Donald A.
                 Celarier and Donald W. Sando --- Predifined floating
                 point type names, uniformity rapporteur group UI-48 /
                 edited by Jon S. Squire.",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada (Computer program language)",
}


bibtype: article
filename: elefunt.bib
label: Squire:1991:PSG
author: J. S. Squire
title: Proposed standard for a generic package of complex elementary functions (Ada)
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 140--165
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Mar 20 07:41:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.20 07:41:09 MST
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
classcodes: C6140D (High level languages); C7310 (Mathematics); C6110B (Software engineering techniques)
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: J. S. Squire
rawtitle: Proposed standard for a generic package of complex elementary functions ({Ada})
keywords:
ACM SIGAda; Ada; Ada-Europe Numerics Working Group; applications; complex elementary functions; complex mathematical routines; COMPLEX-ELEMENTARY-FUNCTIONS; generic package; GENERIC-; international standard; joint proposal; mathematics computing; Numerics Working Group; portable; reusable; software reusability; standards; WG9 Numerics Rapporteur Group

entry:
@Article{Squire:1991:PSG,
  author =       "J. S. Squire",
  title =        "Proposed standard for a generic package of complex
                 elementary functions ({Ada})",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "140--165",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics);
                 C6110B (Software engineering techniques)",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "ACM SIGAda; Ada; Ada-Europe Numerics Working Group;
                 applications; complex elementary functions; complex
                 mathematical routines; COMPLEX-ELEMENTARY-FUNCTIONS;
                 generic package; GENERIC-; international standard;
                 joint proposal; mathematics computing; Numerics Working
                 Group; portable; reusable; software reusability;
                 standards; WG9 Numerics Rapporteur Group",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Squire:1991:RPS
author: Jon S. Squire
title: Rationale for the proposed standard for a generic package of complex elementary functions (Ada)
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 166--179
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Mar 20 07:41:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/sigada.bib
bibtimestamp: 1997.03.20 07:41:09 MST
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
classcodes: C6140D (High level languages); C7310 (Mathematics); C6110B (Software engineering techniques)
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: Jon S. Squire
rawtitle: Rationale for the proposed standard for a generic package of complex elementary functions ({Ada})
keywords:
ACM SIGAda Numerics Working Group; Ada; Ada-; basic complex mathematical; complex; COMPLEX-ELEMENTARY-FUNCTIONS; elementary functions; error bounds; Europe Numerics Working Group; generic package; GENERIC-; mathematics computing; proposed standard; reusable applications; routines; software reusability; specification; standards

entry:
@Article{Squire:1991:RPS,
  author =       "Jon S. Squire",
  title =        "Rationale for the proposed standard for a generic
                 package of complex elementary functions ({Ada})",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "166--179",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics);
                 C6110B (Software engineering techniques)",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "ACM SIGAda Numerics Working Group; Ada; Ada-; basic
                 complex mathematical; complex;
                 COMPLEX-ELEMENTARY-FUNCTIONS; elementary functions;
                 error bounds; Europe Numerics Working Group; generic
                 package; GENERIC-; mathematics computing; proposed
                 standard; reusable applications; routines; software
                 reusability; specification; standards",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Squire:1991:TVG
author: J. S. Squire
title: Towards validation of generic elementary functions and other standard Ada numerics packages
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 217--243
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Mar 20 07:41:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.20 07:41:09 MST
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: J. S. Squire
rawtitle: Towards validation of generic elementary functions and other standard {Ada} numerics packages
keywords:
Ada; Ada listings; computing; conformance testing; conformance tests; generic elementary functions; implementors guide; mathematics; program testing; proposed ISO; prototype tests; standard Ada numerics packages; standards; test suite

classcodes:
C6150G (Diagnostic, testing, debugging and evaluating systems); C7310 (Mathematics); C6140D (High level languages)

entry:
@Article{Squire:1991:TVG,
  author =       "J. S. Squire",
  title =        "Towards validation of generic elementary functions and
                 other standard {Ada} numerics packages",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "217--243",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6150G (Diagnostic, testing, debugging and evaluating
                 systems); C7310 (Mathematics); C6140D (High level
                 languages)",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; Ada listings; computing; conformance testing;
                 conformance tests; generic elementary functions;
                 implementors guide; mathematics; program testing;
                 proposed ISO; prototype tests; standard Ada numerics
                 packages; standards; test suite",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Takagi:1991:RCM
author: N. Takagi and T. Asada and S. Yajima
title: Redundant CORDIC Methods with a Constant Scale Factor for Sine and Cosine Computation
journal: j-IEEE-TRANS-COMPUT
volume: 40
number: 9
pages: 989--995
month: sep
monthnumber: 9
year: 1991
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.83660
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 12:52:24 MDT 2011
bibtimestamp: 2011.07.07 12:52:24 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83660
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: N. Takagi and T. Asada and S. Yajima
rawtitle: Redundant {CORDIC} Methods with a Constant Scale Factor for Sine and Cosine Computation
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Takagi:1991:RCM,
  author =       "N. Takagi and T. Asada and S. Yajima",
  title =        "Redundant {CORDIC} Methods with a Constant Scale
                 Factor for Sine and Cosine Computation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "9",
  pages =        "989--995",
  month =        sep,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.83660",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 12:52:24 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83660",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Tang:1991:PGE
author: Ping Tak Peter Tang
title: A portable generic elementary function package in Ada and an accurate test suite
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 181--216
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Mar 20 07:41:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.20 07:41:09 MST
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: Ping Tak Peter Tang
rawtitle: A portable generic elementary function package in {Ada} and an accurate test suite
keywords:
accurate test; Ada; function libraries; mathematics computing; portability; portable generic elementary function package; program testing; resolution; rigorous analysis; software; suite; test programs

classcodes:
C7310 (Mathematics); C6140D (High level languages); C6110B (Software engineering techniques); C6150G (Diagnostic, testing, debugging and evaluating systems)

entry:
@Article{Tang:1991:PGE,
  author =       "Ping Tak Peter Tang",
  title =        "A portable generic elementary function package in
                 {Ada} and an accurate test suite",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "181--216",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C7310 (Mathematics); C6140D (High level languages);
                 C6110B (Software engineering techniques); C6150G
                 (Diagnostic, testing, debugging and evaluating
                 systems)",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "accurate test; Ada; function libraries; mathematics
                 computing; portability; portable generic elementary
                 function package; program testing; resolution; rigorous
                 analysis; software; suite; test programs",
  treatment =    "P Practical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Tang:1991:TLA
author: Ping Tak Peter Tang
title: Table-Lookup Algorithms for Elementary Functions and Their Error Analysis
crossref: Kornerup:1991:PIS
pages: 232--236
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.11.27 12:40:58 MST
acknowledgement: ack-nj
rawauthor: Ping Tak Peter Tang
rawtitle: Table-Lookup Algorithms for Elementary Functions and Their Error Analysis
entry:
@InProceedings{Tang:1991:TLA,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Lookup Algorithms for Elementary Functions and
                 Their Error Analysis",
  crossref =     "Kornerup:1991:PIS",
  pages =        "232--236",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Wong:1991:FHA
author: W. F. Wong and E. Goto
title: Fast Hardware-based Algorithms for Elementary Function Computations
crossref: Anonymous:1991:PIS
pages: 56--65
year: 1991
bibdate: Sat Jan 11 10:14:06 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 10:14:06 MST
acknowledgement: ack-nhfb
rawauthor: W. F. Wong and E. Goto
rawtitle: Fast Hardware-based Algorithms for Elementary Function Computations
entry:
@InProceedings{Wong:1991:FHA,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast Hardware-based Algorithms for Elementary Function
                 Computations",
  crossref =     "Anonymous:1991:PIS",
  pages =        "56--65",
  year =         "1991",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  searchkey =    "ti:elementary function",
}


bibtype: article
filename: elefunt.bib
label: Zeilberger:1991:MPP
author: Doron Zeilberger
title: A Maple program for proving hypergeometric identities
journal: j-SIGSAM
volume: 25
number: 3
pages: 4--13
month: jul
monthnumber: 7
year: 1991
CODEN: SIGSBZ
ISSN: 0163-5824 (print), 1557-9492 (electronic) OR 01635824 (print), 15579492 (electronic)
ISSNL: 0163-5824 OR 01635824
bibdate: Fri Feb 8 18:27:01 MST 2002
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.02.08 18:27:01 MST
fjournal: SIGSAM Bulletin
acknowledgement: ack-nhfb
affiliation: Dept. of Math. and Comput. Sci., Drexel Univ., Philadelphia, PA, USA
classcodes: C7310 (Mathematics)
corpsource: Dept. of Math. and Comput. Sci., Drexel Univ., Philadelphia, PA, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J1000
thesaurus: Mathematics computing; Public domain software; Symbol manipulation; Theorem proving
treatment: P Practical
issue: 97
rawauthor: Doron Zeilberger
rawtitle: A {Maple} program for proving hypergeometric identities
abstract:
Gives the listing of a MAPLE program for implementing an algorithm for proving any terminating definite hypergeometric identity, and more generally, for finding the linear recurrence satisfied by any definite hypergeometric sum R(n):= Sigma /sub k/F(n,k), where F(n,k) has the form x/sup k/( Pi /sub i=1//sup m/( alpha /sub i/n+ beta /sub i/k+c/sub i/)!/ Pi /sub i'=1//sup m'/( alpha '/sub i'/n+ beta '/sub i'/k+c'/sub i'/)!). The algorithm for definite hypergeometric summation relies on Gosper's (1978) ingenious decision procedure for indefinite summation, but not in the obvious way!.

keywords:
definite; Definite hypergeometric summation; hypergeometric identity; hypergeometric summation; linear recurrence; Linear recurrence; manipulation; MAPLE program; mathematics computing; proofs; Proofs; public domain software; shareware; Shareware; symbol; terminating definite; Terminating definite hypergeometric identity; theorem proving

rawabstract:
Gives the listing of a MAPLE program for implementing an algorithm for proving any terminating definite hypergeometric identity, and more generally, for finding the linear recurrence satisfied by any definite hypergeometric sum R(n):= Sigma /sub k/F(n,k), where F(n,k) has the form x/sup k/( Pi /sub i=1//sup m/( alpha /sub i/n+ beta /sub i/k+c/sub i/)!/ Pi /sub i'=1//sup m'/( alpha '/sub i'/n+ beta '/sub i'/k+c'/sub i'/)!). The algorithm for definite hypergeometric summation relies on Gosper's (1978) ingenious decision procedure for indefinite summation, but not in the obvious way!.

