%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.65", %%% date = "16 March 2019", %%% time = "12:15:20 MDT", %%% filename = "numana2010.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "http://www.math.utah.edu/~beebe", %%% checksum = "27605 10143 53777 517284", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography; BibTeX; numerical analysis", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This bibliography collects publications %%% in the large field of numerical analysis %%% from books and conference proceedings, but %%% excluding journal articles, which are covered %%% in separate bibliographies in the TeX User %%% Group archive. %%% %%% This file includes publications for the %%% decade 2010--2019. %%% %%% At version 1.65, the year coverage looked %%% like this: %%% %%% 2010 ( 31) 2013 ( 19) 2016 ( 5) %%% 2011 ( 30) 2014 ( 21) 2017 ( 8) %%% 2012 ( 26) 2015 ( 7) 2018 ( 5) %%% %%% Article: 3 %%% Book: 142 %%% Proceedings: 7 %%% %%% Total entries: 152 %%% %%% The initial draft of entries for 2000--2009 %%% was derived from the OCLC Proceedings %%% database, from the MathSciNet database, from %%% the University of California Melvyl catalog, %%% and from the U.S. Library of Congress %%% catalog. %%% %%% In this bibliography, entries are sorted %%% first by ascending year, and within each %%% year, alphabetically by author or editor, %%% and then, if necessary, by the 3-letter %%% abbreviation at the end of the BibTeX %%% citation tag, using the bibsort -byyear %%% utility. Year order has been chosen to %%% make it easier to identify the most recent %%% work. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ====================================================================

@Preamble{ "\ifx \undefined \booktitle \def \booktitle #1{{{\em #1}}} \fi" # "\ifx \undefined \k \let \k = \c \fi" # "\ifx \undefined \circled \def \circled #1{(#1)}\fi" # "\ifx \undefined \reg \def \reg {\circled{R}}\fi" }

%%%===================================================================== %%% Acknowledgement abbreviations:

@String{ack-nhfb= "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|http://www.math.utah.edu/~beebe/|"}

%%%===================================================================== %%% Journal abbreviations:

@String{j-AMER-MATH-MONTHLY= "American Mathematical Monthly"} @String{j-HIST-MATH= "Historia Mathematica"} @String{j-SIAM-REVIEW= "SIAM Review"}

%%%===================================================================== %%% Publishers and their addresses:

@String{pub-ACADEMIC= "Academic Press"} @String{pub-ACADEMIC:adr= "New York, NY, USA"} @String{pub-AMS= "American Mathematical Society"} @String{pub-AMS:adr= "Providence, RI, USA"} @String{pub-BIRKHAUSER= "Birkh{\"{a}}user"} @String{pub-BIRKHAUSER:adr= "Cambridge, MA, USA; Berlin, Germany; Basel, Switzerland"} @String{pub-BIRKHAUSER-BOSTON= "Birkh{\"a}user Boston Inc."} @String{pub-BIRKHAUSER-BOSTON:adr= "Cambridge, MA, USA"} @String{pub-CAMBRIDGE= "Cambridge University Press"} @String{pub-CAMBRIDGE:adr= "Cambridge, UK"} @String{pub-CHAPMAN-HALL-CRC= "Chapman and Hall/CRC"} @String{pub-CHAPMAN-HALL-CRC:adr= "Boca Raton, FL, USA"} @String{pub-CLARENDON= "Clarendon Press"} @String{pub-CLARENDON:adr= "New York, NY, USA"} @String{pub-CRC= "CRC Press"} @String{pub-CRC:adr= "2000 N.W. Corporate Blvd., Boca Raton, FL 33431-9868, USA"} @String{pub-DOVER= "Dover"} @String{pub-DOVER:adr= "New York, NY, USA"} @String{pub-ELSEVIER-ACADEMIC= "Elsevier Academic Press"} @String{pub-ELSEVIER-ACADEMIC:adr= "Amsterdam, The Netherlands"} @String{pub-GRUYTER= "Walter de Gruyter"} @String{pub-GRUYTER:adr= "New York"} @String{pub-JOHNS-HOPKINS= "The Johns Hopkins University Press"} @String{pub-JOHNS-HOPKINS:adr= "Baltimore, MD, USA"} @String{pub-KNOPF= "Alfred A. Knopf"} @String{pub-KNOPF:adr= "New York, NY, USA"} @String{pub-OLDENBOURG= "R. Oldenbourg"} @String{pub-OLDENBOURG:adr= "M{\"u}nchen, Germany"} @String{pub-OXFORD= "Oxford University Press"} @String{pub-OXFORD:adr= "Walton Street, Oxford OX2 6DP, UK"} @String{pub-PACKT= "Packt Publishing"} @String{pub-PACKT:adr= "Birmingham, UK"} @String{pub-PH= "Pren{\-}tice-Hall"} @String{pub-PH:adr= "Upper Saddle River, NJ 07458, USA"} @String{pub-PRINCETON= "Princeton University Press"} @String{pub-PRINCETON:adr= "Princeton, NJ, USA"} @String{pub-SIAM= "Society for Industrial and Applied Mathematics"} @String{pub-SIAM:adr= "Philadelphia, PA, USA"} @String{pub-SV= "Springer-Verlag"} @String{pub-SV:adr= "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-WILEY= "Wiley"} @String{pub-WILEY:adr= "New York, NY, USA"} @String{pub-WORLD-SCI= "World Scientific Publishing Co."} @String{pub-WORLD-SCI:adr= "Singapore; Philadelphia, PA, USA; River Edge, NJ, USA"}

%%% ==================================================================== %%% Series abbreviations:

@String{ser-LECT-NOTES-MATH= "Lecture Notes in Mathematics"} @String{ser-LNAI= "Lecture Notes in Artificial Intelligence"} @String{ser-LNCS= "Lecture Notes in Computer Science"} @String{ser-LNCSE= "Lecture Notes in Computational Science and Engineering"}

%%%===================================================================== %%% Bibliography entries, sorted by year, and then by citation label, %%% with `bibsort -byyear':

@Book{Ackleh:2010:CMN, author = "Azmy S. Ackleh and Edward James Allen and Ralph Baker Kearfott and Padmanabhan Seshaiyer", title = "Classical and modern numerical analysis: theory, methods and practice", publisher = pub-CRC, address = pub-CRC:adr, pages = "xix + 608", year = "2010", ISBN = "1-4200-9157-3 (hardcover)", ISBN-13 = "978-1-4200-9157-1 (hardcover)", LCCN = "QA297 .C53 2010", MRclass = "65-01", MRnumber = "2555915", bibdate = "Tue May 27 12:10:25 MDT 2014", bibsource = "aubrey.tamu.edu:7090/voyager; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", note = "Theory, methods and practice", series = "Chapman and Hall/CRC numerical analysis and scientific computing", abstract = "The book provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis. The text covers the main areas of introductory numerical analysis, including the solution of nonlinear equations, numerical linear algebra, ordinary differential equations, approximation theory, numerical integration, and boundary value problems. Focusing on interval computing in numerical analysis, it explains interval arithmetic, interval computation, and interval algorithms. The authors illustrate the concepts with many examples as well as analytical and computational exercises at the end of each chapter. This advanced, graduate-level introduction to the theory and methods of numerical analysis supplies the necessary background in numerical methods so that students can apply the techniques and understand the mathematical literature in this area.", acknowledgement = ack-nhfb, subject = "Numerical analysis; Data processing", xxeditor = "Azmy S. Ackleh and Padmanabhan Seshaiyer and Ralph Baker Kearfott and Edward James Allen", } @Book{BaezLopez:2010:MAE, author = "David {B{\'a}ez L{\'o}pez}", title = "{MATLAB} with applications to engineering, physics and finance", publisher = pub-CRC, address = pub-CRC:adr, pages = "xiv + 412", year = "2010", ISBN = "1-4398-0697-7 (hardcover)", ISBN-13 = "978-1-4398-0697-5 (hardcover)", LCCN = "QA297 .B28 2010", MRclass = "65-01", MRnumber = "2574020", bibdate = "Tue May 27 12:31:50 MDT 2014", bibsource = "clas.caltech.edu:210/INNOPAC; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, remark = "``A Chapman and Hall book.''.", subject = "Numerical analysis; Data processing; MATLAB", } @Book{Baumgarte:2010:NRS, author = "Thomas W. Baumgarte and Stuart L. (Stuart Louis) Shapiro", title = "Numerical relativity: solving {Einstein}'s equations on the computer", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "xviii + 698", year = "2010", ISBN = "0-521-51407-X", ISBN-13 = "978-0-521-51407-1", LCCN = "QC173.6 .B38 2010", bibdate = "Fri Oct 7 08:35:27 MDT 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/einstein.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "General relativity (Physics); Einstein field equations; Numerical calculations", tableofcontents = "General relativity preliminaries \\ The $3 + 1$ decomposition of Einstein's equations \\ Constructing initial data \\ Choosing coordinates: the lapse and shift \\ Matter sources \\ Numerical methods \\ Locating black hole horizons \\ Spherically symmetric spacetimes \\ Gravitational waves \\ Collapse of collisionless clusters in axisymmetry \\ Recasting the evolution equations \\ Binary black hole initial data \\ Binary black hole evolution \\ Rotating stars \\ Binary neutron star initial data \\ Binary neutron star evolution \\ Binary black hole-neutron stars: initial data and evolution", } @Book{Bockhorn:2010:MMA, editor = "Henning Bockhorn and Dieter Mewes and Wolfgang Peukert and Hans-Joachim Warnecke", title = "Micro- and macromixing: analysis, simulation and numerical calculation", publisher = pub-SV, address = pub-SV:adr, pages = "xi + 346", year = "2010", DOI = "https://doi.org/10.1007/978-3-642-04549-3", ISBN = "3-642-04549-9, 3-642-04548-0", ISBN-13 = "978-3-642-04549-3, 978-3-642-04548-6", LCCN = "TP156.M5 M537 2010", bibdate = "Mon Aug 23 11:05:53 MDT 2010", bibsource = "aubrey.tamu.edu:7090/voyager; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Heat and mass transfer", acknowledgement = ack-nhfb, subject = "mixing; equipment and supplies; mathematical models", } @Book{Burden:2010:NA, author = "Richard L. Burden and J. Douglas Faires", title = "Numerical analysis", publisher = "Cengage Learning", address = "Boston, MA, USA", edition = "Nineth", pages = "????", year = "2010", ISBN = "0-538-73351-9", ISBN-13 = "978-0-538-73351-9", LCCN = "????", bibdate = "Mon Aug 23 10:50:14 MDT 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, } @Book{Christensen:2010:FSE, author = "Ole Christensen", title = "Functions, spaces, and expansions: mathematical tools in physics and engineering", publisher = pub-BIRKHAUSER-BOSTON, address = pub-BIRKHAUSER-BOSTON:adr, pages = "xix + 263", year = "2010", DOI = "https://doi.org/10.1007/978-0-8176-4980-7", ISBN = "0-8176-4980-8", ISBN-13 = "978-0-8176-4980-7", LCCN = "QA331.7 .C57 2010", bibdate = "Mon Aug 23 11:22:11 2010", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.gbv.de:20011/gvk", series = "Applied and numerical harmonic analysis", acknowledgement = ack-nhfb, subject = "computer science; engineering mathematics; Fourier analysis; functional analysis; functions, special; mathematical physics; mathematics", } @Book{Datta:2010:NLA, author = "Biswa Nath Datta", title = "Numerical linear algebra and applications", publisher = pub-SIAM, address = pub-SIAM:adr, edition = "Second", pages = "xxiv + 530", year = "2010", DOI = "https://doi.org/10.1137/1.9780898717655", ISBN = "0-534-17466-3 (paperback), 0-89871-685-3", ISBN-13 = "978-0-534-17466-8 (paperback), 978-0-89871-685-6", LCCN = "QA184.2 .D38 2010", MRclass = "65-01 (65Fxx)", MRnumber = "2596938", bibdate = "Tue May 27 12:31:49 MDT 2014", bibsource = "clas.caltech.edu:210/INNOPAC; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; prodorbis.library.yale.edu:7090/voyager; z3950.gbv.de:20011/gvk; z3950.loc.gov:7090/Voyager", URL = "http://www.gbv.de/dms/ilmenau/toc/603672094.PDF; http://www.loc.gov/catdir/enhancements/fy1001/2009025104-b.html; http://www.loc.gov/catdir/enhancements/fy1001/2009025104-d.html; http://www.loc.gov/catdir/enhancements/fy1001/2009025104-t.html; http://www.zentralblatt-math.org/zmath/en/search/?an=1187.65027", acknowledgement = ack-nhfb, subject = "Algebras, Linear; Numerical analysis", tableofcontents = "Linear algebra problems, their importance, and computational difficulties \\ A review of some required concepts from core linear algebra \\ Floating point numbers and errors in computation \\ Stability of algorithms and conditioning of problems \\ Gaussian elimination and $LU$ factorization \\ Numerical solutions of linear systems \\ $QR$ factorization, singular value decomposition, and projections \\ Least-squares solutions to linear systems \\ Numerical matrix eigenvalue problems \\ Numerical symmetric eigenvalue problem and singular value decomposition \\ Generalized and quadratic eigenvalue problems \\ Iterative methods for large and sparse problems: an overview \\ Some key terms in numerical linear algebra", } @Book{Etter:2010:IM, author = "Delores M. Etter", title = "Introduction to {MATLAB}", publisher = pub-PH, address = pub-PH:adr, edition = "Second", pages = "????", year = "2010", ISBN = "0-13-608123-1", ISBN-13 = "978-0-13-608123-4", LCCN = "TA345 .E8724 2010", bibdate = "Mon Jan 31 15:09:54 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "Engineering mathematics; Data processing; MATLAB; Numerical analysis", } @Book{Golub:2010:MMQ, author = "Gene H. Golub and G{\'e}rard Meurant", title = "Matrices, Moments and Quadrature with Applications", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "xii + 363", year = "2010", ISBN = "0-691-14341-2", ISBN-13 = "978-0-691-14341-5", MRclass = "65-02 (65D30)", MRnumber = "MR2582949", bibdate = "Mon May 17 14:08:36 MDT 2010", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Princeton Series in Applied Mathematics", ZMnumber = "1217.65056", ZMnumber = "pre05661633", abstract = "This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", shorttableofcontents = "Preface / xi \\ Part 1. Theory / 1 \\ 1: Introduction / 3 \\ 2: Orthogonal Polynomials / 8 \\ 3: Properties of Tridiagonal Matrices / 24 \\ 4: The Lanczos and Conjugate Gradient Algorithms / 39 \\ 5: Computation of the Jacobi Matrices / 55 \\ 6: Gauss Quadrature / 84 \\ 7: Bounds for Bilinear Forms $u^T f(A) v$ / 112 \\ 8: Extensions to Nonsymmetric Matrices / 117 \\ 9: Solving Secular Equations / 122 \\ 10: Examples of Gauss Quadrature Rules / 139 \\ 11: Bounds and Estimates for Elements of Functions of Matrices / 162 \\ 12: Estimates of Norms of Errors in the Conjugate Gradient Algorithm / 200 \\ 13: Least Squares Problems / 227 \\ 14: Total Least Squares / 256 \\ 15: Discrete Ill-Posed Problems / 280 \\ Bibliography / 335 \\ Index / 361", tableofcontents = "Preface / xi \\ Part 1. Theory / 1 \\ 1: Introduction / 3 \\ 2: Orthogonal Polynomials / 8 \\ 2.1 Definition of Orthogonal Polynomials / 8 \\ 2.2 Three-Term Recurrences / 10 \\ 2.3 Properties of Zeros / 14 \\ 2.4 Historical Remarks / 15 \\ 2.5 Examples of Orthogonal Polynomials / 15 \\ 2.6 Variable-Signed Weight Functions / 20 \\ 2.7 Matrix Orthogonal Polynomials / 21 \\ 3: Properties of Tridiagonal Matrices / 24 \\ 3.1 Similarity / 24 \\ 3.2 Cholesky Factorizations of a Tridiagonal Matrix / 25 \\ 3.3 Eigenvalues and Eigenvectors / 27 \\ 3.4 Elements of the Inverse / 29 \\ 3.5 The $Q D$ Algorithm / 32 \\ 4: The Lanczos and Conjugate Gradient Algorithms / 39 \\ 4.1 The Lanczos Algorithm / 39 \\ 4.2 The Nonsymmetric Lanczos Algorithm / 43 \\ 4.3 The Golub--Kahan Bidiagonalization Algorithms / 45 \\ 4.4 The Block Lanczos Algorithm / 47 \\ 4.5 The Conjugate Gradient Algorithm / 49 \\ 5: Computation of the Jacobi Matrices / 55 \\ 5.1 The Stieltjes Procedure / 55 \\ 5.2 Computing the Coefficients from the Moments / 56 \\ 5.3 The Modified Chebyshev Algorithm / 58 \\ 5.4 The Modified Chebyshev Algorithm for Indefinite Weight Functions / 61 \\ 5.5 Relations between the Lanczos and Chebyshev Semi-Iterative Algorithms / 62 \\ 5.6 Inverse Eigenvalue Problems / 66 \\ 5.7 Modifications of Weight Functions / 72 \\ 6: Gauss Quadrature / 84 \\ 6.1 Quadrature Rules / 84 \\ 6.2 The Gauss Quadrature Rules / 86 \\ 6.3 The Anti-Gauss Quadrature Rule / 92 \\ 6.4 The Gauss-Kronrod Quadrature Rule / 95 \\ 6.5 The Nonsymmetric Gauss Quadrature Rules / 99 \\ 6.6 The Block Gauss Quadrature Rules / 102 \\ 7: Bounds for Bilinear Forms $u^T f(A) v$ / 112 \\ 7.1 Introduction / 112 \\ 7.2 The Case $u = v$ / 113 \\ 7.3 The Case $u \neq v$ / 114 \\ 7.4 The Block Case / 115 \\ 7.5 Other Algorithms for $u \neq v$ / 115 \\ 8: Extensions to Nonsymmetric Matrices / 117 \\ 8.1 Rules Based on the Nonsymmetric Lanczos Algorithm / 118 \\ 8.2 Rules Based on the Arnoldi Algorithm / 119 \\ 9: Solving Secular Equations / 122 \\ 9.1 Examples of Secular Equations / 122 \\ 9.2 Secular Equation Solvers / 129 \\ 9.3 Numerical Experiments / 134 \\ Part 2. Applications / 137 \\ 10: Examples of Gauss Quadrature Rules / 139 \\ 10.1 The Golub and Welsch Approach / 139 \\ 10.2 Comparisons with Tables / 140 \\ 10.3 Using the Full $Q R$ Algorithm / 141 \\ 10.4 Another Implementation of $Q R$ / 143 \\ 10.5 Using the $Q L$ Algorithm / 144 \\ 10.6 Gauss--Radau Quadrature Rules / 144 \\ 10.7 Gauss--Lobatto Quadrature Rules / 146 \\ 10.8 Anti-Gauss Quadrature Rule / 148 \\ 10.9 Gauss--Kronrod Quadrature Rule / 148 \\ 10.10 Computation of Integrals / 149 \\ 10.11 Modification Algorithms / 155 \\ 10.12 Inverse Eigenvalue Problems / 156 \\ 11: Bounds and Estimates for Elements of Functions of Matrices / 162 \\ 11.1 Introduction / 162 \\ 11.2 Analytic Bounds for the Elements of the Inverse / 163 \\ 11.3 Analytic Bounds for Elements of Other Functions / 166 \\ 11.4 Computing Bounds for Elements of $f(A)$ / 167 \\ 11.5 Solving $A x = c$ and Looking at $d^T x$ / 167 \\ 11.6 Estimates of $\tr(A^{-1})$ and $\det(A)$ / 168 \\ 11.7 Krylov Subspace Spectral Methods / 172 \\ 11.8 Numerical Experiments / 173 \\ 12: Estimates of Norms of Errors in the Conjugate Gradient Algorithm / 200 \\ 12.1 Estimates of Norms of Errors in Solving Linear Systems / 200 \\ 12.2 Formulas for the $A$-Norm of the Error / 202 \\ 12.3 Estimates of the $A$-Norm of the Error / 203 \\ 12.4 Other Approaches / 209 \\ 12.5 Formulas for the $\ell_2$ Norm of the Error / 210 \\ 12.6 Estimates of the $\ell_2$ Norm of the Error / 211 \\ 12.7 Relation to Finite Element Problems / 212 \\ 12.8 Numerical Experiments / 214 \\ 13: Least Squares Problems / 227 \\ 13.1 Introduction to Least Squares / 227 \\ 13.2 Least Squares Data Fitting / 230 \\ 13.3 Numerical Experiments / 237 \\ 13.4 Numerical Experiments for the Backward Error / 253 \\ 14: Total Least Squares / 256 \\ 14.1 Introduction to Total Least Squares / 256 \\ 14.2 Scaled Total Least Squares / 259 \\ 14.3 Total Least Squares Secular Equation Solvers / 261 \\ 15: Discrete Ill-Posed Problems / 280 \\ 15.1 Introduction to Ill-Posed Problems / 280 \\ 15.2 Iterative Methods for Ill-Posed Problems / 295 \\ 15.3 Test Problems / 298 \\ 15.4 Study of the GCV Function / 300 \\ 15.5 Optimization of Finding the GCV Minimum / 305 \\ 15.6 Study of the $L$-Curve / 313 \\ 15.7 Comparison of Methods for Computing the Regularization Parameter / 325 \\ Bibliography / 335 \\ Index / 361", } @Book{Griffiths:2010:NMO, author = "David F. (David Francis) Griffiths and Desmond J. (Desmond J.) Higham", title = "Numerical methods for ordinary differential equations: initial value problems", publisher = pub-SV, address = pub-SV:adr, pages = "xiv + 271", year = "2010", DOI = "https://doi.org/10.1007/978-0-85729-148-6", ISBN = "0-85729-147-5", ISBN-13 = "978-0-85729-147-9", LCCN = "QA371 .G72 2010", MRclass = "65-01 (65Lxx)", MRnumber = "2759806 (2012g:65002)", MRreviewer = "Philip W. Sharp", bibdate = "Tue May 27 12:31:11 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; prodorbis.library.yale.edu:7090/voyager", note = "Initial value problems", series = "Springer Undergraduate Mathematics Series", acknowledgement = ack-nhfb, subject = "Differential equations; Numerical solutions", } @Book{King:2010:NSM, author = "Michael R. King and Nipa A. Mody", title = "Numerical and statistical methods for bioengineering: applications in {MATLAB}", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "xii + 581", year = "2010", ISBN = "0-521-87158-1, 0-511-90984-5 (e-book)", ISBN-13 = "978-0-521-87158-7, 978-0-511-90984-9 (e-book)", LCCN = "R857.M34 K56 2010eb", bibdate = "Tue May 27 12:31:06 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; prodorbis.library.yale.edu:7090/voyager; z3950.loc.gov:7090/Voyager", series = "Cambridge texts in biomedical engineering", URL = "http://assets.cambridge.org/97805218/71587/cover/9780521871587.jpg; http://site.ebrary.com//lib/yale/Doc?id=10431397", abstract = "The first MATLAB-based numerical methods textbook for bioengineers that uniquely integrates modelling concepts with statistical analysis, while maintaining a focus on enabling the user to report the error or uncertainty in their result. Between traditional numerical method topics of linear modelling concepts, nonlinear root finding, and numerical integration, chapters on hypothesis testing, data regression and probability are interweaved. A unique feature of the book is the inclusion of examples from clinical trials and bioinformatics, which are not found in other numerical methods textbooks for engineers. With a wealth of biomedical engineering examples, case studies on topical biomedical research, and the inclusion of end of chapter problems, this is a perfect core text for a one-semester undergraduate course", acknowledgement = ack-nhfb, subject = "Biomedical engineering; Statistical methods; Mathematics; MATLAB; TECHNOLOGY and ENGINEERING; Biomedical.; MEDICAL; Family and General Practice.; Allied Health Services; Medical Technology.; Biotechnology.; Lasers in Medicine.", tableofcontents = "1. Types and sources of numerical error \\ 2. Systems of linear equations \\ 3. Statistics and probability \\ 4. Hypothesis testing \\ 5. Root finding techniques for nonlinear equations \\ 6. Numerical quadrature \\ 7. Numerical integration of ordinary differential equations \\ 8. Nonlinear data regression and optimization \\ 9. Basic algorithms of bioinformatics \\ Appendix A. Introduction to MATLAB \\ Appendix B. Location of nodes for Gauss-Legendre quadrature", } @Book{Kiusalaas:2010:NMEa, author = "Jaan Kiusalaas", title = "Numerical methods in engineering with {MATLAB\reg}", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, edition = "Second", pages = "xi + 431", year = "2010", ISBN = "0-521-19133-5 (hardback)", ISBN-13 = "978-0-521-19133-3 (hardback)", LCCN = "TA345 .K58 2010", MRclass = "65-01", MRnumber = "2554310", bibdate = "Tue May 27 12:10:06 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; melvyl.cdlib.org:210/CDL90; z3950.loc.gov:7090/Voyager", abstract = "Numerical Methods in Engineering with MATLAB is a text for engineering students and a reference for practicing engineers. The choice of numerical methods was based on their relevance to engineering problems. Every method is discussed thoroughly and illustrated with problems involving both hand computation and programming. MATLAB M-files accompany each method and are available on the book website. This code is made simple and easy to understand by avoiding complex book-keeping schemes, while maintaining the essential features of the method. MATLAB was chosen as the example language because of its ubiquitous use in engineering studies and practice. This new edition includes the new MATLAB anonymous functions, which allow the programmer to embed functions into the program rather than storing them as separate files. Other changes include the addition of rational function interpolation in Chapter 3, the addition of Ridder's method in place of Brent's method in Chapter 4, and the addition of downhill simplex method in place of the Fletcher--Reeves method of optimization in Chapter 10.", acknowledgement = ack-nhfb, subject = "MATLAB; Engineering mathematics; Data processing; Numerical analysis", tableofcontents = "Introduction to MATLAB \\ Systems of linear algebraic equations \\ Interpolation and curve fitting \\ Roots of equations \\ Numerical differentiation \\ Numerical integration \\ Initial value problems \\ Two-point boundary value problems \\ Symmetric matrix eigenvalue problems \\ Introduction to optimization", } @Book{Kiusalaas:2010:NMEb, author = "Jaan Kiusalaas", title = "Numerical methods in engineering with {Python}", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, edition = "Second", pages = "x + 422", year = "2010", ISBN = "0-521-19132-7 (hardcover), 0-511-67694-8 (e-book)", ISBN-13 = "978-0-521-19132-6 (hardcover), 978-0-511-67694-9 (e-book)", LCCN = "TA345 .K584 2010", bibdate = "Mon Jan 31 15:16:50 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/python.bib; melvyl.cdlib.org:210/CDL90; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "Python (computer program language); MATLAB; engineering mathematics; data processing; numerical analysis; Python (Computer program language); Engineering mathematics; Data processing; Numerical analysis; Engineering; Civil engineering; Data processing.; Python (Computer program language)", tableofcontents = "Cover \\ Half-title \\ Title \\ Copyright \\ Contents \\ Preface to the First Edition \\ Preface to the Second Edition \\ 1 Introduction to Python \\ 2 Systems of Linear Algebraic Equations \\ 3 Interpolation and Curve Fitting \\ 4 Roots of Equations \\ 5 Numerical Differentiation \\ 6 Numerical Integration \\ 7 Initial Value Problems \\ 8 Two-Point Boundary Value Problems \\ 9 Symmetric Matrix Eigenvalue Problems \\ 10 Introduction to Optimization \\ Appendices \\ List of Program Modules (by Chapter) \\ Index", } @Book{Kornerup:2010:FPN, author = "Peter Kornerup and David W. Matula", title = "Finite Precision Number Systems and Arithmetic", volume = "133", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "xv + 699", year = "2010", ISBN = "0-521-76135-2 (hardcover)", ISBN-13 = "978-0-521-76135-2 (hardcover)", LCCN = "QA248 .K627 2010", bibdate = "Sun Jun 19 14:21:37 MDT 2016", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Encyclopedia of mathematics and its applications", URL = "http://assets.cambridge.org/97805217/61352/cover/9780521761352.jpg; http://catdir.loc.gov/catdir/enhancements/fy1011/2010030521-b.html; http://catdir.loc.gov/catdir/enhancements/fy1011/2010030521-d.html; http://catdir.loc.gov/catdir/enhancements/fy1011/2010030521-t.html", abstract = "Fundamental arithmetic operations support virtually all of the engineering, scientific, and financial computations required for practical applications, from cryptography, to financial planning, to rocket science. This comprehensive reference provides researchers with the thorough understanding of number representations that is a necessary foundation for designing efficient arithmetic algorithms. Using the elementary foundations of radix number systems as a basis for arithmetic, the authors develop and compare alternative algorithms for the fundamental operations of addition, multiplication, division, and square root with precisely defined roundings. Various finite precision number systems are investigated, with the focus on comparative analysis of practically efficient algorithms for closed arithmetic operations over these systems. Each chapter begins with an introduction to its contents and ends with bibliographic notes and an extensive bibliography. The book may also be used for graduate teaching: problems and exercises are scattered throughout the text and a solutions manual is available for instructors.", acknowledgement = ack-nhfb, subject = "Arithmetic; Foundations", tableofcontents = "Preface / xi \\ 1. Radix polynomial representations / 1 \\ 2. Base and digit set conversion / 59 \\ 3. Addition / \\ 4. Multiplication / \\ 5. Division / 275 \\ 6. Square root / 398 \\ 7. Floating-point number systems / 447 \\ 8. Modular arithmetic and residue number systems / 528 \\ 9. Rational arithmetic / 63 \\ Author index / 691 \\ Index / 693", } @Book{Kurzak:2010:SCM, editor = "Jakub Kurzak and David A. Bader and J. J. Dongarra", title = "Scientific computing with multicore and accelerators", volume = "10", publisher = pub-CRC, address = pub-CRC:adr, pages = "xxxiii + 480", year = "2010", ISBN = "1-4398-2536-X (hardback)", ISBN-13 = "978-1-4398-2536-5 (hardback)", LCCN = "Q183.9 .S325 2010", bibdate = "Fri Nov 16 06:29:59 MST 2012", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/super.bib; z3950.loc.gov:7090/Voyager", series = "Chapman and Hall/CRC computational science", acknowledgement = ack-nhfb, subject = "Science; Data processing; Engineering; High performance computing; Multiprocessors; MATHEMATICS / General; MATHEMATICS / Advanced; MATHEMATICS / Number Systems", } @Book{Lange:2010:NAS, author = "Kenneth Lange", title = "Numerical analysis for statisticians", publisher = pub-SV, address = pub-SV:adr, edition = "Second", pages = "xvi + 604", year = "2010", DOI = "https://doi.org/10.1007/978-1-4419-5945-4", ISBN = "1-4419-5944-0 (hardcover)", ISBN-13 = "978-1-4419-5944-7 (hardcover)", LCCN = "QA297 .L34 2010", bibdate = "Mon Aug 23 10:50:36 MDT 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Statistics and Computing", acknowledgement = ack-nhfb, subject = "mathematical statistics; statistics", } @Book{Magoules:2010:FGC, editor = "F. (Fr{\'e}d{\'e}ric) Magoul{\`e}s", title = "Fundamentals of grid computing: theory, algorithms and technologies", publisher = pub-CRC, address = pub-CRC:adr, pages = "xxi + 298", year = "2010", ISBN = "1-4398-0367-6 (hardcover)", ISBN-13 = "978-1-4398-0367-7 (hardcover)", LCCN = "QA76.9.C58 F86 2010", bibdate = "Mon Aug 23 11:06:01 MDT 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Chapman and Hall/CRC numerical analysis and scientific computing", acknowledgement = ack-nhfb, subject = "computational grids (computer systems)", } @Book{Moin:2010:FEN, author = "Parviz Moin", title = "Fundamentals of engineering numerical analysis", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, edition = "Second", pages = "xiv + 241", year = "2010", ISBN = "0-521-88432-2 (hardcover), 0-521-71123-1", ISBN-13 = "978-0-521-88432-7 (hardcover), 978-0-521-71123-4", LCCN = "TA335 .M65 2010", MRclass = "65-01", MRnumber = "2721984 (2011j:65001)", bibdate = "Tue May 27 11:24:21 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", abstract = "Publisher's note: Since the original publication of this book, available computer power has increased greatly. Today, scientific computing is playing an ever more prominent role as a tool in scientific discovery and engineering analysis. In this second edition, the key addition is an introduction to the finite element method. This is a widely used technique for solving partial differential equations (PDEs) in complex domains. This text introduces numerical methods and shows how to develop, analyze, and use them. Complete MATLAB programs for all the worked examples are now available at www.cambridge.org/Moin, and more than 30 exercises have been added. This thorough and practical book is intended as a first course in numerical analysis, primarily for new graduate students in engineering and physical science. Along with mastering the fundamentals of numerical methods, students will learn to write their own computer programs using standard numerical methods.", acknowledgement = ack-nhfb, subject = "engineering mathematics; numerical analysis", tableofcontents = "1. Interpolation \\ 2. Numerical differentiation - finite differences \\ 3. Numerical integration \\ 4. Numerical solution of ordinary differential equations \\ 5. Numerical solution of partial differential equations \\ 6. Discrete transform methods \\ Appendix. A review of linear algebra", } @Book{Oberkampf:2010:VVS, author = "William L. Oberkampf and Christopher J. Roy", title = "Verification and validation in scientific computing", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "????", year = "2010", ISBN = "0-521-11360-1", ISBN-13 = "978-0-521-11360-1", LCCN = "Q183.9 .O24 2010", bibdate = "Tue Apr 26 08:20:49 MDT 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", URL = "http://assets.cambridge.org/97805211/13601/cover/9780521113601.jpg", abstract = "Advances in scientific computing have made modelling and simulation an important part of the decision-making process in engineering, science, and public policy. This book provides a comprehensive and systematic development of the basic concepts, principles, and procedures for verification and validation of models and simulations. The emphasis is placed on models that are described by partial differential and integral equations and the simulations that result from their numerical solution. The methods described can be applied to a wide range of technical fields, from the physical sciences, engineering and technology and industry, through to environmental regulations and safety, product and plant safety, financial investing, and governmental regulations. This book will be genuinely welcomed by researchers, practitioners, and decision makers in a broad range of fields, who seek to improve the credibility and reliability of simulation results. It will also be appropriate either for university courses or for independent study", acknowledgement = ack-nhfb, remark = "Exchanges between the book's authors and members of the reliable\_computing mailing list in early May 2011 discuss the extent to which this book is, or is not, about interval arithmetic.", subject = "Science \\ Data processing \\ Numerical calculations \\ Verification \\ Computer programs \\ Validation \\ Decision making \\ Mathematical models", tableofcontents = "Preface \\ 1. Introduction \\ Part I. Fundamental Concepts: \\ 2. Fundamental concepts and terminology \\ 3. Modeling and computational simulation \\ Part II. Code Verification: \\ 4. Software engineering \\ 5. Code verification \\ 6. Exact solutions \\ Part III. Solution Verification: \\ 7. Solution verification \\ 8. Discretization error \\ 9. Solution adaptation \\ Part IV. Model Validation and Prediction: \\ 10. Model validation fundamentals \\ 11. Design and execution of validation experiments \\ 12. Model accuracy assessment \\ 13. Predictive capability \\ Part V. Planning, Management, and Implementation Issues: \\ 14. Planning and prioritization in modeling and simulation \\ 15. Maturity assessment of modeling and simulation \\ 16. Development and responsibilities for verification, validation and uncertainty quantification \\ Appendix. Programming practices \\ Index", } @Book{Onate:2010:SAF, author = "Eugenio O{\~n}ate", title = "Structural analysis with the finite element method: linear statistics", publisher = pub-SV, address = pub-SV:adr, pages = "xxiv + 472", year = "2010", DOI = "https://doi.org/10.1007/978-1-4020-8733-2", ISBN = "1-4020-8733-0", ISBN-13 = "978-1-4020-8733-2", LCCN = "TA347.F5 O63 2009", bibdate = "Mon Aug 23 11:24:08 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Lecture notes on numerical methods in engineering and sciences.", acknowledgement = ack-nhfb, remark = "Volume 1: The basis and solids. Volume 2: Beams, plates and shells", subject = "Finite element method; Structural analysis (Engineering)", } @Book{Quarteroni:2010:SCM, author = "Alfio Quarteroni and Fausto Saleri and Paola Gervasio", title = "Scientific computing with {Matlab} and {Octave}", volume = "2", publisher = pub-SV, address = pub-SV:adr, pages = "xvi + 360", year = "2010", DOI = "https://doi.org/10.1007/978-3-642-12430-3", ISBN = "3-642-12429-1", ISBN-13 = "978-3-642-12429-7", LCCN = "????", MRclass = "65-01", MRnumber = "2680972", bibdate = "Tue May 27 11:24:21 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", note = "Third edition [of MR2253397]", series = "Texts in Computational Science and Engineering", acknowledgement = ack-nhfb, } @Book{Robert:2010:IMC, author = "Christian P. Robert and George Casella", title = "Introducing {Monte Carlo} methods with {R}", publisher = pub-SV, address = pub-SV:adr, pages = "xix + 283", year = "2010", DOI = "https://doi.org/10.1007/978-1-4419-1576-4", ISBN = "1-4419-1575-3 (paperback), 1-4419-1576-1 (ebk.)", ISBN-13 = "978-1-4419-1575-7 (paperback), 978-1-4419-1576-4 (ebk.)", LCCN = "QA298 .R63 2010", MRclass = "65-01 (65C05)", MRnumber = "2572239", bibdate = "Tue May 27 12:31:49 MDT 2014", bibsource = "clas.caltech.edu:210/INNOPAC; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Use R!", acknowledgement = ack-nhfb, subject = "Monte Carlo method; Computer programs; Mathematical statistics; Data processing; R (Computer program language); Markov processes; Mathematical Computing; Monte Carlo-methode.; R (computerprogramma); Monte-Carlo-Simulation.; R (Programm)", } @Book{Trappenberg:2010:FCN, author = "Thomas P. Trappenberg", title = "Fundamentals of computational neuroscience", publisher = pub-OXFORD, address = pub-OXFORD:adr, edition = "Second", pages = "xxv + 390", year = "2010", ISBN = "0-19-956841-3 (paperback)", ISBN-13 = "978-0-19-956841-3 (paperback)", LCCN = "QP357.5 .T746 2010", bibdate = "Mon Jan 31 15:17:33 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; melvyl.cdlib.org:210/CDL90; z3950.loc.gov:7090/Voyager", abstract = "Computational neuroscience is the theoretical study of the brain to uncover the principles and mechanisms that guide the development, organization, information processing, and mental functions of the nervous system. Although not a new area, it is only recently that enough knowledge has been gathered to establish computational neuroscience as a scientific discipline in its own right. Given the complexity of the field, and its increasing importance in progressing our understanding of how the brain works, there has long been a need for an introductory text on what is often assumed to be an impenetrable topic. The new edition of Fundamentals of Computational Neuroscience build on the success and strengths of the first edition. It introduces the theoretical foundations of neuroscience with a focus on the nature of information processing in the brain. The book covers the introduction and motivation of simplified models of neurons that are suitable for exploring information processing in large brain-like networks. Additionally, it introduces several fundamental network architectures and discusses their relevance for information processing in the brain, giving some examples of models of higher-order cognitive functions to demonstrate the advanced insight that can be gained with such studies. Each chapter starts by introducing its topic with experimental facts and conceptual questions related to the study of brain function. An additional feature is the inclusion of simple Matlab programs that can be used to explore many of the mechanisms explained in the book. An accompanying webpage includes programs for download. The book is aimed at those within the brain and cognitive sciences, from graduate level and upwards.", acknowledgement = ack-nhfb, subject = "Computational neuroscience; Neurons; physiology; Brain; Computational Biology; methods; Models, Neurological; Nerve Net; Neurosciences", tableofcontents = "Introduction \\ Basic Nuerons \\ Neurons and conductance-based models \\ Simplified neuron and population models \\ Associators and synaptic plasticity \\ Basic Networks \\ Cortical organizations and simple networks \\ Feed-forward mapping networks \\ Cortical feature maps and competitive population coding \\ Recurrent associative networks and episodic memory \\ System-Level Models \\ Modular networks, motor control, and reinforcement learning \\ The cognitive brain \\ Some useful mathematics \\ Numerical calculus \\ Basic probability theory \\ Basic information theory \\ A brief introduction to MATLAB", } @Book{Tveito:2010:ESC, author = "Aslak Tveito and Hans Petter Langtangen and Bj{\o}rn Frederik Nielsen and Xing Cai", title = "Elements of scientific computing: with 88 figures and 18 tables", volume = "7", publisher = pub-SV, address = pub-SV:adr, pages = "xii + 459", year = "2010", DOI = "https://doi.org/10.1007/978-3-642-11299-7", ISBN = "3-642-11298-6", ISBN-13 = "978-3-642-11298-0, 978-3-642-11299-7 (eISBN)", ISSN = "1611-0994", LCCN = "Q183.9 .E446 2010", MRclass = "65-01", MRnumber = "2723363", bibdate = "Tue May 27 12:08:24 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Texts in Computational Science and Engineering", acknowledgement = ack-nhfb, subject = "Science; Data processing; Numerical analysis", tableofcontents = "Computing integrals \\ Differential equations: the first steps \\ Systems of ordinary differential equations \\ Nonlinear algebraic equations \\ Method of least squares \\ About scientific software \\ Diffusion equation \\ Analysis of the diffusion equation \\ Parameter estimation and inverse problems \\ Glimpse of parallel computing", } @Book{VanLoan:2010:ITC, author = "Charles F. {Van Loan} and K.-Y. Daisy Fan", title = "Insight through computing: a {MATLAB} introduction to computational science and engineering", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xviii + 434", year = "2010", ISBN = "0-89871-691-8", ISBN-13 = "978-0-89871-691-7", LCCN = "QA297 .V25 2010", bibdate = "Fri Nov 16 10:03:00 MST 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/java2010.bib; http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/enhancements/fy1007/2009030277-b.html; http://www.loc.gov/catdir/enhancements/fy1007/2009030277-d.html; http://www.loc.gov/catdir/enhancements/fy1007/2009030277-t.html", acknowledgement = ack-nhfb, subject = "Numerical analysis; Data processing; Science; Computer simulation; Engineering mathematics; MATLAB", tableofcontents = "Preface \\ MATLAB glossary \\ Programming topics \\ Software \\ 1. From formula to program \\ 2. Limits and error \\ 3. Approximation with fractions \\ 4. The discrete versus the continuous \\ 5. Abstraction \\ 6. Randomness \\ 7. The second dimension \\ 8. Reordering \\ 9. Search \\ 10. Points, polygons and circles \\ 11. Text file processing \\ 12. The matrix: part II \\ 13. Acoustic file processing \\ 14. Divide and conquer \\ 15. Optimization \\ Appendix A. Refined graphics \\ Appendix B. Mathematical facts \\ Appendix C. MATLAB, Java, and C \\ Appendix D. Exit interview \\ Index", } @Book{Watkins:2010:FMC, author = "David S. Watkins", title = "Fundamentals of Matrix Computations", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Third", pages = "xvi + 644", year = "2010", ISBN = "0-470-52833-8 (hardcover)", ISBN-13 = "978-0-470-52833-4 (hardcover)", LCCN = "QA188 .W38 2010", MRclass = "65-01 (65Fxx)", MRnumber = "2778339 (2012a:65002)", bibdate = "Tue May 27 12:31:46 MDT 2014", bibsource = "clas.caltech.edu:210/INNOPAC; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Pure and applied mathematics.", acknowledgement = ack-nhfb, subject = "Matrices", } @Book{Ascher:2011:FCN, author = "Uri M. (Uri M.) Ascher and Chen Greif", title = "A first course in numerical methods", volume = "7", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xxii + 552", year = "2011", DOI = "https://doi.org/10.1137/1.9780898719987", ISBN = "0-89871-997-6", ISBN-13 = "978-0-89871-997-0", LCCN = "QA297 .A748 2011", MRclass = "65-01", MRnumber = "2839122", bibdate = "Tue May 27 12:30:46 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; prodorbis.library.yale.edu:7090/voyager; z3950.gbv.de:20011/gvk; z3950.loc.gov:7090/Voyager", series = "Computational science and engineering", URL = "http://www.loc.gov/catdir/enhancements/fy1111/2011007041-b.html; http://www.loc.gov/catdir/enhancements/fy1111/2011007041-d.html; http://www.loc.gov/catdir/enhancements/fy1111/2011007041-t.html", acknowledgement = ack-nhfb, subject = "Numerical calculations; Data processing; Numerical analysis; Algorithms", tableofcontents = "Numerical algorithms \\ Roundoff errors \\ Nonlinear equations in one variable \\ Linear algebra background \\ Linear systems: direct methods \\ Linear least squares problems \\ Linear systems: iterative methods \\ Eigenvalues and singular values \\ Nonlinear systems and optimization \\ Polynomial interpolation \\ Piecewise polynomial interpolation \\ Best approximation \\ Fourier transform \\ Numerical differentiation \\ Numerical integration \\ Differential equations", } @Book{Babuska:2011:FEI, author = "Ivo Babu{\v{s}}ka and J. R. (John Robert) Whiteman and Theofanis Strouboulis", title = "Finite elements: an introduction to the method and error estimation", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "xii + 323", year = "2011", ISBN = "0-19-850670-8", ISBN-13 = "978-0-19-850670-6", LCCN = "QA276.8 .B33X 2011", bibdate = "Tue May 27 12:30:44 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; prodorbis.library.yale.edu:7090/voyager; z3950.loc.gov:7090/Voyager", note = "An introduction to the method and error estimation", URL = "http://www.loc.gov/catdir/enhancements/fy1108/2010033235-b.html; http://www.loc.gov/catdir/enhancements/fy1108/2010033235-d.html; http://www.loc.gov/catdir/enhancements/fy1108/2010033235-t.html", acknowledgement = ack-nhfb, subject = "Finite element method; Estimation theory; Error analysis (Mathematics)", } @Book{Bailey:2011:PTS, editor = "David H. Bailey and Robert F. Lucas and Samuel Watkins Williams", title = "Performance tuning of scientific applications", volume = "11", publisher = pub-CRC, address = pub-CRC:adr, pages = "????", year = "2011", ISBN = "1-4398-1569-0 (hardback)", ISBN-13 = "978-1-4398-1569-4 (hardback)", LCCN = "Q183.9 .P47 2011", bibdate = "Thu Nov 15 17:15:34 MST 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/super.bib; z3950.loc.gov:7090/Voyager", series = "Chapman and Hall/CRC computational science", abstract = "This book presents an overview of recent research and applications in computer system performance for scientific and high performance computing. After a brief introduction to the field of scientific computer performance, the text provides comprehensive coverage of performance measurement and tools, performance modeling, and automatic performance tuning. It also includes performance tools and techniques for real-world scientific applications. Various chapters address such topics as performance benchmarks, hardware performance counters, the PMaC modeling system, source code-based performance modeling, climate modeling codes, automatic tuning with ATLAS, and much more.", acknowledgement = ack-nhfb, subject = "Science; Data processing; Evaluation; Electronic digital computers; System design; Computer programs; COMPUTERS / Computer Engineering; MATHEMATICS / Advanced; MATHEMATICS / Number Systems", } @Book{Banerjee:2011:LAM, author = "Sudipto Banerjee and Anindya Roy", title = "Linear Algebra and Matrix Analysis for Statistics", publisher = pub-CRC, address = pub-CRC:adr, pages = "xvii + 565", year = "2011", ISBN = "1-4200-9538-2 (hardback)", ISBN-13 = "978-1-4200-9538-8 (hardback)", LCCN = "QA184.2 .B36 2014", bibdate = "Mon Sep 15 18:16:29 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Chapman and Hall/CRC texts in statistical science series", URL = "http://images.tandf.co.uk/common/jackets/websmall/978142009/9781420095388.jpg", abstract = "Linear algebra and the study of matrix algorithms have become fundamental to the development of statistical models. Using a vector-space approach, this book provides an understanding of the major concepts that underlie linear algebra and matrix analysis. Each chapter introduces a key topic, such as infinite-dimensional spaces, and provides illustrative examples. The authors examine recent developments in diverse fields such as spatial statistics, machine learning, data mining, and social network analysis. Complete in its coverage and accessible to students without prior knowledge of linear algebra, the text also includes results that are useful for traditional statistical applications.", acknowledgement = ack-nhfb, subject = "Algebras, Linear; Matrices; Mathematical statistics; MATHEMATICS / Algebra / General.; MATHEMATICS / Probability and Statistics / General.; Algebras, Linear.; Mathematical statistics.; Matrices.", } @Book{Borwein:2011:IMM, author = "Jonathan M. Borwein and Matthew P. Skerritt", title = "An introduction to modern mathematical computing", publisher = pub-SV, address = pub-SV:adr, pages = "xvi + 216", year = "2011", DOI = "https://doi.org/10.1007/978-1-4614-0122-3", ISBN = "1-4614-0121-6", ISBN-13 = "978-1-4614-0121-6", MRclass = "65-01 (15-01 26-01 68-01)", MRnumber = "2808248", bibdate = "Tue May 27 11:24:21 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib", note = "With Maple$ {^{}{\rm {T}}M} $", series = "Springer Undergraduate Texts in Mathematics and Technology", acknowledgement = ack-nhfb, } @Book{Chen:2011:FEM, author = "Zhangxin Chen", title = "The finite element method: its fundamentals and applications in engineering", publisher = pub-WORLD-SCI, address = pub-WORLD-SCI:adr, pages = "xxi + 326", year = "2011", ISBN = "981-4350-56-7 (hardcover), 981-4350-57-5 (paperback)", ISBN-13 = "978-981-4350-56-3 (hardcover), 978-981-4350-57-0 (paperback)", LCCN = "TA347.F5 C467 2011", MRclass = "65-01 (65M60 65N30)", MRnumber = "2985965", MRreviewer = "Tsu-Fen Chen", bibdate = "Tue May 27 12:31:40 MDT 2014", bibsource = "clas.caltech.edu:210/INNOPAC; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", note = "Its fundamentals and applications in engineering", acknowledgement = ack-nhfb, subject = "Finite element method; Problems, exercises, etc; Engineering mathematics; Finite-Elemente-Methode.", } @Book{Cohen:2011:NAM, author = "Harold Cohen", title = "Numerical approximation methods", publisher = pub-SV, address = pub-SV:adr, pages = "xiv + 485", year = "2011", DOI = "https://doi.org/10.1007/978-1-4419-9837-8", ISBN = "1-4419-9836-5", ISBN-13 = "978-1-4419-9836-1", MRclass = "65-01", MRnumber = "2883150", bibdate = "Tue May 27 11:24:21 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib", acknowledgement = ack-nhfb, } @Book{Davies:2011:FEM, author = "Alan J. Davies", title = "The finite element method: an introduction with partial differential equations", publisher = pub-OXFORD, address = pub-OXFORD:adr, edition = "Second", pages = "ix + 297", year = "2011", ISBN = "0-19-960913-6", ISBN-13 = "978-0-19-960913-0", LCCN = "TA347.F5 D38 2011", MRclass = "65-01 (65M60 65N30)", MRnumber = "3087393", bibdate = "Tue May 27 12:31:39 MDT 2014", bibsource = "clas.caltech.edu:210/INNOPAC; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", note = "An introduction with partial differential equations", URL = "http://www.loc.gov/catdir/enhancements/fy1211/2011022386-b.html; http://www.loc.gov/catdir/enhancements/fy1211/2011022386-d.html; http://www.loc.gov/catdir/enhancements/fy1211/2011022386-t.html", acknowledgement = ack-nhfb, subject = "Finite element method", } @Book{Davis:2011:MP, author = "Timothy A. Davis", title = "{MATLAB} primer", publisher = pub-CRC, address = pub-CRC:adr, edition = "Eighth", pages = "xvi + 232", year = "2011", ISBN = "1-4398-2862-8", ISBN-13 = "978-1-4398-2862-5", LCCN = "QA297 .D38 2011", bibdate = "Mon Jan 31 14:24:46 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "MATLAB; Numerical analysis; Data processing", } @Book{Deuflhard:2011:NM, author = "Peter Deuflhard and Martin Weiser", title = "{Numerische Mathematik 3} ({German}) [{Numerical} mathematics 3]", publisher = pub-GRUYTER, address = pub-GRUYTER:adr, pages = "x + 432", year = "2011", ISBN = "3-11-021802-X", ISBN-13 = "978-3-11-021802-2", MRclass = "65-01 (65M06 65M50 65M60 65N06 65N30 65N50)", MRnumber = "2779847 (2012a:65001)", MRreviewer = "Othmar Koch", bibdate = "Tue May 27 11:24:21 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib", note = "Adaptive L{\"o}sung partieller Differentialgleichungen. [Adaptive solutions of partial differential equations]", series = "de Gruyter Lehrbuch [de Gruyter Textbook]", acknowledgement = ack-nhfb, language = "German", } @Book{Fiedler:2011:MGG, author = "Miroslav Fiedler", title = "Matrices and Graphs in Geometry", volume = "139", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "viii + 197", year = "2011", ISBN = "0-521-46193-6", ISBN-13 = "978-0-521-46193-1", LCCN = "QA447 .F45 2011", bibdate = "Tue Feb 7 16:22:53 MST 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/linala2010.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Encyclopedia of Mathematics and its Applications", URL = "http://assets.cambridge.org/97805214/61931/cover/9780521461931.jpg; http://catdir.loc.gov/catdir/enhancements/fy1101/2010046601-b.html; http://catdir.loc.gov/catdir/enhancements/fy1101/2010046601-d.html; http://catdir.loc.gov/catdir/enhancements/fy1101/2010046601-t.html", abstract = "Simplex geometry is a topic generalizing geometry of the triangle and tetrahedron. The appropriate tool for its study is matrix theory, but applications usually involve solving huge systems of linear equations or eigenvalue problems, and geometry can help in visualizing the behaviour of the problem. In many cases, solving such systems may depend more on the distribution of non-zero coefficients than on their values, so graph theory is also useful. The author has discovered a method that in many (symmetric) cases helps to split huge systems into smaller parts. Many readers will welcome this book, from undergraduates to specialists in mathematics, as well as non-specialists who only use mathematics occasionally, and anyone who enjoys geometric theorems. It acquaints the reader with basic matrix theory, graph theory and elementary Euclidean geometry so that they too can appreciate the underlying connections between these various areas of mathematics and computer science.\par This book comprises, in addition to auxiliary material, the research on which I have worked for the past more than 50 years. Some of the results appear here for the first time. The impetus for writing the book came from the late Victor Klee, after my talk in Minneapolis in 1991. The main subject is simplex geometry, a topic which fascinated me from my student times, caused, in fact, by the richness of triangle and tetrahedron geometry on one side and matrix theory on the other side. A large part of the content is concerned with qualitative properties of a simplex. This can be understood as studying not just relations of equalities but also inequalities. It seems that this direction is starting to have important consequences in practical (and important) applications, such as finite element methods.", acknowledgement = ack-nhfb, subject = "Geometry; Matrices; Graphic methods", tableofcontents = "Matricial approach to Euclidean geometry \\ Simplex geometry \\ Qualitative properties of the angles in a simplex --- Special simplexes \\ Further geometric objects \\ Applications", } @Book{Galvis:2011:IAN, author = "Juan Galvis and Henrique Versieux", title = "Introdu{\c{c}}{\~a}o {\`a} aproxima{\c{c}}{\~a}o num{\'e}rica de equa{\c{c}}{\~o}es diferenciais parciais via o m{\'e}todo de elementos finitos. ({Portuguese}) [{Introduction} to numerical approximation of partial differential equations via the finite-element method]", publisher = "Instituto Nacional de Matem\'atica Pura e Aplicada (IMPA)", address = "Rio de Janeiro, Brasil", pages = "91", year = "2011", ISBN = "85-244-0325-X", ISBN-13 = "978-85-244-0325-5", MRclass = "65-01 (65M60 65N30)", MRnumber = "2816863 (2012f:65001)", MRreviewer = "Carlos V{\'a}zquez Cend{\'o}n", bibdate = "Tue May 27 11:24:21 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib", note = "28$ {^{}{\rm {o}}} $ Col{\'o}quio Brasileiro de Matem{\'a}tica. [28th Brazilian Mathematics Colloquium]", series = "Publica\c c\~oes Matem\'aticas do IMPA. [IMPA Mathematical Publications]", acknowledgement = ack-nhfb, language = "Portuguese", } @Book{Gustafsson:2011:FSC, author = "Bertil Gustafsson", title = "Fundamentals of scientific computing", volume = "8", publisher = pub-SV, address = pub-SV:adr, pages = "xiv + 316", year = "2011", DOI = "https://doi.org/10.1007/978-3-642-19495-5", ISBN = "3-642-19494-X", ISBN-13 = "978-3-642-19494-8", MRclass = "65-01", MRnumber = "2808067", bibdate = "Tue May 27 11:24:21 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Texts in Computational Science and Engineering", acknowledgement = ack-nhfb, } @Book{Hermann:2011:NM, author = "Martin Hermann", title = "Numerische {Mathematik}", publisher = pub-OLDENBOURG, address = pub-OLDENBOURG:adr, edition = "Expanded", pages = "xiv + 563", year = "2011", ISBN = "3-486-70820-1", ISBN-13 = "978-3-486-70820-2", MRclass = "65-01", MRnumber = "2933531", bibdate = "Tue May 27 11:24:21 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib", acknowledgement = ack-nhfb, } @Book{Johnson:2011:EMS, author = "Richard K. Johnson", title = "The elements of {MATLAB} style", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "????", year = "2011", ISBN = "0-521-73258-1", ISBN-13 = "978-0-521-73258-1", LCCN = "QA76.73.M296 J64 2011", bibdate = "Mon Jan 31 14:25:07 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", abstract = "A guide for MATLAB programmers that offers a collection of standards and guidelines for creating MATLAB code that will be easy to understand, enhance, and maintain. Avoid doing things that would be an unpleasant surprise to other software developers. The interfaces and the behavior exhibited by your software must be predictable and consistent. If they are not, the documentation must clearly identify and justify any unusual instances of use or behavior.", acknowledgement = ack-nhfb, subject = "MATLAB; Computer programming; Computer software; Quality control; Numerical analysis; Data processing", tableofcontents = "1. General principles \\ 2. Formatting \\ 3. Naming \\ 4. Documentation \\ 5. Programming \\ 6. Files and organization \\ 7. Development", } @Book{Kepner:2011:GAL, author = "Jeremy V. Kepner and J. R. (John R.) Gilbert", title = "Graph algorithms in the language of linear algebra", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xxvii + 361", year = "2011", ISBN = "0-89871-990-9 (hardcover)", ISBN-13 = "978-0-89871-990-1 (hardcover)", LCCN = "QA166.245 .K47 2011", bibdate = "Fri Nov 16 09:38:48 MST 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Software, environments, and tools", URL = "http://www.loc.gov/catdir/enhancements/fy1113/2011003774-b.html; http://www.loc.gov/catdir/enhancements/fy1113/2011003774-d.html; http://www.loc.gov/catdir/enhancements/fy1113/2011003774-t.html", acknowledgement = ack-nhfb, subject = "Graph algorithms; Algebras, Linear", } @Book{King:2011:NSM, author = "Michael R. King and Nipa A. Mody", title = "Numerical and statistical methods for bioengineering: applications in {MATLAB}", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "xii + 581", year = "2011", ISBN = "0-521-87158-1 (hardback)", ISBN-13 = "978-0-521-87158-7 (hardback)", LCCN = "R857.M34 K56 2011; R857.M34 K56X 2011 (LC)", MRclass = "65-01 (62-01 62P10 92B05)", MRnumber = "2767120", bibdate = "Tue May 27 12:31:06 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; prodorbis.library.yale.edu:7090/voyager", note = "Applications in MATLAB", series = "Cambridge Texts in Biomedical Engineering", abstract = "The first MATLAB-based numerical methods textbook for bioengineers that uniquely integrates modelling concepts with statistical analysis, while maintaining a focus on enabling the user to report the error or uncertainty in their result. Between traditional numerical method topics of linear modelling concepts, nonlinear root finding, and numerical integration, chapters on hypothesis testing, data regression and probability are interweaved. A unique feature of the book is the inclusion of examples from clinical trials and bioinformatics, which are not found in other numerical methods textbooks for engineers. With a wealth of biomedical engineering examples, case studies on topical biomedical research, and the inclusion of end of chapter problems, this is a perfect core text for a one-semester undergraduate course.