entry:
@Article{Zeilberger:1991:MPP,
  author =       "Doron Zeilberger",
  title =        "A {Maple} program for proving hypergeometric
                 identities",
  journal =      j-SIGSAM,
  volume =       "25",
  number =       "3",
  pages =        "4--13",
  month =        jul,
  year =         "1991",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Fri Feb 8 18:27:01 MST 2002",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Gives the listing of a MAPLE program for implementing
                 an algorithm for proving any terminating definite
                 hypergeometric identity, and more generally, for
                 finding the linear recurrence satisfied by any definite
                 hypergeometric sum R(n):= Sigma /sub k/F(n,k), where
                 F(n,k) has the form x/sup k/( Pi /sub i=1//sup m/(
                 alpha /sub i/n+ beta /sub i/k+c/sub i/)!/ Pi /sub
                 i'=1//sup m'/( alpha '/sub i'/n+ beta '/sub i'/k+c'/sub
                 i'/)!). The algorithm for definite hypergeometric
                 summation relies on Gosper's (1978) ingenious decision
                 procedure for indefinite summation, but not in the
                 obvious way!.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. and Comput. Sci., Drexel Univ.,
                 Philadelphia, PA, USA",
  classcodes =   "C7310 (Mathematics)",
  classification = "C7310 (Mathematics)",
  corpsource =   "Dept. of Math. and Comput. Sci., Drexel Univ.,
                 Philadelphia, PA, USA",
  fjournal =     "SIGSAM Bulletin",
  issue =        "97",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
  keywords =     "definite; Definite hypergeometric summation;
                 hypergeometric identity; hypergeometric summation;
                 linear recurrence; Linear recurrence; manipulation;
                 MAPLE program; mathematics computing; proofs; Proofs;
                 public domain software; shareware; Shareware; symbol;
                 terminating definite; Terminating definite
                 hypergeometric identity; theorem proving",
  thesaurus =    "Mathematics computing; Public domain software; Symbol
                 manipulation; Theorem proving",
  treatment =    "P Practical",
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bibtype: article
filename: elefunt.bib
label: Ziv:1991:FEE
author: Abraham Ziv
title: Fast Evaluation of Elementary Mathematical Functions with Correctly Rounded Last Bit
journal: j-TOMS
volume: 17
number: 3
pages: 410--423
month: sep
monthnumber: 9
year: 1991
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Sep 1 10:15:31 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 10:15:31 ???
URL: http://www.acm.org/pubs/toc/Abstracts/toms/116813.html
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; standardization; theory
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/toms
rawauthor: Abraham Ziv
rawtitle: Fast Evaluation of Elementary Mathematical Functions with Correctly Rounded Last Bit
subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.

entry:
@Article{Ziv:1991:FEE,
  author =       "Abraham Ziv",
  title =        "Fast Evaluation of Elementary Mathematical Functions
                 with Correctly Rounded Last Bit",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "410--423",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/toms/116813.html",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; standardization; theory",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency.",
}


bibtype: book
filename: elefunt.bib
label: Achieser:1992:TA
author: N. I. Achieser
title: Theory of Approximation
publisher: pub-DOVER
address: pub-DOVER:adr
pages: x + 307
year: 1992
ISBN: 0-486-67129-1 (paperback) OR 0486671291 (paperback)
ISBN13: 978-0-486-67129-1 (paperback) OR 9780486671291 (paperback)
LCCN: QA221 .A533 1992
bibdate: Fri Oct 20 08:06:59 MDT 2023
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.20 08:06:59 MDT
series: Dover books on advanced mathematics
subject: Mathematical analysis
acknowledgement: ack-nhfb
rawauthor: N. I. Achieser
rawtitle: Theory of Approximation
remark:
Translation of Russian original, Leketisii po teorii approksimaetisii. Reprint of English translation cite Achieser:1956:TA.

TOC:
Approximation Problems in Linear Normalized Spaces Formulation of the Principal Problem in the Theory of Approximation / 1 The Concept of Metric Space / 1 The Concept of Linear Normalized Space / 2 Examples of Linear Normalized Spaces / 3 The Inequalities of Holder and Minkowski / 4 Additional Examples of Linear Normalized Spaces / 7 Hilbert Space / 8 The Fundamental Theorem of Approximation Theory in Linear Normalized Spaces / 10 Strictly Normalized Spaces / 11 An Example of Approximation in the Space $L^p$ / 12 Geometric Interpretation / 13 Separable and Complete Spaces / 14 Approximation Theorems in Hilbert Space / 15 An Example of Approximation in Hilbert Space / 19 More About the Approximation Problem in Hilbert Space / 21 Orthonormalized Vector Systems in Hilbert Space / 22 Orthogonalization of Vector Systems / 23 Infinite Orthonormalized Systems / 25 An Example of a Non-Separable System / 29 Weierstrass' First Theorem / 29 Weierstrass' Second Theorem / 32 The Separability of the Space C / 33 The Separability of the Space $L^p$ / 34 Generalization of Weierstrass' Theorem to the Space $L^p$ / 37 The Completeness of the Space $L^p$ / 38 Examples of Complete Orthonormalized Systems in L[superscript 2] / 40 Muntz's Theorem / 43 The Concept of the Linear Functional / 46 F. Riesz's Theorem / 47 A Criterion for the Closure of a Set of Vectors in Linear Normalized Spaces / 49 P. L. Tchebysheff's Domain of Ideas Statement of the Problem / 51 A Generalization of the Theorem of de la Vallee-Poussin / 52 The Existence Theorem / 53 Tchebysheff's Theorem / 55 A Special Case of Tchebysheff's Theorem / 57 The Tchebysheff Polynomials of Least Deviation from Zero / 57 A Further Example of P. Tchebysheff's Theorem / 58 An Example for the Application of the General Theorem of de la Vallee-Poussin / 60 An Example for the Application of P. L. Tchebysheff's General Theorem / 62 The Passage to Periodic Functions / 64 An Example of Approximating with the Aid of Periodic Functions / 66 The Weierstrass Function / 66 Haar's Problem / 67 Proof of the Necessity of Haar's Condition / 68 Proof of the Sufficiency of Haar's Condition / 69 An Example Related to Haar's Problem / 72 P. L. Tchebysheff's Systems of Functions / 73 Generalization of P. L. Tchebysheff's Theorem / 74 On a Question Pertaining to the Approximation of a Continuous Function in the Space $L$ / 76 A. A. Markoff's Theorem / 82 Special Cases of the Theorem of A. A. Markoff / 85 Elements of Harmonic Analysis The Simplest Properties of Fourier Series / 89 Fourier Series for Functions of Bounded Variation / 93 The Parseval Equation for Fourier Series / 97 Examples of Fourier Series / 98 Trigonometric Integrals / 101 The Riemann--Lebesgue Theorem / 103 Plancherel's Theory / 104 Watson's Theorem / 106 Plancherel's Theorem / 108 Fejer's Theorem / 110 Integral-Operators of the Fejer Type / 113 The Theorem of Young and Hardy / 116 Examples of Kernels of the Fejer Type / 118 The Fourier Transformation of Integrable Functions / 120 The Faltung of two Functions / 122 V. A. Stekloff's Functions / 123 Multimonotonic Functions / 125 Conjugate Functions / 126 Certain Extremal Properties of Integral Transcendental Functions of the Exponential Type Integral Functions of the Exponential Type / 130 The Borel Transformation / 132 The Theorem of Wiener and Paley / 134 Integral Functions of the Exponential Type which are Bounded along the Real Axis / 137 S. N. Bernstein's Inequality / 140 B. M. Levitan's Polynomials / 146 The Theorem of Fejer and Riesz. A Generalization of This Theorem / 152 A Criterion for the Representation of Continuous Functions as Fourier--Stieltjes Integrals / 154 Questions Regarding the Best Harmonic Approximation of Functions Preliminary Remarks / 160 The Modulus of Continuity / 161 The Generalization to the Space $L^p$ ($p geq 1$) / 162 An Example of Harmonic Approximation / 165 Some Estimates for Fourier Coefficients / 169 More about V. A. Stekloff's Functions / 173 Two Lemmas / 175 The Direct Problem of Harmonic Approximation / 176 A Criterion due to B. Sz.-Nagy / 183 The Best Approximation of Differentiable Functions / 187 Direct Observations Concerning Periodic Functions / 195 Jackson's Second Theorem / 199 The Generalized Fejer Method / 201 Berstein's Theorem / 206 Priwaloff's Theorem / 210 Generalizations of Bernstein's Theorems to the Space $L^p$ ($p geq 1$) / 211 The Best Harmonic Approximation of Analytic Functions / 214 A Different Formulation of the Result of the Preceding Section / 218 The Converse of Bernstein's Theorem / 221 Wiener's Theorem on Approximation Wiener's Problem / 224 The Necessity of Wiener's Condition / 224 Some Definitions and Notation / 225 Several Lemmas / 227 The Wiener--Levy Theorem / 230 Proof of the Sufficiency of Wiener's Condition / 233 Wiener's General Tauber Theorem / 234 Weakly Decreasing Functions / 235 Remarks on the Terminology / 237 Ikehara's Theorem / 238 Carleman's Tauber Theorem / 241 Various Addenda and Problems Elementary Extremal Problems and Certain Closure Criteria / 243 Szego's Theorem and Some of Its Applications / 256 Further Examples of Closed Sequences of Functions / 267 The Caratheodory--Fejer Problem and Similar Problems / 270 Solotareff's Problems and Related Problems / 280 The Best Harmonic Approximation of the Simplest Analytic Functions / 289 Notes / 296 Index / 306

rawTOC:
Approximation Problems in Linear Normalized Spaces \\ Formulation of the Principal Problem in the Theory of Approximation / 1 \\ The Concept of Metric Space / 1 \\ The Concept of Linear Normalized Space / 2 \\ Examples of Linear Normalized Spaces / 3 \\ The Inequalities of Holder and Minkowski / 4 \\ Additional Examples of Linear Normalized Spaces / 7 \\ Hilbert Space / 8 \\ The Fundamental Theorem of Approximation Theory in Linear Normalized Spaces / 10 \\ Strictly Normalized Spaces / 11 \\ An Example of Approximation in the Space $L^p$ / 12 \\ Geometric Interpretation / 13 \\ Separable and Complete Spaces / 14 \\ Approximation Theorems in Hilbert Space / 15 \\ An Example of Approximation in Hilbert Space / 19 \\ More About the Approximation Problem in Hilbert Space / 21 \\ Orthonormalized Vector Systems in Hilbert Space / 22 \\ Orthogonalization of Vector Systems / 23 \\ Infinite Orthonormalized Systems / 25 \\ An Example of a Non-Separable System / 29 \\ Weierstrass' First Theorem / 29 \\ Weierstrass' Second Theorem / 32 \\ The Separability of the Space C / 33 \\ The Separability of the Space $L^p$ / 34 \\ Generalization of Weierstrass' Theorem to the Space $L^p$ / 37 \\ The Completeness of the Space $L^p$ / 38 \\ Examples of Complete Orthonormalized Systems in L[superscript 2] / 40 \\ Muntz's Theorem / 43 \\ The Concept of the Linear Functional / 46 \\ F. Riesz's Theorem / 47 \\ A Criterion for the Closure of a Set of Vectors in Linear Normalized Spaces / 49 \\ P. L. Tchebysheff's Domain of Ideas \\ Statement of the Problem / 51 \\ A Generalization of the Theorem of de la Vallee-Poussin / 52 \\ The Existence Theorem / 53 \\ Tchebysheff's Theorem / 55 \\ A Special Case of Tchebysheff's Theorem / 57 \\ The Tchebysheff Polynomials of Least Deviation from Zero / 57 \\ A Further Example of P. Tchebysheff's Theorem / 58 \\ An Example for the Application of the General Theorem of de la Vallee-Poussin / 60 \\ An Example for the Application of P. L. Tchebysheff's General Theorem / 62 \\ The Passage to Periodic Functions / 64 \\ An Example of Approximating with the Aid of Periodic Functions / 66 \\ The Weierstrass Function / 66 \\ Haar's Problem / 67 \\ Proof of the Necessity of Haar's Condition / 68 \\ Proof of the Sufficiency of Haar's Condition / 69 \\ An Example Related to Haar's Problem / 72 \\ P. L. Tchebysheff's Systems of Functions / 73 \\ Generalization of P. L. Tchebysheff's Theorem / 74 \\ On a Question Pertaining to the Approximation of a Continuous Function in the Space $L$ / 76 \\ A. A. Markoff's Theorem / 82 \\ Special Cases of the Theorem of A. A. Markoff / 85 \\ Elements of Harmonic Analysis \\ The Simplest Properties of Fourier Series / 89 \\ Fourier Series for Functions of Bounded Variation / 93 \\ The Parseval Equation for Fourier Series / 97 \\ Examples of Fourier Series / 98 \\ Trigonometric Integrals / 101 \\ The Riemann--Lebesgue Theorem / 103 \\ Plancherel's Theory / 104 \\ Watson's Theorem / 106 \\ Plancherel's Theorem / 108 \\ Fejer's Theorem / 110 \\ Integral-Operators of the Fejer Type / 113 \\ The Theorem of Young and Hardy / 116 \\ Examples of Kernels of the Fejer Type / 118 \\ The Fourier Transformation of Integrable Functions / 120 \\ The Faltung of two Functions / 122 \\ V. A. Stekloff's Functions / 123 \\ Multimonotonic Functions / 125 \\ Conjugate Functions / 126 \\ Certain Extremal Properties of Integral Transcendental Functions of the Exponential Type \\ Integral Functions of the Exponential Type / 130 \\ The Borel Transformation / 132 \\ The Theorem of Wiener and Paley / 134 \\ Integral Functions of the Exponential Type which are Bounded along the Real Axis / 137 \\ S. N. Bernstein's Inequality / 140 \\ B. M. Levitan's Polynomials / 146 \\ The Theorem of Fejer and Riesz. A Generalization of This Theorem / 152 \\ A Criterion for the Representation of Continuous Functions as Fourier--Stieltjes Integrals / 154 \\ Questions Regarding the Best Harmonic Approximation of Functions Preliminary Remarks / 160 \\ The Modulus of Continuity / 161 \\ The Generalization to the Space $L^p$ ($p \geq 1$) / 162 \\ An Example of Harmonic Approximation / 165 \\ Some Estimates for Fourier Coefficients / 169 \\ More about V. A. Stekloff's Functions / 173 \\ Two Lemmas / 175 \\ The Direct Problem of Harmonic Approximation / 176 \\ A Criterion due to B. Sz.-Nagy / 183 \\ The Best Approximation of Differentiable Functions / 187 \\ Direct Observations Concerning Periodic Functions / 195 \\ Jackson's Second Theorem / 199 \\ The Generalized Fejer Method / 201 \\ Berstein's Theorem / 206 \\ Priwaloff's Theorem / 210 \\ Generalizations of Bernstein's Theorems to the Space $L^p$ ($p \geq 1$) / 211 \\ The Best Harmonic Approximation of Analytic Functions / 214 \\ A Different Formulation of the Result of the Preceding Section / 218 \\ The Converse of Bernstein's Theorem / 221 \\ Wiener's Theorem on Approximation \\ Wiener's Problem / 224 \\ The Necessity of Wiener's Condition / 224 \\ Some Definitions and Notation / 225 \\ Several Lemmas / 227 \\ The Wiener--Levy Theorem / 230 \\ Proof of the Sufficiency of Wiener's Condition / 233 \\ Wiener's General Tauber Theorem / 234 \\ Weakly Decreasing Functions / 235 \\ Remarks on the Terminology / 237 \\ Ikehara's Theorem / 238 \\ Carleman's Tauber Theorem / 241 \\ Various Addenda and Problems \\ Elementary Extremal Problems and Certain Closure Criteria / 243 \\ Szego's Theorem and Some of Its Applications / 256 \\ Further Examples of Closed Sequences of Functions / 267 \\ The Caratheodory--Fejer Problem and Similar Problems / 270 \\ Solotareff's Problems and Related Problems / 280 \\ The Best Harmonic Approximation of the Simplest Analytic Functions / 289 \\ Notes / 296 \\ Index / 306

entry:
@Book{Achieser:1992:TA,
  author =       "N. I. Achieser",
  title =        "Theory of Approximation",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "x + 307",
  year =         "1992",
  ISBN =         "0-486-67129-1 (paperback)",
  ISBN-13 =      "978-0-486-67129-1 (paperback)",
  LCCN =         "QA221 .A533 1992",
  bibdate =      "Fri Oct 20 08:06:59 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Dover books on advanced mathematics",
  acknowledgement = ack-nhfb,
  remark =       "Translation of Russian original, Lek{\"e}t{\`\i}sii po
                 teorii approksima{\"e}t{\`\i}sii. Reprint of English
                 translation \cite{Achieser:1956:TA}.",
  subject =      "Mathematical analysis",
  tableofcontents = "Approximation Problems in Linear Normalized Spaces
                 \\
                 Formulation of the Principal Problem in the Theory of
                 Approximation / 1 \\
                 The Concept of Metric Space / 1 \\
                 The Concept of Linear Normalized Space / 2 \\
                 Examples of Linear Normalized Spaces / 3 \\
                 The Inequalities of Holder and Minkowski / 4 \\
                 Additional Examples of Linear Normalized Spaces / 7 \\
                 Hilbert Space / 8 \\
                 The Fundamental Theorem of Approximation Theory in
                 Linear Normalized Spaces / 10 \\
                 Strictly Normalized Spaces / 11 \\
                 An Example of Approximation in the Space $L^p$ / 12 \\
                 Geometric Interpretation / 13 \\
                 Separable and Complete Spaces / 14 \\
                 Approximation Theorems in Hilbert Space / 15 \\
                 An Example of Approximation in Hilbert Space / 19 \\
                 More About the Approximation Problem in Hilbert Space /
                 21 \\
                 Orthonormalized Vector Systems in Hilbert Space / 22
                 \\
                 Orthogonalization of Vector Systems / 23 \\
                 Infinite Orthonormalized Systems / 25 \\
                 An Example of a Non-Separable System / 29 \\
                 Weierstrass' First Theorem / 29 \\
                 Weierstrass' Second Theorem / 32 \\
                 The Separability of the Space C / 33 \\
                 The Separability of the Space $L^p$ / 34 \\
                 Generalization of Weierstrass' Theorem to the Space
                 $L^p$ / 37 \\
                 The Completeness of the Space $L^p$ / 38 \\
                 Examples of Complete Orthonormalized Systems in
                 L[superscript 2] / 40 \\
                 Muntz's Theorem / 43 \\
                 The Concept of the Linear Functional / 46 \\
                 F. Riesz's Theorem / 47 \\
                 A Criterion for the Closure of a Set of Vectors in
                 Linear Normalized Spaces / 49 \\
                 P. L. Tchebysheff's Domain of Ideas \\
                 Statement of the Problem / 51 \\
                 A Generalization of the Theorem of de la Vallee-Poussin
                 / 52 \\
                 The Existence Theorem / 53 \\
                 Tchebysheff's Theorem / 55 \\
                 A Special Case of Tchebysheff's Theorem / 57 \\
                 The Tchebysheff Polynomials of Least Deviation from
                 Zero / 57 \\
                 A Further Example of P. Tchebysheff's Theorem / 58 \\
                 An Example for the Application of the General Theorem
                 of de la Vallee-Poussin / 60 \\
                 An Example for the Application of P. L. Tchebysheff's
                 General Theorem / 62 \\
                 The Passage to Periodic Functions / 64 \\
                 An Example of Approximating with the Aid of Periodic
                 Functions / 66 \\
                 The Weierstrass Function / 66 \\
                 Haar's Problem / 67 \\
                 Proof of the Necessity of Haar's Condition / 68 \\
                 Proof of the Sufficiency of Haar's Condition / 69 \\
                 An Example Related to Haar's Problem / 72 \\
                 P. L. Tchebysheff's Systems of Functions / 73 \\
                 Generalization of P. L. Tchebysheff's Theorem / 74 \\
                 On a Question Pertaining to the Approximation of a
                 Continuous Function in the Space $L$ / 76 \\
                 A. A. Markoff's Theorem / 82 \\
                 Special Cases of the Theorem of A. A. Markoff / 85 \\
                 Elements of Harmonic Analysis \\
                 The Simplest Properties of Fourier Series / 89 \\
                 Fourier Series for Functions of Bounded Variation / 93
                 \\
                 The Parseval Equation for Fourier Series / 97 \\
                 Examples of Fourier Series / 98 \\
                 Trigonometric Integrals / 101 \\
                 The Riemann--Lebesgue Theorem / 103 \\
                 Plancherel's Theory / 104 \\
                 Watson's Theorem / 106 \\
                 Plancherel's Theorem / 108 \\
                 Fejer's Theorem / 110 \\
                 Integral-Operators of the Fejer Type / 113 \\
                 The Theorem of Young and Hardy / 116 \\
                 Examples of Kernels of the Fejer Type / 118 \\
                 The Fourier Transformation of Integrable Functions /
                 120 \\
                 The Faltung of two Functions / 122 \\
                 V. A. Stekloff's Functions / 123 \\
                 Multimonotonic Functions / 125 \\
                 Conjugate Functions / 126 \\
                 Certain Extremal Properties of Integral Transcendental
                 Functions of the Exponential Type \\
                 Integral Functions of the Exponential Type / 130 \\
                 The Borel Transformation / 132 \\
                 The Theorem of Wiener and Paley / 134 \\
                 Integral Functions of the Exponential Type which are
                 Bounded along the Real Axis / 137 \\
                 S. N. Bernstein's Inequality / 140 \\
                 B. M. Levitan's Polynomials / 146 \\
                 The Theorem of Fejer and Riesz. A Generalization of
                 This Theorem / 152 \\
                 A Criterion for the Representation of Continuous
                 Functions as Fourier--Stieltjes Integrals / 154 \\
                 Questions Regarding the Best Harmonic Approximation of
                 Functions Preliminary Remarks / 160 \\
                 The Modulus of Continuity / 161 \\
                 The Generalization to the Space $L^p$ ($p \geq 1$) /
                 162 \\
                 An Example of Harmonic Approximation / 165 \\
                 Some Estimates for Fourier Coefficients / 169 \\
                 More about V. A. Stekloff's Functions / 173 \\
                 Two Lemmas / 175 \\
                 The Direct Problem of Harmonic Approximation / 176 \\
                 A Criterion due to B. Sz.-Nagy / 183 \\
                 The Best Approximation of Differentiable Functions /
                 187 \\
                 Direct Observations Concerning Periodic Functions / 195
                 \\
                 Jackson's Second Theorem / 199 \\
                 The Generalized Fejer Method / 201 \\
                 Berstein's Theorem / 206 \\
                 Priwaloff's Theorem / 210 \\
                 Generalizations of Bernstein's Theorems to the Space
                 $L^p$ ($p \geq 1$) / 211 \\
                 The Best Harmonic Approximation of Analytic Functions /
                 214 \\
                 A Different Formulation of the Result of the Preceding
                 Section / 218 \\
                 The Converse of Bernstein's Theorem / 221 \\
                 Wiener's Theorem on Approximation \\
                 Wiener's Problem / 224 \\
                 The Necessity of Wiener's Condition / 224 \\
                 Some Definitions and Notation / 225 \\
                 Several Lemmas / 227 \\
                 The Wiener--Levy Theorem / 230 \\
                 Proof of the Sufficiency of Wiener's Condition / 233
                 \\
                 Wiener's General Tauber Theorem / 234 \\
                 Weakly Decreasing Functions / 235 \\
                 Remarks on the Terminology / 237 \\
                 Ikehara's Theorem / 238 \\
                 Carleman's Tauber Theorem / 241 \\
                 Various Addenda and Problems \\
                 Elementary Extremal Problems and Certain Closure
                 Criteria / 243 \\
                 Szego's Theorem and Some of Its Applications / 256 \\
                 Further Examples of Closed Sequences of Functions / 267
                 \\
                 The Caratheodory--Fejer Problem and Similar Problems /
                 270 \\
                 Solotareff's Problems and Related Problems / 280 \\
                 The Best Harmonic Approximation of the Simplest
                 Analytic Functions / 289 \\
                 Notes / 296 \\
                 Index / 306",
}