\par Cambridge Texts in Biomedical Engineering provides a forum for high-quality accessible textbooks targeted at undergraduate and graduate courses in biomedical engineering. It will cover a broad range of biomedical engineering topics from introductory texts to advanced topics including, but not limited to, biomechanics, physiology, biomedical instrumentation, imaging, signals and systems, cell engineering, and bioinformatics. The series will blend theory and practice, aimed primarily at biomedical engineering students but will be suitable for broader courses in engineering, the life sciences and medicine", acknowledgement = ack-nhfb, subject = "Biomedical engineering; Statistical methods; Mathematics; MATLAB", tableofcontents = "1. Types and sources of numerical error \\ 2. Systems of linear equations \\ 3. Probability and statistics \\ 4. Hypothesis testing \\ 5. Root-finding techniques for nonlinear equations \\ 6. Numerical quadrature \\ 7. Numerical integration of ordinary differential equations \\ 8. Nonlinear data regression and optimization \\ 9. Basic algorithms of bioinformatics \\ Appendix A. Introduction to MATLAB \\ Appendix B. Location of nodes for Gauss-Legendre quadrature", } @Book{Klee:2011:SDS, author = "Harold Klee and Randal Allen", title = "Simulation of dynamic systems with {MATLAB\reg} and {Simulink\reg}", publisher = pub-CRC, address = pub-CRC:adr, edition = "Second", pages = "xix + 795", year = "2011", ISBN = "1-4398-3673-6 (hardback)", ISBN-13 = "978-1-4398-3673-6 (hardback)", LCCN = "QA76.9.C65 K585 2011", MRclass = "65-01 (34-04 65Lxx 93-04)", MRnumber = "2768103 (2011m:65001)", bibdate = "Tue May 27 12:31:45 MDT 2014", bibsource = "clas.caltech.edu:210/INNOPAC; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", note = "With a foreword by Chris Bauer and Chris Schwarz", abstract = "``Employing the widely adopted MATLAB and Simulink software packages, this book offers the scientific and engineering communities integrated coverage of continuous simulation and the essential prerequisites in one resource. It also provides a complete introduction to the Real-Time Workshop. The text takes the reader through the process of converting a mathematical model of a continuous or discrete system into a simulation model and source code implementation, which can be explored to better understand the dynamic behavior of the system. The second edition addresses common nonlinearities, expands coverage of the Kalman filter, and features extensive treatment of numerical parameters. \par In the first article of SIMULATION magazine in Fall 1963, the editor John McLeod proclaimed simulation to mean ``the act of representing some aspects of the real world by numbers or symbols which may be easily manipulated to facilitate their study.'' Two years later, it was modified to ``the development and use of models for the study of the dynamics of existing or hypothesized systems.'' More than forty years later, the simulation community has yet to converge upon a universally accepted definition", acknowledgement = ack-nhfb, subject = "Computer simulation; SIMULINK; MATLAB", } @Book{Monahan:2011:NMS, author = "John F. Monahan", title = "Numerical methods of statistics", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, edition = "Second", pages = "xvi + 447", year = "2011", DOI = "https://doi.org/10.1017/CBO9780511977176", ISBN = "0-521-13951-1 (paperback), 0-521-19158-0", ISBN-13 = "978-0-521-13951-9 (paperback), 978-0-521-19158-6", LCCN = "QA276.4 .M65 2011 (LC); QA276.4 .M65 2011", MRclass = "65-01 (60-04 62-04 65C60)", MRnumber = "2791641", bibdate = "Tue May 27 12:30:59 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; prodorbis.library.yale.edu:7090/voyager", series = "Cambridge Series in Statistical and Probabilistic Mathematics", acknowledgement = ack-nhfb, subject = "Mathematical statistics; Data processing", } @Book{Nahin:2011:NCT, author = "Paul J. Nahin", title = "Number-crunching: taming unruly computational problems from mathematical physics to science fiction", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "xxvi + 376", year = "2011", ISBN = "0-691-14425-7 (hardcover), 1-4008-3958-0 (e-book)", ISBN-13 = "978-0-691-14425-2 (hardcover), 978-1-4008-3958-2 (e-book)", LCCN = "QC20.7.E4 N34 2011", bibdate = "Wed Oct 22 08:11:12 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.jstor.org/stable/10.2307/j.ctt7rk7v", abstract = "How do technicians repair broken communications cables at the bottom of the ocean without actually seeing them? What's the likelihood of plucking a needle out of a haystack the size of the Earth? And is it possible to use computers to create a universal library of everything ever written or every photo ever taken? These are just some of the intriguing questions that best-selling popular math writer Paul Nahin tackles in Number-Crunching. Through brilliant math ideas and entertaining stories, Nahin demonstrates how odd and unusual math problems can be solved by bringing together basic physics ideas and today's powerful computers. Some of the outcomes discussed are so counterintuitive they will leave readers astonished. Nahin looks at how the art of number-crunching has changed since the advent of computers, and how high-speed technology helps to solve fascinating conundrums such as the three-body, Monte Carlo, leapfrog, and gambler's ruin problems. Along the way, Nahin traverses topics that include algebra, trigonometry, geometry, calculus, number theory, differential equations, Fourier series, electronics, and computers in science fiction. He gives historical background for the problems presented, offers many examples and numerous challenges, supplies MATLAB codes for all the theories discussed, and includes detailed and complete solutions.", acknowledgement = ack-nhfb, remark = "A collection of challenging problems in mathematical physics that roar like lions when attacked analytically, but which purr like kittens when confronted by a high-speed electronic computer and its powerful scientific software (plus some speculations for the future from science fiction).", subject = "Mathematical physics; Data processing; Problems, exercises, etc", tableofcontents = "Feynman meets Fermat \\ Just for fun: two quick number-crunching problems \\ Computers and mathematical physics \\ The astonishing problem of the hanging masses \\ The three-body problem and computers \\ Electrical circuit analysis and computers \\ The leapfrog problem \\ Science fiction: when computers become like us \\ A cautionary epilogue", } @Book{Naumann:2011:ADC, author = "Uwe Naumann", title = "The art of differentiating computer programs: an introduction to algorithmic differentiation", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xviii + 340", year = "2011", ISBN = "1-61197-206-X", ISBN-13 = "978-1-61197-206-1", LCCN = "QA76.76.A98 N38 2011", bibdate = "Fri Nov 16 09:54:38 MST 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Software, environments, and tools", URL = "http://www.loc.gov/catdir/enhancements/fy1201/2011032262-b.html; http://www.loc.gov/catdir/enhancements/fy1201/2011032262-d.html; http://www.loc.gov/catdir/enhancements/fy1201/2011032262-t.html", acknowledgement = ack-nhfb, subject = "Computer programs; Automatic differentiations; Sensitivity theory (Mathematics)", } @Book{Razavy:2011:HQM, author = "Mohsen Razavy", title = "{Heisenberg}'s quantum mechanics", publisher = pub-WORLD-SCI, address = pub-WORLD-SCI:adr, pages = "xix + 657", year = "2011", ISBN = "981-4304-11-5 (paperback), 981-4304-10-7", ISBN-13 = "978-981-4304-11-5 (paperback), 978-981-4304-10-8", LCCN = "QC174.12 .R39 2011", bibdate = "Mon Nov 28 08:38:47 MST 2011", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib; http://www.math.utah.edu/pub/tex/bib/einstein.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.gbv.de:20011/gvk", abstract = "This book provides a detailed account of quantum theory with a much greater emphasis on the Heisenberg equations of motion and the matrix method. The book features a deeper treatment of the fundamental concepts such as the rules of constructing quantum mechanical operators and the classical-quantal correspondence; the exact and approximate methods based on the Heisenberg equations; the determinantal approach to the scattering theory and the LSZ reduction formalism where the latter method is used to obtain the transition matrix. The uncertainty relations for a number of different observables are derived and discussed. A comprehensive chapter on the quantization of systems with nonlocalized interaction is included. Exact solvable models, and approximate techniques for solution of realistic many-body problems are also considered. The book takes a unified look in the final chapter, examining the question of measurement in quantum theory, with an introduction to the Bell's inequalities.", acknowledgement = ack-nhfb, tableofcontents = "1.1: The Lagrangian and the Hamilton Principle \\ 1.2: Noether's Theorem \\ 1.3: The Hamiltonian Formulation \\ 1.4: Canonical Transformation \\ 1.5: Action-Angle Variables \\ 1.6: Poisson Brackets \\ 1.7: Time Development of Dynamical Variables and Poisson Brackets \\ 1.8: Infinitesimal Canonical Transformation \\ 1.9: Action Principle with Variable End Points \\ 1.10: Symmetry and Degeneracy in Classical Dynamics \\ 1.11: Closed Orbits and Accidental Degeneracy \\ 1.12: Time-Dependent Exact Invariants \\ 2.1: Equivalence of Wave and Matrix Mechanics \\ 3.1: Vectors and Vector Spaces \\ 3.2: Special Types of Operators \\ 3.3: Vector Calculus for the Operators \\ 3.4: Construction of Hermitian and Self-Adjoint Operators \\ 3.5: Symmetrization Rule \\ 3.6: Weyl's Rule \\ 3.7: Dirac's Rule \\ 3.8: Von Neumann's Rules \\ 3.9: Self-Adjoint Operators \\ 3.10: Momentum Operator in a Curvilinear Coordinates \\ 3.11: Summation Over Normal Modes \\ 4.1: The Uncertainty Principle \\ 4.2: Application of the Uncertainty Principle for Calculating Bound State Energies \\ 4.3: Time-Energy Uncertainty Relation \\ 4.4: Uncertainty Relations for Angular Momentum-Angle Variables \\ 4.5: Local Heisenberg Inequalities \\ 4.6: The Correspondence Principle \\ 4.7: Determination of the State of a System \\ 5.1: Schwinger's Action Principle and Heisenberg's equations of Motion \\ 5.2: Nonuniqueness of the Commutation Relations \\ 5.3: First Integrals of Motion \\ 6.1: Galilean Invariance \\ 6.2: Wave Equation and the Galilean Transformation \\ 6.3: Decay Problem in Nonrelativistic Quantum Mechanics and Mass Superselection Rule \\ 6.4: Time-Reversal Invariance \\ 6.5: Parity of a State \\ 6.6: Permutation Symmetry \\ 6.7: Lattice Translation \\ 6.8: Classical and Quantum Integrability \\ 6.9: Classical and Quantum Mechanical Degeneracies \\ 7.1: Klein's Method \\ 7.2: The Anharmonic Oscillator \\ 7.3: The Double-Well Potential \\ 7.4: Chasman's Method \\ 7.5: Heisenberg's Equations of Motion for Impulsive Forces \\ 7.6: Motion of a Wave Packet \\ 7.7: Heisenberg's and Newton's Equations of Motion \\ 8.1: Energy Spectrum of the Two-Dimensional Harmonic Oscillator \\ 8.2: Exactly Solvable Potentials Obtained from Heisenberg's Equation \\ 8.3: Creation and Annihilation Operators \\ 8.4: Determination of the Eigenvalues by Factorization Method \\ 8.5: A General Method for Factorization \\ 8.6: Supersymmetry and Superpotential \\ 8.7: Shape Invariant Potentials \\ 8.8: Solvable Examples of Periodic Potentials \\ 9.1: The Angular Momentum Operator \\ 9.2: Determination of the Angular Momentum Eigenvalues \\ 9.3: Matrix Elements of Scalars and Vectors and the Selection Rules \\ 9.4: Spin Angular Momentum \\ 9.5: Angular Momentum Eigenvalues Determined from the Eigenvalues of Two Uncoupled Oscillators \\ 9.6: Rotations in Coordinate Space and in Spin Space \\ 9.7: Motion of a Particle Inside a Sphere \\ Almost Degenerate Perturbation Theory \\ 9.8: The Hydrogen Atom \\ 9.9: Calculation of the Energy Eigenvalues Using the Runge[-]Lenz Vector \\ 9.10: Classical Limit of Hydrogen Atom \\ 9.11: Self-Adjoint Ladder Operator \\ 9.12: Self-Adjoint Ladder Operator tiff Angular Momentum \\ 9.13: Generalized Spin Operators \\ 9.14: The Ladder Operator \\ 10.1: Discrete-Time Formulation of the Heisenberg's Equations of Motion \\ 10.2: Quantum Tunneling Using Discrete-Time Formulation \\ 10.3: Determination of Eigenvalues from Finite-Difference Equations \\ 10.4: Systems with Several Degrees of Freedom \\ 10.5: Weyl-Ordered Polynomials and Bender[-]Dunne Algebra \\ 10.6: Integration of the Operator Differential Equations \\ 10.7: Iterative Solution for Polynomial Potentials \\ 10.8: Another Numerical Method for the Integration of the Equations of Motion \\ 10.9: Motion of a Wave Packet \\ 11.1: Perturbation Theory Applied to the Problem of a Quartic Oscillator \\ 11.2: Degenerate Perturbation Theory \\ 11.3: Almost Degenerate Perturbation Theory \\ 11.4: van der Waals Interaction \\ 11.5: Time-Dependent Perturbation Theory \\ 11.6: The Adiabatic Approximation \\ 11.7: Transition Probability to the First Order \\ 12.1: WKB Approximation for Bound States \\ 12.2: Approximate Determination of the Eigenvalues for Nonpolynomial Potentials \\ 12.3: Generalization of the Semiclassical Approximation to Systems with N Degrees of Freedom \\ 12.4: A Variational Method Based on Heisenberg's Equation of Motion \\ 12.5: Raleigh--Ritz Variational Principle \\ 12.6: Tight-Binding Approximation \\ 12.7: Heisenberg's Correspondence Principle \\ 12.8: Bohr and Heisenberg Correspondence and the Frequencies and Intensities of the Emitted Radiation \\ 13.1: Equations of Motion of Finite Order \\ 13.2: Equation of Motion of Infinite Order \\ 13.3: Classical Expression for the Energy \\ 13.4: Energy Eigenvalues when the Equation of Motion is of Infinite Order \\ 14.1: Determinantal Method in Potential Scattering 14.2: Two Solvable Problems \\ 14.3: Time-Dependent Scattering Theory \\ 14.4: The Scattering Matrix \\ 14.5: The Lippmann[-]Schwinger Equation \\ 14.6: Analytical Properties of the Radial Wave Function \\ 14.7: The Jost Function \\ 14.8: Zeros of the Jost Function and Bound Sates \\ 14.9: Dispersion Relation \\ 14.10: Central Local Potentials having Identical Phase Shifts and Bound States \\ 14.11: The Levinson Theorem \\ 14.12: Number of Bound States for a Given Partial Wave \\ 14.13: Analyticity of the S-Matrix and the Principle of Casuality \\ 14.14: Resonance Scattering \\ 14.15: The Born Series \\ 14.16: Impact Parameter Representation of the Scattering Amplitude \\ 14.17: Determination of the Impact Parameter Phase Shift from the Differential Cross Section \\ 14.18: Elastic Scattering of Identical Particles \\ 14.19: Transition Probability \\ 14.20: Transition Probabilities for Forced Harmonic Oscillator \\ 15.1: Diffraction in Time \\ 15.2: High Energy Scattering from an Absorptive Target \\ 16.1: The Aharonov--Bohm Effect \\ 16.2: Time-Dependent Interaction \\ 16.3: Harmonic Oscillator with Time-Dependent Frequency \\ 16.4: Heisenberg's Equations for Harmonic Oscillator with Time-Dependent Frequency \\ 16.5: Neutron Interferometry \\ 16.6: Gravity-Induced Quantum Interference \\ 16.7: Quantum Beats in Waveguides with Time-Dependent Boundaries \\ 16.8: Spin Magnetic Moment \\ 16.9: Stern--Gerlach Experiment \\ 16.10: Precession of Spin Magnetic Moment in a Constant Magnetic Field \\ 16.11: Spin Resonance \\ 16.12: A Simple Model of Atomic Clock \\ 16.13: Berry's Phase \\ 17.1: Ground State of Two-Electron Atom \\ 17.2: Hartree and Hartree-Fock Approximations \\ 17.3: Second Quantization \\ 17.4: Second-Quantized Formulation of the Many-Boson Problem \\ 17.5: Many-Fermion Problem \\ 17.6: Pair Correlations Between Fermions \\ 17.7: Uncertainty Relations for a Many-Fermion System \\ 17.8: Pair Correlation Function for Noninteracting Bosons \\ 17.9: Bogoliubov Transformation for a Many-Boson System \\ 17.10: Scattering of Two Quasi-Particles \\ 17.11: Bogoliubov Transformation for Fermions Interacting through Pairing Forces \\ 17.12: Damped Harmonic Oscillator \\ 18.1: Coherent State of the Radiation Field \\ 18.2: Casimir Force \\ 18.3: Casimir Force Between Parallel Conductors \\ 18.4: Casimir Force in a Cavity with Conducting Walls \\ 19.1: Theory of Natural Line Width \\ 19.2: The Lamb Shift \\ 19.3: Heisenberg's Equations for Interaction of an Atom with Radiation \\ 20.1: EPR Experiment with Particles \\ 20.2: Classical and Quantum Mechanical Operational Concepts of Measurement \\ 20.3: Collapse of the Wave Function \\ 20.4: Quantum versus Classical Correlations", } @Book{Scott:2011:NA, author = "L. Ridgway Scott", title = "Numerical analysis", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "xiv + 325", year = "2011", ISBN = "0-691-14686-1 (hardcover)", ISBN-13 = "978-0-691-14686-7 (hardcover)", LCCN = "QA297 .S38 2011; QA297 .S393 2011", MRclass = "65-01 (41A05 41A10)", MRnumber = "2796928", bibdate = "Tue May 27 12:30:57 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; prodorbis.library.yale.edu:7090/voyager; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "Numerical analysis", tableofcontents = "Ch. 1. Numerical algorithms \\ Ch. 2. Nonlinear equations \\ Ch. 3. Linear systems \\ Ch. 4. Direct solvers \\ Ch. 5. Vector spaces \\ Ch. 6. Operators \\ Ch. 7. Nonlinear systems \\ Ch. 8. Iterative methods \\ Ch. 9. Conjugate gradients \\ Ch. 10. Polynominal interpolation \\ Ch. 11. Chebyshev and Hermite interpolation \\ Ch. 12. Approximation theory \\ Ch. 13. Numerical quadrature \\ Ch. 14. Eigenvalue problems \\ Ch. 15. Eigenvalue algorithms \\ Ch. 16. Ordinary differential equations \\ Ch. 17. Higher-order ODE discretization methods \\ Ch. 18. Floating point \\ Ch. 19. Notation", } @Book{Stenger:2011:HSN, author = "Frank Stenger", title = "Handbook of Sinc Numerical Methods", publisher = pub-CRC, address = pub-CRC:adr, pages = "xx + 463", year = "2011", ISBN = "1-4398-2158-5 (hardback), 1-4398-2159-3 (e-book)", ISBN-13 = "978-1-4398-2158-9 (hardback), 978-1-4398-2159-6 (e-book)", LCCN = "QA372 .S8195 2010", bibdate = "Mon Apr 21 17:35:42 2014", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Chapman and Hall/CRC numerical analysis and scientific computation series", URL = "http://www.crcpress.com/product/isbn/9781439821589", ZMnumber = "Zbl 1208.65143", abstract = "This handbook is essential for solving numerical problems in mathematics, computer science, and engineering. The methods presented are similar to finite elements but more adept at solving analytic problems with singularities over irregularly shaped yet analytically described regions. The author makes sinc methods accessible to potential users by limiting details as to how or why these methods work. From calculus to partial differential and integral equations, the book can be used to approximate almost every type of operation. It includes more than 470 MATLAB programs, along with a CD-ROM containing these programs for ease of use", acknowledgement = ack-nhfb, subject = "Galerkin methods; Differential equations; Numerical solutions; mathematics / applied; mathematics / differential equations; mathematics / number systems", tableofcontents = "One-Dimensional Sinc Theory \\ Introduction and Summary \\ Sampling over the Real Line \\ More General Sinc Approximation on $R$ \\ Sinc, Wavelets, Trigonometric and Algebraic Polynomials and Quadratures \\ Sinc Methods on $\Gamma$ \\ Rational Approximation at Sinc Points \\ Polynomial Methods at Sinc Points \\ \\ Sinc Convolution-BIE Methods for PDE and IE \\ Introduction and Summary \\ Some Properties of Green's Functions \\ Free-Space Green's Functions for PDE \\ Laplace Transforms of Green's Functions \\ Multi-Dimensional Convolution Based on Sinc \\ Theory of Separation of Variables \\ \\ Explicit 1-d Program Solutions via Sinc-Pack \\ Introduction and Summary \\ Sinc Interpolation \\ Approximation of Derivatives \\ Sinc Quadrature \\ Sinc Indefinite Integration \\ Sinc Indefinite Convolution \\ Laplace Transform Inversion \\ Hilbert and Cauchy Transforms \\ Sinc Solution of ODE \\ Wavelet Examples \\ \\ Explicit Program Solutions of PDE via Sinc-Pack \\ Introduction and Summary \\ Elliptic PDE \\ Hyperbolic PDE \\ Parabolic PDE \\ Performance Comparisons \\ \\ Directory of Programs \\ Wavelet Formulas \\ One Dimensional Sinc Programs \\ Multi-Dimensional Laplace Transform Programs \\ \\ Bibliography \\ \\ Index", } @Book{Tucker:2011:VNS, author = "Warwick Tucker", title = "Validated numerics: a short introduction to rigorous computations", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "????", year = "2011", ISBN = "0-691-14781-7 (hardcover)", ISBN-13 = "978-0-691-14781-9 (hardcover)", LCCN = "QA76.95 .T83 2011", bibdate = "Mon May 16 19:10:17 MDT 2011", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", acknowledgement = ack-nhfb, subject = "Numerical calculations; Verification; Science; Data processing", } @Article{Watkins:2011:FA, author = "David S. Watkins", title = "{Francis}'s Algorithm", journal = j-AMER-MATH-MONTHLY, volume = "118", number = "5", pages = "387--403", month = may, year = "2011", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Thu May 26 16:28:05 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib", URL = "http://www.jstor.org/stable/info/10.4169/amer.math.monthly.118.05.387", abstract = "John Francis's implicitly shifted QR algorithm turned the problem of matrix eigenvalue computation from difficult to routine almost overnight about fifty years ago. It was named one of the top ten algorithms of the twentieth century by Dongarra and Sullivan, and it deserves to be more widely known and understood by the general mathematical community. This article provides an efficient introduction to Francis's algorithm that follows a novel path. Efficiency is gained by omitting the traditional but wholly unnecessary detour through the basic QR algorithm. A brief history of the algorithm is also included. It was not a one-man show; some other important names are Rutishauser, Wilkinson, and Kublanovskaya. Francis was never a specialist in matrix computations. He was employed in the early computer industry, spent some time on the problem of eigenvalue computation and did amazing work, and then moved on to other things. He never looked back, and he remained unaware of the huge impact of his work until many years later.", acknowledgement = ack-nhfb, } @Book{Zhang:2011:MTB, author = "Fuzhen Zhang", title = "Matrix Theory: Basic Results and Techniques", publisher = pub-SV, address = pub-SV:adr, edition = "Second", pages = "xviii + 399", year = "2011", DOI = "https://doi.org/10.1007/978-1-4614-1099-7", ISBN = "1-4614-1098-3 (paperback), 1-4614-1099-1 (e-book)", ISBN-13 = "978-1-4614-1098-0 (paperback), 978-1-4614-1099-7 (e-book)", LCCN = "QA188 .Z47 2011", MRclass = "15-02 (15A09 15A15 15A18 15A45 15A54 15A60)", MRnumber = "2857760 (2012h:15001)", MRreviewer = "Mohammad Sal Moslehian", bibdate = "Fri Nov 21 06:49:56 2014", bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Universitext", URL = "http://www.loc.gov/catdir/enhancements/fy1406/2011935372-b.html; http://www.loc.gov/catdir/enhancements/fy1406/2011935372-d.html; http://www.loc.gov/catdir/enhancements/fy1406/2011935372-t.html", abstract = "The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. The book contains ten chapters covering various topics ranging from similarity and special types of matrices to Schur complements and matrix normality. This book can be used as a textbook or a supplement for a linear algebra and matrix theory class or a seminar for senior undergraduate or graduate students. The book can also serve as a reference for instructors and researchers in the fields of algebra, matrix analysis, operator theory, statistics, computer science, engineering, operations research, economics, and other fields. Major changes in this revised and expanded second edition: * Expansion of topics such as matrix functions, nonnegative matrices, and (unitarily invariant) matrix norms; * A new chapter, Chapter 4, with updated material on