bibtype: article
filename: elefunt.bib
label: Anderson:1992:FIH
author: G. D. Anderson and M. K. Vamanamurthy and M. Vuorinen
title: Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
journal: j-SIAM-J-MATH-ANA
volume: 23
number: 2
pages: 512--524
month: mar
monthnumber: 3
year: 1992
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 33C05 (33C75)
MRnumber: 93b:33001
MRreviewer: J. M. H. Peters
bibdate: Sat Dec 5 18:14:13 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.12.05 18:14:13 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: G. D. Anderson and M. K. Vamanamurthy and M. Vuorinen
rawtitle: Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
entry:
@Article{Anderson:1992:FIH,
  author =       "G. D. Anderson and M. K. Vamanamurthy and M.
                 Vuorinen",
  title =        "Functional Inequalities for Hypergeometric Functions
                 and Complete Elliptic Integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "23",
  number =       "2",
  pages =        "512--524",
  month =        mar,
  year =         "1992",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33C05 (33C75)",
  MRnumber =     "93b:33001",
  MRreviewer =   "J. M. H. Peters",
  bibdate =      "Sat Dec 5 18:14:13 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: book
filename: elefunt.bib
label: Baker:1992:CMF
author: Louis Baker
title: C Mathematical Function Handbook
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
pages: xviii + 757
year: 1992
ISBN: 0-07-911158-0 OR 0079111580
ISBN13: 978-0-07-911158-6 OR 9780079111586
LCCN: QA351.B17 1991; QA351 .B17 1992
bibdate: Fri Aug 31 18:54:02 MDT 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; melvyl.cdlib.org:210/CDL90
bibtimestamp: 2007.08.31 18:54:02 MDT
series: McGraw-Hill programming tools for scientists and engineers
remark: System requirements for computer disk: PC; C or C++ compiler.
subject: Functions, Special; Computer programs; C (Computer program language)
acknowledgement: ack-nhfb
rawauthor: Louis Baker
rawtitle: {C} Mathematical Function Handbook
TOC:
Preface / xv 1. Special Functions and Numerical Analysis / 1 Correspondence with Abramowitz and Stegun / 1 Numerical Analysis / 1 The IEEE-754 Standard / 1 Practical Considerations / 3 Reference / 6 2. Special Functions in C and C++ / 8 C and C++ / 8 Portability, ANSI C, and C++ / 8 Infinite Loops / 9 Header Files COMPLEX.H, CMLIB.H, PROTOM.H / 10 Error Handling / 10 Pitfalls with Special Functions / 11 Normalization Conventions / 12 Tips and Pitfalls in C / 12 Calling C from C++ / 14 References / 15 Cmlib.h / 16 COMPLEX.H Header File / 17 Prototypes for booktitle C Mathematical Function Handbook / 19 3. Elementary Analytical Methods / 33 Powers and Roots / 33 Complex Numbers / 34 Roots of Polynomials / 35 Quadratics / 35 Cubics / 35 Quartics (biquadratics) / 36 Implementation Considerations / 37 Ouintics / 38 References / 38 Complex Variable Auxiliary Routines / 39 Powers and Roots / 45 Polynomial Root Finders / 48 Test Driver for Programs of Chapters 3-4 / 60 4. Elementary Transcendental Functions / 72 Elementary Functions / 72 Complex Elementary Functions / 73 Gudermannian / 74 References / 74 5. Exponential Integral and Relatives / 75 Exponential and Related Integrals / 75 Methods / 76 References / 76 Shi(x) and Chi(x) / 76 Exponential Integral / 78 Test Driver Results: Exponential Integral and Relatives / 95 6. Gamma Function and Related Integrals / 100 Gamma Function and Relatives / 100 The Pochhammer Symbol / 100 Methods / 101 Asymptotic Series / 101 Reference / 101 Gamma Function and Relatives / 102 Digamma and First 2 Polygamma Functions / 111 7. Error Function and Relatives / 115 Error Function and Relatives / 115 Methods / 117 Recurrence Relations / 117 C Code / 118 References / 118 Figure: Dawson's Integral / 118 Plasma Dispersion Function / 120 Iterated Error Function / 127 Boehmer (generalized Fresnel) Integral / 129 Complementary Error Function for Complex Arguments / 133 Test Driver Chapter 7 / 134 8. Legendre Functions / 142 Legendre Functions / 142 Derivatives / 143 Applications / 143 Methods / 144 References / 144 Legendre and Associated Legendre Functions / 146 Legendre Functions for $|x| > 1$ / 155 Toroidal $P|x| > 1$ / 163 Mehler (Conical Legendre) Functions / 164 Test Driver for Legendre Functions of Chapter 8 / 166 9. Bessel Functions / 177 Struve Functions / 178 Anger and Weber Functions / 179 Relationship to Confluent Hypergeometric Function / 179 Derivatives / 179 Other Related Functions / 179 Zeros of Bessel Functions / 180 Applications / 180 Methods / 180 References / 181 Bessel Functions for Complex Arguments / 182 Bessel Functions: Rational Approximations / 194 Bessel Function Tables as a Function of (Integral) n / 201 Zeros of Bessel Functions / 205 Test Driver for Bessel Functions / 211 Test Driver Bessel Zero / 220 Output of Bessel Function Test Driver / 221 Output of Test Driver for Zerobess() / 237 10. Bessel Functions of Fractional Order / 239 Introduction / 239 Spherical Bessel Functions / 239 Airy Functions / 239 Applications / 240 Asymptotics / 240 Caustics / 240 Schroedinger's Equation, Turning Points and the WKB Method / 242 Methods / 243 The $|A|$ Function / 243 References / 244 Spherical Bessel Functions and Allied Routines / 245 Airy, Bessel Functions and Integrals Thereof / 250 11. Integrals of Bessel Functions / 265 Introduction / 265 Applications / 265 Methods / 265 Bickley Functions / 265 Adaptive Quadrature / 266 Repeated Integrals of Jn / 266 Other Integrals / 266 References / 266 Figures of Integrals of Bessel Functions / 267 Integrals of Bessel Functions / 277 Adaptive Integration Routine / 242 12. Struve and Anger--Weber Functions / 284 Introduction / 284 Struve Functions / 284 Anger--Weber Functions / 284 Methods / 285 References / 285 Figures / 286 Struve Functions General Order / 289 Struve Functions Lowest Order / 291 Integrals of Struve HO, HO/t, LO / 295 Integral of Anger--Weber Function / 297 13. Confluent Hypergeometric Functions and Relatives / 301 Introduction / 301 Airy Functions / 303 Applications / 303 Methods / 304 References / 304 Confluent Hypergeometric Function Complex Arguments / 305 Test Drive Confluent Hypergeometric Function / 318 Confluent Hypergeometric Function U / 322 Test Driver U.c / 331 Test Output: Confluent-Hypergeometric Function / 332 Test Output: U / 334 14. Coulomb Wave Functions / 335 Introduction / 335 Methods / 336 References / 337 Coulomb Wave Functions / 339 Test Driver Coulomb Wave Functions / 343 Test Output: Coulomb wave Functions / 344 15. The Hypergeometric Function / 345 Introduction / 345 Applications / 346 Methods / 346 References / 346 Hypergeometric Function Complex Arguments / 347 Legendre Function $P$ for Complex Parameters / 364 Legendre $Q$ for Complex Arguments / 366 Test Driver $_2F_1$ / 369 Output: Gauss Hypergeometric Functions / 370 Real Hypergeometric Function and Relatives / 371 16. The Elliptic Functions / 373 Introduction / 373 Applications / 376 Methods / 376 References / 377 Figure / 378 Basic Elliptic Functions Real Arguments / 380 Elliptic Integral of Third Kind / 391 Jacobian Elliptic Function Complex Argument / 397 Complex Elliptic Theta Functions / 406 Output: Test Driver for Elliptic Functions / 411 17. The Elliptic Integrals / 416 Introduction / 415 Caveat / 416 References / 417 Figures / 417 18. The Weierstrass Elliptic Function and Relatives / 425 Introduction / 425 Methods / 427 References / 427 Inverse of Weierstrass Elliptic P . / 428 Brent Root Finder / 430 19. The Parabolic Cylinder Functions / 432 Introduction / 432 Methods / 432 Figures / 432 Parabolic Cylinder Functions / 435 Test Driver Parabolic Cylinder Function / 442 20. The Mathieu Functions / 444 Introduction / 444 Method / 443 References / 445 Figures / 445 Mathieu Functions / 449 Mathieu Functions Test Driver / 465 Test Output: Mathieu Functions / 467 21. The Spheroidal Wave Functions / 475 Introduction / 475 Spheroidal Wave Functions / 475 Generalized Spheroidal Wave Functions / 477 Caveat / 477 Method / 477 References / 478 Figures / 478 Spheroidal Wave Functions / 486 Legptable Pn,m for n = m to ntop / 500 Test Driver Spheroidal Wave Functions / 501 Test Output: Spheroidal Wave Functions / 504 22. Orthogonal Polynomials / 509 Introduction / 509 Contents / 509 Applications / 509 Method / 509 Orthogonal Polynomials / 510 Test Driver Orthogonal Polynomials / 513 23. Bernoulli and Euler Numbers and Polynomials, Riemann Zeta Function / 516 Introduction / 516 Riemann Zeta Function / 516 Bernoulli Polynomials and Numbers / 517 Euler Polynomials and Numbers / 517 Methods / 517 References / 517 Riemann Zeta (real arguments) / 519 Test Driver Riemann Zeta (Real) / 527 Test Output: Riemann Zeta, Bernoulli, Euler Numbers / 324 24. Combinatorics. Stirling Numbers / 529 Introduction / 529 Methods / 529 References / 529 Stirling Numbers First and Second Kind / 530 Fibonacci Numbers / 531 Binomial Coefficients / 532 Test Driver for Stirling Numbers / 533 Test Output: Stirling, Fibonacci, Binomial Coefficients / 534 25. Numerical Analysis / 535 Discussion / 535 Reference / 536 26. Statistical Functions, Probability Distributions, and Random Variables / 537 Introduction / 537 Methods / 537 References / 537 Random Numbers / 538 Random Distributions / 544 Test Driver for Random Number / 551 Test Output: Random Numbers and Distributions / 560 Calculator Version of Stat.c Routines / 565 27. Miscellaneous Functions / 592 Introduction / 592 Debye Functions / 592 Method / 593 Sievert / 593 Method / 593 Abramowitz and Kruse--Ramsey / 593 Method / 593 Ritchie / 593 Method / 593 Dilogarithm and Polylogarithms / 593 Method / 594 Claussen / 594 Method / 594 Lobachevsky / 594 Method / 594 Clebsch--Gordon and Relatives / 594 Method / 595 v and Relatives / 595 Method / 596 References / 596 Figures / 595 Sievert Integral Chapter 27 / 605 Dilogarithm / 606 Polylogarithm Function / 607 ``Abramowitz'' Functions f1, f2, f3 from Chapter 27 / 608 Nu and Mu Integrals of Erdelyi Vol III p. 217 / 612 Lobachevsky Function / 614 Test Driver Miscellaneous Functions / 616 Test Driver Ritchie's Integral / 619 Test Output: Miscellaneous Functions / 620 Test Output: Ritchie's Integral / 624 Clebsch--Gordon, Wigner, Related Coefficients / 625 Test Driver Wigner / 631 Wigner Sample Output / 635 28. Scales of Notation / 636 29. C++ Programs / 637 Hurwitz Zeta and Lerch Phi Transcendent / 638 Methods / 638 Meijer $G$ and Generalized Hypergeometric Functions / 638 Methods / 639 Elliptic Functions / 639 Applications / 639 Methods / 639 Fock Functions / 640 Methods / 541 References / 641 // Complex.hpp / 643 Elliptic Functions / 646 Arithmetic--Geometric Mean (AGM) Supplemental / 656 Test Driver for: Elliptic Functions / 662 // Cvector.hpp / 665 // cmatrix.hpp / 666 Test Output: Elliptic Functions / 667 Complex C++ Utilities / 669 Fock Functions / 674 Test Output: Fock Functions / 682 ``Abramowitz'' Functions f1, f2, f3 from Chapter 27 / 697 Test Output: Abramowitz Functions, Complex Arguments / 701 Riemann and Hurwitz / 712 Riemann and Hurwitz: Pade / 716 Lerch Phi Transcendent / 720 Generalized Hypergeometric Function and Meijer $G$ / 723 Test Output: Meijer $G$ / 730 Generalized Hypergeometric Function and Meijer $G$ / 731 Test Output: Meijer $G$ with Pade / 738 MacRobert E Function / 739 30. Xref / 740 Other Listings / 741 Adaptive Quadrature (from C loops) / 741 Test Driver Chaps. 16--18 / 743 Index to C Functions / 747 Index / 753

rawTOC:
Preface / xv \\ 1. Special Functions and Numerical Analysis / 1 \\ \\ Correspondence with Abramowitz and Stegun / 1 \\ Numerical Analysis / 1 \\ The IEEE-754 Standard / 1 \\ Practical Considerations / 3 \\ Reference / 6 \\ \\ 2. Special Functions in C and C++ / 8 \\ C and C++ / 8 \\ Portability, ANSI C, and C++ / 8 \\ Infinite Loops / 9 \\ Header Files COMPLEX.H, CMLIB.H, PROTOM.H / 10 \\ Error Handling / 10 \\ Pitfalls with Special Functions / 11 \\ Normalization Conventions / 12 \\ Tips and Pitfalls in C / 12 \\ Calling C from C++ / 14 \\ References / 15 \\ Cmlib.h / 16 \\ COMPLEX.H Header File / 17 \\ Prototypes for \booktitle{C Mathematical Function Handbook} / 19 \\ \\ 3. Elementary Analytical Methods / 33 \\ Powers and Roots / 33 \\ Complex Numbers / 34 \\ Roots of Polynomials / 35 \\ Quadratics / 35 \\ Cubics / 35 \\ Quartics (biquadratics) / 36 \\ Implementation Considerations / 37 \\ Ouintics / 38 \\ References / 38 \\ Complex Variable Auxiliary Routines / 39 \\ Powers and Roots / 45 \\ Polynomial Root Finders / 48 \\ Test Driver for Programs of Chapters 3-4 / 60 \\ \\ 4. Elementary Transcendental Functions / 72 \\ Elementary Functions / 72 \\ Complex Elementary Functions / 73 \\ Gudermannian / 74 \\ References / 74 \\ \\ 5. Exponential Integral and Relatives / 75 \\ Exponential and Related Integrals / 75 \\ Methods / 76 \\ References / 76 \\ Shi(x) and Chi(x) / 76 \\ Exponential Integral / 78 \\ Test Driver Results: Exponential Integral and Relatives / 95 \\ \\ 6. Gamma Function and Related Integrals / 100 \\ Gamma Function and Relatives / 100 \\ The Pochhammer Symbol / 100 \\ Methods / 101 \\ Asymptotic Series / 101 \\ Reference / 101 \\ Gamma Function and Relatives / 102 \\ Digamma and First 2 Polygamma Functions / 111 \\ \\ 7. Error Function and Relatives / 115 \\ Error Function and Relatives / 115 \\ Methods / 117 \\ Recurrence Relations / 117 \\ C Code / 118 \\ References / 118 \\ Figure: Dawson's Integral / 118 \\ Plasma Dispersion Function / 120 \\ Iterated Error Function / 127 \\ Boehmer (generalized Fresnel) Integral / 129 \\ Complementary Error Function for Complex Arguments / 133 \\ Test Driver Chapter 7 / 134 \\ \\ 8. Legendre Functions / 142 \\ Legendre Functions / 142 \\ Derivatives / 143 \\ Applications / 143 \\ Methods / 144 \\ References / 144 \\ Legendre and Associated Legendre Functions / 146 \\ Legendre Functions for $|x| > 1$ / 155 \\ Toroidal $P|x| > 1$ / 163 \\ Mehler (Conical Legendre) Functions / 164 \\ Test Driver for Legendre Functions of Chapter 8 / 166 \\ \\ 9. Bessel Functions / 177 \\ Struve Functions / 178 \\ Anger and Weber Functions / 179 \\ Relationship to Confluent Hypergeometric Function / 179 \\ Derivatives / 179 \\ Other Related Functions / 179 \\ Zeros of Bessel Functions / 180 \\ Applications / 180 \\ Methods / 180 \\ References / 181 \\ Bessel Functions for Complex Arguments / 182 \\ Bessel Functions: Rational Approximations / 194 \\ Bessel Function Tables as a Function of (Integral) n / 201 \\ Zeros of Bessel Functions / 205 \\ Test Driver for Bessel Functions / 211 \\ Test Driver Bessel Zero / 220 \\ Output of Bessel Function Test Driver / 221 \\ Output of Test Driver for Zerobess() / 237 \\ \\ 10. Bessel Functions of Fractional Order / 239 \\ Introduction / 239 \\ Spherical Bessel Functions / 239 \\ Airy Functions / 239 \\ Applications / 240 \\ Asymptotics / 240 \\ Caustics / 240 \\ Schroedinger's Equation, Turning Points and the WKB Method / 242 \\ Methods / 243 \\ The $|A|$ Function / 243 \\ References / 244 \\ Spherical Bessel Functions and Allied Routines / 245 \\ Airy, Bessel Functions and Integrals Thereof / 250 \\ \\ 11. Integrals of Bessel Functions / 265 \\ Introduction / 265 \\ Applications / 265 \\ Methods / 265 \\ Bickley Functions / 265 \\ Adaptive Quadrature / 266 \\ Repeated Integrals of Jn / 266 \\ Other Integrals / 266 \\ References / 266 \\ Figures of Integrals of Bessel Functions / 267 \\ Integrals of Bessel Functions / 277 \\ Adaptive Integration Routine / 242 \\ \\ 12. Struve and Anger--Weber Functions / 284 \\ Introduction / 284 \\ Struve Functions / 284 \\ Anger--Weber Functions / 284 \\ Methods / 285 \\ References / 285 \\ Figures / 286 \\ Struve Functions General Order / 289 \\ Struve Functions Lowest Order / 291 \\ Integrals of Struve HO, HO/t, LO / 295 \\ Integral of Anger--Weber Function / 297 \\ \\ 13. Confluent Hypergeometric Functions and Relatives / 301 \\ Introduction / 301 \\ Airy Functions / 303 \\ Applications / 303 \\ Methods / 304 \\ References / 304 \\ Confluent Hypergeometric Function Complex Arguments / 305 \\ Test Drive Confluent Hypergeometric Function / 318 \\ Confluent Hypergeometric Function U / 322 \\ Test Driver U.c / 331 \\ Test Output: Confluent-Hypergeometric Function / 332 \\ Test Output: U / 334 \\ \\ 14. Coulomb Wave Functions / 335 \\ Introduction / 335 \\ Methods / 336 \\ References / 337 \\ Coulomb Wave Functions / 339 \\ Test Driver Coulomb Wave Functions / 343 \\ Test Output: Coulomb wave Functions / 344 \\ \\ 15. The Hypergeometric Function / 345 \\ Introduction / 345 \\ Applications / 346 \\ Methods / 346 \\ References / 346 \\ Hypergeometric Function Complex Arguments / 347 \\ Legendre Function $P$ for Complex Parameters / 364 \\ Legendre $Q$ for Complex Arguments / 366 \\ Test Driver $_2F_1$ / 369 \\ Output: Gauss Hypergeometric Functions / 370 \\ Real Hypergeometric Function and Relatives / 371 \\ \\ 16. The Elliptic Functions / 373 \\ Introduction / 373 \\ Applications / 376 \\ Methods / 376 \\ References / 377 \\ Figure / 378 \\ Basic Elliptic Functions Real Arguments / 380 \\ Elliptic Integral of Third Kind / 391 \\ Jacobian Elliptic Function Complex Argument / 397 \\ Complex Elliptic Theta Functions / 406 \\ Output: Test Driver for Elliptic Functions / 411 \\ \\ 17. The Elliptic Integrals / 416 \\ Introduction / 415 \\ Caveat / 416 \\ References / 417 \\ Figures / 417 \\ \\ 18. The Weierstrass Elliptic Function and Relatives / 425 \\ Introduction / 425 \\ Methods / 427 \\ References / 427 \\ Inverse of Weierstrass Elliptic P . / 428 \\ Brent Root Finder / 430 \\ \\ 19. The Parabolic Cylinder Functions / 432 \\ Introduction / 432 \\ Methods / 432 \\ Figures / 432 \\ Parabolic Cylinder Functions / 435 \\ Test Driver Parabolic Cylinder Function / 442 \\ \\ 20. The Mathieu Functions / 444 \\ Introduction / 444 \\ Method / 443 \\ References / 445 \\ Figures / 445 \\ Mathieu Functions / 449 \\ Mathieu Functions Test Driver / 465 \\ Test Output: Mathieu Functions / 467 \\ \\ 21. The Spheroidal Wave Functions / 475 \\ Introduction / 475 \\ Spheroidal Wave Functions / 475 \\ Generalized Spheroidal Wave Functions / 477 \\ Caveat / 477 \\ Method / 477 \\ References / 478 \\ Figures / 478 \\ Spheroidal Wave Functions / 486 \\ Legptable Pn,m for n = m to ntop / 500 \\ Test Driver Spheroidal Wave Functions / 501 \\ Test Output: Spheroidal Wave Functions / 504 \\ \\ 22. Orthogonal Polynomials / 509 \\ Introduction / 509 \\ Contents / 509 \\ Applications / 509 \\ Method / 509 \\ Orthogonal Polynomials / 510 \\ Test Driver Orthogonal Polynomials / 513 \\ \\ 23. Bernoulli and Euler Numbers and Polynomials, Riemann Zeta Function / 516 \\ Introduction / 516 \\ Riemann Zeta Function / 516 \\ Bernoulli Polynomials and Numbers / 517 \\ Euler Polynomials and Numbers / 517 \\ Methods / 517 \\ References / 517 \\ Riemann Zeta (real arguments) / 519 \\ Test Driver Riemann Zeta (Real) / 527 \\ Test Output: Riemann Zeta, Bernoulli, Euler Numbers / 324 \\ \\ 24. Combinatorics. Stirling Numbers / 529 \\ Introduction / 529 \\ Methods / 529 \\ References / 529 \\ Stirling Numbers First and Second Kind / 530 \\ Fibonacci Numbers / 531 \\ Binomial Coefficients / 532 \\ Test Driver for Stirling Numbers / 533 \\ Test Output: Stirling, Fibonacci, Binomial Coefficients / 534 \\ \\ 25. Numerical Analysis / 535 \\ Discussion / 535 \\ Reference / 536 \\ \\ 26. Statistical Functions, Probability Distributions, and Random Variables / 537 \\ Introduction / 537 \\ Methods / 537 \\ References / 537 \\ Random Numbers / 538 \\ Random Distributions / 544 \\ Test Driver for Random Number / 551 \\ Test Output: Random Numbers and Distributions / 560 \\ Calculator Version of Stat.c Routines / 565 \\ \\ 27. Miscellaneous Functions / 592 \\ Introduction / 592 \\ Debye Functions / 592 \\ Method / 593 \\ Sievert / 593 \\ Method / 593 \\ Abramowitz and Kruse--Ramsey / 593 \\ Method / 593 \\ Ritchie / 593 \\ Method / 593 \\ Dilogarithm and Polylogarithms / 593 \\ Method / 594 \\ Claussen / 594 \\ Method / 594 \\ Lobachevsky / 594 \\ Method / 594 \\ Clebsch--Gordon and Relatives / 594 \\ Method / 595 \\ v and Relatives / 595 \\ Method / 596 \\ References / 596 \\ Figures / 595 \\ Sievert Integral Chapter 27 / 605 \\ Dilogarithm / 606 \\ Polylogarithm Function / 607 \\ ``Abramowitz'' Functions f1, f2, f3 from Chapter 27 / 608 \\ Nu and Mu Integrals of Erdelyi Vol III p. 217 / 612 \\ Lobachevsky Function / 614 \\ Test Driver Miscellaneous Functions / 616 \\ Test Driver Ritchie's Integral / 619 \\ Test Output: Miscellaneous Functions / 620 \\ Test Output: Ritchie's Integral / 624 \\ Clebsch--Gordon, Wigner, Related Coefficients / 625 \\ Test Driver Wigner / 631 \\ Wigner Sample Output / 635 \\ \\ 28. Scales of Notation / 636 \\ \\ 29. C++ Programs / 637 \\ Hurwitz Zeta and Lerch Phi Transcendent / 638 \\ Methods / 638 \\ Meijer $G$ and Generalized Hypergeometric Functions / 638 \\ Methods / 639 \\ Elliptic Functions / 639 \\ Applications / 639 \\ Methods / 639 \\ Fock Functions / 640 \\ Methods / 541 \\ References / 641 \\ // Complex.hpp / 643 \\ Elliptic Functions / 646 \\ Arithmetic--Geometric Mean (AGM) Supplemental / 656 \\ Test Driver for: Elliptic Functions / 662 \\ // Cvector.hpp / 665 \\ // cmatrix.hpp / 666 \\ Test Output: Elliptic Functions / 667 \\ Complex C++ Utilities / 669 \\ Fock Functions / 674 \\ Test Output: Fock Functions / 682 \\ ``Abramowitz'' Functions f1, f2, f3 from Chapter 27 / 697 \\ Test Output: Abramowitz Functions, Complex Arguments / 701 \\ Riemann and Hurwitz / 712 \\ Riemann and Hurwitz: Pad{\'e} / 716 \\ Lerch Phi Transcendent / 720 \\ Generalized Hypergeometric Function and Meijer $G$ / 723 \\ Test Output: Meijer $G$ / 730 \\ Generalized Hypergeometric Function and Meijer $G$ / 731 \\ Test Output: Meijer $G$ with Pad{\'e} / 738 \\ MacRobert E Function / 739 \\ \\ 30. Xref / 740 \\ Other Listings / 741 \\ Adaptive Quadrature (from C loops) / 741 \\ Test Driver Chaps. 16--18 / 743 \\ Index to C Functions / 747 \\ Index / 753

entry:
@Book{Baker:1992:CMF,
  author =       "Louis Baker",
  title =        "{C} Mathematical Function Handbook",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xviii + 757",
  year =         "1992",
  ISBN =         "0-07-911158-0",
  ISBN-13 =      "978-0-07-911158-6",
  LCCN =         "QA351.B17 1991; QA351 .B17 1992",
  bibdate =      "Fri Aug 31 18:54:02 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "McGraw-Hill programming tools for scientists and
                 engineers",
  acknowledgement = ack-nhfb,
  remark =       "System requirements for computer disk: PC; C or C++
                 compiler.",
  subject =      "Functions, Special; Computer programs; C (Computer
                 program language)",
  tableofcontents = "Preface / xv \\
                 1. Special Functions and Numerical Analysis / 1 \\
                 \\
                 Correspondence with Abramowitz and Stegun / 1 \\
                 Numerical Analysis / 1 \\
                 The IEEE-754 Standard / 1 \\
                 Practical Considerations / 3 \\
                 Reference / 6 \\
                 \\
                 2. Special Functions in C and C++ / 8 \\
                 C and C++ / 8 \\
                 Portability, ANSI C, and C++ / 8 \\
                 Infinite Loops / 9 \\
                 Header Files COMPLEX.H, CMLIB.H, PROTOM.H / 10 \\
                 Error Handling / 10 \\
                 Pitfalls with Special Functions / 11 \\
                 Normalization Conventions / 12 \\
                 Tips and Pitfalls in C / 12 \\
                 Calling C from C++ / 14 \\
                 References / 15 \\
                 Cmlib.h / 16 \\
                 COMPLEX.H Header File / 17 \\
                 Prototypes for \booktitle{C Mathematical Function
                 Handbook} / 19 \\
                 \\
                 3. Elementary Analytical Methods / 33 \\
                 Powers and Roots / 33 \\
                 Complex Numbers / 34 \\
                 Roots of Polynomials / 35 \\
                 Quadratics / 35 \\
                 Cubics / 35 \\
                 Quartics (biquadratics) / 36 \\
                 Implementation Considerations / 37 \\
                 Ouintics / 38 \\
                 References / 38 \\
                 Complex Variable Auxiliary Routines / 39 \\
                 Powers and Roots / 45 \\
                 Polynomial Root Finders / 48 \\
                 Test Driver for Programs of Chapters 3-4 / 60 \\
                 \\
                 4. Elementary Transcendental Functions / 72 \\
                 Elementary Functions / 72 \\
                 Complex Elementary Functions / 73 \\
                 Gudermannian / 74 \\
                 References / 74 \\
                 \\
                 5. Exponential Integral and Relatives / 75 \\
                 Exponential and Related Integrals / 75 \\
                 Methods / 76 \\
                 References / 76 \\
                 Shi(x) and Chi(x) / 76 \\
                 Exponential Integral / 78 \\
                 Test Driver Results: Exponential Integral and Relatives
                 / 95 \\
                 \\
                 6. Gamma Function and Related Integrals / 100 \\
                 Gamma Function and Relatives / 100 \\
                 The Pochhammer Symbol / 100 \\
                 Methods / 101 \\
                 Asymptotic Series / 101 \\
                 Reference / 101 \\
                 Gamma Function and Relatives / 102 \\
                 Digamma and First 2 Polygamma Functions / 111 \\
                 \\
                 7. Error Function and Relatives / 115 \\
                 Error Function and Relatives / 115 \\
                 Methods / 117 \\
                 Recurrence Relations / 117 \\
                 C Code / 118 \\
                 References / 118 \\
                 Figure: Dawson's Integral / 118 \\
                 Plasma Dispersion Function / 120 \\
                 Iterated Error Function / 127 \\
                 Boehmer (generalized Fresnel) Integral / 129 \\
                 Complementary Error Function for Complex Arguments /
                 133 \\
                 Test Driver Chapter 7 / 134 \\
                 \\
                 8. Legendre Functions / 142 \\
                 Legendre Functions / 142 \\
                 Derivatives / 143 \\
                 Applications / 143 \\
                 Methods / 144 \\
                 References / 144 \\
                 Legendre and Associated Legendre Functions / 146 \\
                 Legendre Functions for $|x| > 1$ / 155 \\
                 Toroidal $P|x| > 1$ / 163 \\
                 Mehler (Conical Legendre) Functions / 164 \\
                 Test Driver for Legendre Functions of Chapter 8 / 166
                 \\
                 \\
                 9. Bessel Functions / 177 \\
                 Struve Functions / 178 \\
                 Anger and Weber Functions / 179 \\
                 Relationship to Confluent Hypergeometric Function / 179
                 \\
                 Derivatives / 179 \\
                 Other Related Functions / 179 \\
                 Zeros of Bessel Functions / 180 \\
                 Applications / 180 \\
                 Methods / 180 \\
                 References / 181 \\
                 Bessel Functions for Complex Arguments / 182 \\
                 Bessel Functions: Rational Approximations / 194 \\
                 Bessel Function Tables as a Function of (Integral) n /
                 201 \\
                 Zeros of Bessel Functions / 205 \\
                 Test Driver for Bessel Functions / 211 \\
                 Test Driver Bessel Zero / 220 \\
                 Output of Bessel Function Test Driver / 221 \\
                 Output of Test Driver for Zerobess() / 237 \\
                 \\
                 10. Bessel Functions of Fractional Order / 239 \\
                 Introduction / 239 \\
                 Spherical Bessel Functions / 239 \\
                 Airy Functions / 239 \\
                 Applications / 240 \\
                 Asymptotics / 240 \\
                 Caustics / 240 \\
                 Schroedinger's Equation, Turning Points and the WKB
                 Method / 242 \\
                 Methods / 243 \\
                 The $|A|$ Function / 243 \\
                 References / 244 \\
                 Spherical Bessel Functions and Allied Routines / 245
                 \\
                 Airy, Bessel Functions and Integrals Thereof / 250 \\
                 \\
                 11. Integrals of Bessel Functions / 265 \\
                 Introduction / 265 \\
                 Applications / 265 \\
                 Methods / 265 \\
                 Bickley Functions / 265 \\
                 Adaptive Quadrature / 266 \\
                 Repeated Integrals of Jn / 266 \\
                 Other Integrals / 266 \\
                 References / 266 \\
                 Figures of Integrals of Bessel Functions / 267 \\
                 Integrals of Bessel Functions / 277 \\
                 Adaptive Integration Routine / 242 \\
                 \\
                 12. Struve and Anger--Weber Functions / 284 \\
                 Introduction / 284 \\
                 Struve Functions / 284 \\
                 Anger--Weber Functions / 284 \\
                 Methods / 285 \\
                 References / 285 \\
                 Figures / 286 \\
                 Struve Functions General Order / 289 \\
                 Struve Functions Lowest Order / 291 \\
                 Integrals of Struve HO, HO/t, LO / 295 \\
                 Integral of Anger--Weber Function / 297 \\
                 \\
                 13. Confluent Hypergeometric Functions and Relatives /
                 301 \\
                 Introduction / 301 \\
                 Airy Functions / 303 \\
                 Applications / 303 \\
                 Methods / 304 \\
                 References / 304 \\
                 Confluent Hypergeometric Function Complex Arguments /
                 305 \\
                 Test Drive Confluent Hypergeometric Function / 318 \\
                 Confluent Hypergeometric Function U / 322 \\
                 Test Driver U.c / 331 \\
                 Test Output: Confluent-Hypergeometric Function / 332
                 \\
                 Test Output: U / 334 \\
                 \\
                 14. Coulomb Wave Functions / 335 \\
                 Introduction / 335 \\
                 Methods / 336 \\
                 References / 337 \\
                 Coulomb Wave Functions / 339 \\
                 Test Driver Coulomb Wave Functions / 343 \\
                 Test Output: Coulomb wave Functions / 344 \\
                 \\
                 15. The Hypergeometric Function / 345 \\
                 Introduction / 345 \\
                 Applications / 346 \\
                 Methods / 346 \\
                 References / 346 \\
                 Hypergeometric Function Complex Arguments / 347 \\
                 Legendre Function $P$ for Complex Parameters / 364 \\
                 Legendre $Q$ for Complex Arguments / 366 \\
                 Test Driver $_2F_1$ / 369 \\
                 Output: Gauss Hypergeometric Functions / 370 \\
                 Real Hypergeometric Function and Relatives / 371 \\
                 \\
                 16. The Elliptic Functions / 373 \\
                 Introduction / 373 \\
                 Applications / 376 \\
                 Methods / 376 \\
                 References / 377 \\
                 Figure / 378 \\
                 Basic Elliptic Functions Real Arguments / 380 \\
                 Elliptic Integral of Third Kind / 391 \\
                 Jacobian Elliptic Function Complex Argument / 397 \\
                 Complex Elliptic Theta Functions / 406 \\
                 Output: Test Driver for Elliptic Functions / 411 \\
                 \\
                 17. The Elliptic Integrals / 416 \\
                 Introduction / 415 \\
                 Caveat / 416 \\
                 References / 417 \\
                 Figures / 417 \\
                 \\
                 18. The Weierstrass Elliptic Function and Relatives /
                 425 \\
                 Introduction / 425 \\
                 Methods / 427 \\
                 References / 427 \\
                 Inverse of Weierstrass Elliptic P . / 428 \\
                 Brent Root Finder / 430 \\
                 \\
                 19. The Parabolic Cylinder Functions / 432 \\
                 Introduction / 432 \\
                 Methods / 432 \\
                 Figures / 432 \\
                 Parabolic Cylinder Functions / 435 \\
                 Test Driver Parabolic Cylinder Function / 442 \\
                 \\
                 20. The Mathieu Functions / 444 \\
                 Introduction / 444 \\
                 Method / 443 \\
                 References / 445 \\
                 Figures / 445 \\
                 Mathieu Functions / 449 \\
                 Mathieu Functions Test Driver / 465 \\
                 Test Output: Mathieu Functions / 467 \\
                 \\
                 21. The Spheroidal Wave Functions / 475 \\
                 Introduction / 475 \\
                 Spheroidal Wave Functions / 475 \\
                 Generalized Spheroidal Wave Functions / 477 \\
                 Caveat / 477 \\
                 Method / 477 \\
                 References / 478 \\
                 Figures / 478 \\
                 Spheroidal Wave Functions / 486 \\
                 Legptable Pn,m for n = m to ntop / 500 \\
                 Test Driver Spheroidal Wave Functions / 501 \\
                 Test Output: Spheroidal Wave Functions / 504 \\
                 \\
                 22. Orthogonal Polynomials / 509 \\
                 Introduction / 509 \\
                 Contents / 509 \\
                 Applications / 509 \\
                 Method / 509 \\
                 Orthogonal Polynomials / 510 \\
                 Test Driver Orthogonal Polynomials / 513 \\
                 \\
                 23. Bernoulli and Euler Numbers and Polynomials,
                 Riemann Zeta Function / 516 \\
                 Introduction / 516 \\
                 Riemann Zeta Function / 516 \\
                 Bernoulli Polynomials and Numbers / 517 \\
                 Euler Polynomials and Numbers / 517 \\
                 Methods / 517 \\
                 References / 517 \\
                 Riemann Zeta (real arguments) / 519 \\
                 Test Driver Riemann Zeta (Real) / 527 \\
                 Test Output: Riemann Zeta, Bernoulli, Euler Numbers /
                 324 \\
                 \\
                 24. Combinatorics. Stirling Numbers / 529 \\
                 Introduction / 529 \\
                 Methods / 529 \\
                 References / 529 \\
                 Stirling Numbers First and Second Kind / 530 \\
                 Fibonacci Numbers / 531 \\
                 Binomial Coefficients / 532 \\
                 Test Driver for Stirling Numbers / 533 \\
                 Test Output: Stirling, Fibonacci, Binomial Coefficients
                 / 534 \\
                 \\
                 25. Numerical Analysis / 535 \\
                 Discussion / 535 \\
                 Reference / 536 \\
                 \\
                 26. Statistical Functions, Probability Distributions,
                 and Random Variables / 537 \\
                 Introduction / 537 \\
                 Methods / 537 \\
                 References / 537 \\
                 Random Numbers / 538 \\
                 Random Distributions / 544 \\
                 Test Driver for Random Number / 551 \\
                 Test Output: Random Numbers and Distributions / 560 \\
                 Calculator Version of Stat.c Routines / 565 \\
                 \\
                 27. Miscellaneous Functions / 592 \\
                 Introduction / 592 \\
                 Debye Functions / 592 \\
                 Method / 593 \\
                 Sievert / 593 \\
                 Method / 593 \\
                 Abramowitz and Kruse--Ramsey / 593 \\
                 Method / 593 \\
                 Ritchie / 593 \\
                 Method / 593 \\
                 Dilogarithm and Polylogarithms / 593 \\
                 Method / 594 \\
                 Claussen / 594 \\
                 Method / 594 \\
                 Lobachevsky / 594 \\
                 Method / 594 \\
                 Clebsch--Gordon and Relatives / 594 \\
                 Method / 595 \\
                 v and Relatives / 595 \\
                 Method / 596 \\
                 References / 596 \\
                 Figures / 595 \\
                 Sievert Integral Chapter 27 / 605 \\
                 Dilogarithm / 606 \\
                 Polylogarithm Function / 607 \\
                 ``Abramowitz'' Functions f1, f2, f3 from Chapter 27 /
                 608 \\
                 Nu and Mu Integrals of Erdelyi Vol III p. 217 / 612 \\
                 Lobachevsky Function / 614 \\
                 Test Driver Miscellaneous Functions / 616 \\
                 Test Driver Ritchie's Integral / 619 \\
                 Test Output: Miscellaneous Functions / 620 \\
                 Test Output: Ritchie's Integral / 624 \\
                 Clebsch--Gordon, Wigner, Related Coefficients / 625 \\
                 Test Driver Wigner / 631 \\
                 Wigner Sample Output / 635 \\
                 \\
                 28. Scales of Notation / 636 \\
                 \\
                 29. C++ Programs / 637 \\
                 Hurwitz Zeta and Lerch Phi Transcendent / 638 \\
                 Methods / 638 \\
                 Meijer $G$ and Generalized Hypergeometric Functions /
                 638 \\
                 Methods / 639 \\
                 Elliptic Functions / 639 \\
                 Applications / 639 \\
                 Methods / 639 \\
                 Fock Functions / 640 \\
                 Methods / 541 \\
                 References / 641 \\
                 // Complex.hpp / 643 \\
                 Elliptic Functions / 646 \\
                 Arithmetic--Geometric Mean (AGM) Supplemental / 656 \\
                 Test Driver for: Elliptic Functions / 662 \\
                 // Cvector.hpp / 665 \\
                 // cmatrix.hpp / 666 \\
                 Test Output: Elliptic Functions / 667 \\
                 Complex C++ Utilities / 669 \\
                 Fock Functions / 674 \\
                 Test Output: Fock Functions / 682 \\
                 ``Abramowitz'' Functions f1, f2, f3 from Chapter 27 /
                 697 \\
                 Test Output: Abramowitz Functions, Complex Arguments /
                 701 \\
                 Riemann and Hurwitz / 712 \\
                 Riemann and Hurwitz: Pad{\'e} / 716 \\
                 Lerch Phi Transcendent / 720 \\
                 Generalized Hypergeometric Function and Meijer $G$ /
                 723 \\
                 Test Output: Meijer $G$ / 730 \\
                 Generalized Hypergeometric Function and Meijer $G$ /
                 731 \\
                 Test Output: Meijer $G$ with Pad{\'e} / 738 \\
                 MacRobert E Function / 739 \\
                 \\
                 30. Xref / 740 \\
                 Other Listings / 741 \\
                 Adaptive Quadrature (from C loops) / 741 \\
                 Test Driver Chaps. 16--18 / 743 \\
                 Index to C Functions / 747 \\
                 Index / 753",
}


bibtype: article
filename: elefunt.bib
label: Baker:1992:LCE
author: H. G. Baker
title: Less Complex Elementary Functions
journal: j-SIGPLAN
volume: 27
number: 11
pages: 15--16
month: nov
monthnumber: 11
year: 1992
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Thu Sep 08 08:11:27 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.08 08:11:27 ???
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nj
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: H. G. Baker
rawtitle: Less Complex Elementary Functions
entry:
@Article{Baker:1992:LCE,
  author =       "H. G. Baker",
  title =        "Less Complex Elementary Functions",
  journal =      j-SIGPLAN,
  volume =       "27",
  number =       "11",
  pages =        "15--16",
  month =        nov,
  year =         "1992",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Thu Sep 08 08:11:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}


bibtype: article
filename: elefunt.bib
label: Bohman:1992:FRP
author: Jan Bohman and Carl-Erik Froberg
title: The $ Gamma $-function revisited: power series expansions and real-imaginary zero lines
journal: j-MATH-COMPUT
volume: 58
number: 197
pages: 315--322
month: jan
monthnumber: 1
year: 1992
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33B15 (11Y70 65D20)
MRnumber: 92e:33001
MRreviewer: A. de Castro Brzezicki
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Jan Bohman and Carl-Erik Fr{\"o}berg
rawtitle: The {$ \Gamma $}-function revisited: power series expansions and real-imaginary zero lines
entry:
@Article{Bohman:1992:FRP,
  author =       "Jan Bohman and Carl-Erik Fr{\"o}berg",
  title =        "The {$ \Gamma $}-function revisited: power series
                 expansions and real-imaginary zero lines",
  journal =      j-MATH-COMPUT,
  volume =       "58",
  number =       "197",
  pages =        "315--322",
  month =        jan,
  year =         "1992",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33B15 (11Y70 65D20)",
  MRnumber =     "92e:33001",
  MRreviewer =   "A. de Castro Brzezicki",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Borwein:1992:FEG
author: J. M. Borwein and I. J. Zucker
journal: j-IMA-J-NUMER-ANAL
volume: 12
number: 4
pages: 519--526
year: 1992
CODEN: IJNADH
ISSN: 0272-4979 (print), 1464-3642 (electronic) OR 02724979 (print), 14643642 (electronic)
ISSNL: 0272-4979 OR 02724979
MRclass: 65D20
MRnumber: 93g:65028
bibdate: Sat Dec 23 17:06:35 MST 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; MathSciNet database
bibtimestamp: 2000.12.23 17:06:35 MST
fjournal: IMA Journal of Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://imajna.oxfordjournals.org/content/by/year
rawauthor: J. M. Borwein and I. J. Zucker
title:
Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind

rawtitle:
Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind

entry:
@Article{Borwein:1992:FEG,
  author =       "J. M. Borwein and I. J. Zucker",
  title =        "Fast evaluation of the gamma function for small
                 rational fractions using complete elliptic integrals of
                 the first kind",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "12",
  number =       "4",
  pages =        "519--526",
  year =         "1992",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65D20",
  MRnumber =     "93g:65028",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}


bibtype: article
filename: elefunt.bib
label: Buhring:1992:GHF
author: Wolfgang Buhring
title: Generalized hypergeometric functions at unit argument
journal: j-PROC-AM-MATH-SOC
volume: 114
number: 1
pages: 145--153
year: 1992
CODEN: PAMYAR
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 33C20
MRnumber: MR1068116 (92c:33004)
bibdate: Thu Dec 01 09:52:06 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 09:52:06 ???
fjournal: Proceedings of the American Mathematical Society
remark: The paper treats $_p + 1F_p$ (or equivalently, $_p F_p - 1$ ).
ZMnumber: Zbl 0754.33003
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/journals/proc
rawauthor: Wolfgang B{\"u}hring
rawtitle: Generalized hypergeometric functions at unit argument
entry:
@Article{Buhring:1992:GHF,
  author =       "Wolfgang B{\"u}hring",
  title =        "Generalized hypergeometric functions at unit
                 argument",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "114",
  number =       "1",
  pages =        "145--153",
  month =        "????",
  year =         "1992",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "33C20",
  MRnumber =     "MR1068116 (92c:33004)",
  bibdate =      "Thu Dec 01 09:52:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "Zbl 0754.33003",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  remark =       "The paper treats $_{p + 1F}_p$ (or equivalently, $_p
                 F_{p - 1}$ ).",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1992:TEI
author: B. C. Carlson
title: A Table of Elliptic Integrals: Two Quadratic Factors
journal: j-MATH-COMPUT
volume: 59
number: 199
pages: 165--180
month: jul
monthnumber: 7
year: 1992
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D20 (33C75 33E05)
MRnumber: 92k:65027
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: B. C. Carlson
rawtitle: A Table of Elliptic Integrals: Two Quadratic Factors
entry:
@Article{Carlson:1992:TEI,
  author =       "B. C. Carlson",
  title =        "A Table of Elliptic Integrals: Two Quadratic Factors",
  journal =      j-MATH-COMPUT,
  volume =       "59",
  number =       "199",
  pages =        "165--180",
  month =        jul,
  year =         "1992",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (33C75 33E05)",
  MRnumber =     "92k:65027",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