numerical ranges and radii, matrix norms, and special operations such as the Kronecker and Hadamard products and compound matrices; * A new chapter, Chapter 10, on matrix inequalities, which presents a variety of inequalities on the eigenvalues and singular values of matrices and unitarily invariant norms.", acknowledgement = ack-nhfb # " and " # ack-rah, tableofcontents = "Preface to the Second Edition \\ Preface \\ Frequently Used Notation and Terminology \\ Frequently Used Terms \\ 1 Elementary Linear Algebra Review \\ 2 Partitioned Matrices, Rank, and Eigenvalues \\ 3 Matrix Polynomials and Canonical Forms \\ 4 Numerical Ranges, Matrix Norms, and Special Operations \\ 5 Special Types of Matrices \\ 6 Unitary Matrices and Contractions \\ 7 Positive Semidefinite Matrices \\ 8 Hermitian Matrices \\ 9 Normal Matrices \\ 10 Majorization and Matrix Inequalities \\ References \\ Notation \\ Index", } @Book{Altman:2012:USM, author = "Yair M. Altman", title = "Undocumented secrets of {MATLAB--Java} programming", publisher = pub-CRC, address = pub-CRC:adr, pages = "xxi + 663 + 16", year = "2012", ISBN = "1-4398-6904-9 (electronic bk.), 1-4398-6903-0 (hardback), 1-4398-6903-0", ISBN-13 = "978-1-4398-6904-8 (electronic bk.), 978-1-4398-6903-1 (hardback), 978-1-4398-6903-1", LCCN = "QA297 .A544 2012", bibdate = "Fri Nov 16 08:10:20 MST 2012", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", acknowledgement = ack-nhfb, subject = "MATLAB; Numerical analysis; Data processing; Java (Computer program language); COMPUTERS / Programming / Algorithms; COMPUTERS / Computer Engineering; MATHEMATICS / Number Systems. MATHEMATICS / Numerical Analysis", tableofcontents = "1.: Introduction to Java in MATLAB \\ 2.: Using non-GUI Java libraries in MATLAB \\ 3.: Rich GUI using Java Swing \\ 4.: Uitools \\ 5.: Built-in MATLAB widgets and Java classes \\ 6.: Customizing MATLAB controls \\ 7.: The Java frame \\ 8.: The MATLAB desktop \\ 9.: Using MATLAB from within Java \\ 10.: Putting it all together \\ Appendix A.: What Is Java? \\ Appendix B.: UDD \\ Appendix C.: Open questions", } @Book{Antia:2012:NMS, author = "H. M. Antia", title = "Numerical methods for scientists and engineers", volume = "2", publisher = "Hindustan Book Agency, New Delhi", address = "New Delhi", edition = "Third", pages = "xxxii + 855", year = "2012", ISBN = "93-80250-40-1 (hardcover)", ISBN-13 = "978-93-80250-40-3 (hardcover)", LCCN = "TA335 .A58 2012", MRclass = "65-01", MRnumber = "3025059", bibdate = "Tue May 27 12:31:37 MDT 2014", bibsource = "clas.caltech.edu:210/INNOPAC; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; prodorbis.library.yale.edu:7090/voyager", series = "Texts and Readings in Physical Sciences", acknowledgement = ack-nhfb, remark = "Previous ed.: Basel: Birkh{\"a}user, 2002.", subject = "Numerical analysis; Engineering mathematics", } @Book{Atkinson:2012:SHA, author = "Kendall Atkinson and Weimin Han", title = "Spherical Harmonics and Approximations on the Unit Sphere: an Introduction", volume = "2044", publisher = pub-SV, address = pub-SV:adr, pages = "ix + 244", year = "2012", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/978-3-642-25983-8", ISBN = "3-642-25982-0 (print), 3-642-25983-9 (e-book)", ISBN-13 = "978-3-642-25982-1 (print), 978-3-642-25983-8 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", LCCN = "QA3 .L28 no. 2044; QA406 .A85 2012", MRclass = "41A30 (65N30 65R20); 41-02 (33C55 41A30 41A63 42A10)", MRnumber = "2934227", MRreviewer = "Feng Dai", bibdate = "Tue May 6 14:56:41 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/lnm2010.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = ser-LECT-NOTES-MATH, URL = "http://link.springer.com/book/10.1007/978-3-642-25983-8; http://www.springerlink.com/content/978-3-642-25983-8; http://www.springerlink.com/content/u58550t8417n/", abstract = "These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well asan overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions.", acknowledgement = ack-nhfb, series-URL = "http://link.springer.com/bookseries/304", tableofcontents = "1. Preliminaries \\ 2. Spherical harmonics \\ 3. Differentiation and integration over the sphere \\ 4. Approximation theory \\ 5. Numerical quadrature \\ 6. Applications: spectral methods", } @Book{Attaway:2012:MPI, author = "Stormy Attaway", title = "{MATLAB}: a practical introduction to programming and problem solving", publisher = "Butterworth-Heinemann", address = "Waltham, MA, USA", edition = "Second", pages = "xx + 518", year = "2012", ISBN = "0-12-385081-9", ISBN-13 = "978-0-12-385081-2", LCCN = "QA297 .A87 2012", bibdate = "Thu May 3 08:07:25 MDT 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "Numerical analysis; Data processing; MATLAB; Computer programming", } @Book{Chaitin-Chatelin:2012:EM, author = "Fran{\c{c}}oise Chaitin-Chatelin and Mario Ahu{\'e}s and Walter Ledermann", title = "Eigenvalues of matrices", volume = "71", publisher = pub-SIAM, address = pub-SIAM:adr, edition = "Revised", pages = "xxx + 410", year = "2012", ISBN = "1-61197-245-0", ISBN-13 = "978-1-61197-245-0", LCCN = "QA188 .C44 2012", bibdate = "Tue Aug 12 15:33:32 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Classics in applied mathematics", URL = "http://www.loc.gov/catdir/enhancements/fy1305/2012033049-d.html; http://www.loc.gov/catdir/enhancements/fy1305/2012033049-t.html; http://www.loc.gov/catdir/enhancements/fy1307/2012033049-b.html", acknowledgement = ack-nhfb, remark = "Translated from the original French.", subject = "Matrices; Eigenvalues", tableofcontents = "Supplements from linear algebra \\ Elements of spectral theory \\ Why compute eigenvalues? \\ Error analysis \\ Foundations of methods for computing eigenvalues \\ Numerical methods for large matrices \\ Chebyshev's iterative methods \\ Polymorphic information processing with matrices", } @Book{Davis:2012:LAP, author = "Ernest Davis", title = "Linear algebra and probability for computer science applications", publisher = pub-CRC, address = pub-CRC:adr, pages = "xviii + 413", year = "2012", ISBN = "1-4665-0155-3 (hardcover)", ISBN-13 = "978-1-4665-0155-3 (hardcover)", LCCN = "QA76.9.M35 D38 2012", bibdate = "Tue May 5 16:14:05 MDT 2015", bibsource = "http://www.math.utah.edu/pub/tex/bib/datacompression.bib; http://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib; http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", abstract = "Taking a computer scientist's point of view, this classroom-tested text gives an introduction to linear algebra and probability theory, including some basic aspects of statistics. It discusses examples of applications from a wide range of areas of computer science, including computer graphics, computer vision, robotics, natural language processing, web search, machine learning, statistical analysis, game playing, graph theory, scientific computing, decision theory, coding, cryptography, network analysis, data compression, and signal processing. It includes an extensive discussion of MATLAB, and includes numerous MATLAB exercises and programming assignments.", acknowledgement = ack-nhfb, subject = "Computer science; Mathematics; Algebras, Linear; Probabilities", } @Book{Eubank:2012:SCC, author = "Randall L. Eubank and Ana Kupresanin", title = "Statistical computing in {C++} and {R}", publisher = pub-CRC, address = pub-CRC:adr, pages = "xv + 540", year = "2012", ISBN = "1-4200-6650-1 (hardcover)", ISBN-13 = "978-1-4200-6650-0 (hardcover)", LCCN = "QA276.4 .E87 2012", bibdate = "Thu Jul 10 13:05:53 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/s-plus.bib; z3950.loc.gov:7090/Voyager", series = "Chapman and Hall/CRC the R series", abstract = "When one looks at a book with `statistical computing' in the title, the expectation is most likely for a treatment of the topic that has close ties to numerical analysis. There are many texts written from this perspective that provide valuable resources for those who are actively involved in the solution of computing problems that arise in statistics. The presentation in the present text represents a departure from this classical emphasis in that it concentrates on the writing of code rather than the development and study of algorithms, per se. The goal is to provide a treatment of statistical computing that lays a foundation for original code development in a research environment. The advancement of statistical methodology is now inextricably linked to the use of computers. New methodological ideas must be translated into usable code and then numerically evaluated relative to competing procedures. As a result, many statisticians expend significant amounts of their creative energy while sitting in front of a computer monitor. The end products from the vast majority of these efforts are unlikely to be reflected in changes to core aspects of numerical methods or computer hardware. Nonetheless, they are modern statisticians that are (often very) involved in computing. This book is written with that particular audience in mind. What does a modern statistician need to know about computing? Our belief is that they need to understand at least the basic principles of algorithmic thinking. The translation of a mathematical problem into its computational analog (or analogs) is a skill that must be learned, like any other, by actively solving relevant problems.", acknowledgement = ack-nhfb, author-dates = "1952--", subject = "Statistics; Data processing; C++ (Computer program language); R (Computer program language); MATHEMATICS / Probability and Statistics / General.", tableofcontents = "1.1. Programming paradigms \\ 1.2. Object-oriented programming \\ 1.3. What lies ahead \\ 2.1. Introduction \\ 2.2. Storage in C++ \\ 2.3. Integers \\ 2.4. Floating-point representation \\ 2.5. Errors \\ 2.6. Computing a sample variance \\ 2.7. Storage in R \\ 2.8. Exercises \\ 3.1. Introduction \\ 3.2. Variables and scope \\ 3.3. Arithmetic and logical operators \\ 3.4. Control structures \\ 3.5. Using arrays and pointers \\ 3.6. Functions \\ 3.7. Classes, objects and methods \\ 3.8. Miscellaneous topics \\ 3.8.1. Structs \\ 3.8.2. The this pointer \\ 3.8.3.const correctness \\ 3.8.4. Forward references \\ 3.8.5. Strings \\ 3.8.6. Namespaces \\ 3.8.7. Handling errors \\ 3.8.8. Timing a program \\ 3.9. Matrix and vector classes \\ 3.10. Input, output and templates \\ 3.11. Function templates \\ 3.12. Exercises \\ 4.1. Introduction \\ 4.2. Congruential methods \\ 4.3. Lehmer type generators in C++ \\ 4.4. An FM2 class \\ 4.5. Other generation methods \\ 4.6. Nonuniform generation \\ 4.7. Generating random normals \\ 4.8. Generating random numbers in R \\ 4.9. Using the R Standalone Math Library \\ 4.10. Exercises \\ 5.1. Introduction \\ 5.2. File input and output \\ 5.3. Classes, methods and namespaces \\ 5.4. Writing R functions \\ 5.5. Avoiding loops in R \\ 5.6. An example \\ 5.7. Using C/C++ code in R \\ 5.8. Exercises \\ 6.1. Introduction \\ 6.2. Creating a new class \\ 6.3. Generic methods \\ 6.4. An example \\ 6.5. Exercises \\ 7.1. Introduction \\ 7.2. Solving linear equations \\ 7.2.1. Solving triangular systems \\ 7.2.2. Gaussian elimination \\ 7.2.3. Cholesky decomposition \\ 7.2.4. Banded matrices \\ 7.2.5. An application: linear smoothing splines \\ 7.2.6. Banded matrices via inheritance \\ 7.3. Eigenvalues and eigenvectors \\ 7.4. Singular value decomposition \\ 7.5. Least squares \\ 7.6. The Template Numerical Toolkit \\ 7.7. Exercises \\ 8.1. Introduction \\ 8.2. Function objects \\ 8.3. Golden section \\ 8.3.1. Dealing with multiple minima \\ 8.3.2. An application: linear smoothing splines revisited \\ 8.4. Newton's method \\ 8.5. Maximum likelihood \\ 8.6. Random search \\ 8.7. Exercises \\ 9.1. Introduction \\ 9.2. ADT dictionary \\ 9.2.1. Dynamic arrays and quicksort \\ 9.2.2. Linked lists and mergesort \\ 9.2.3. Stacks and queues \\ 9.2.4. Hash tables \\ 9.3. ADT priority queue \\ 9.3.1. Heaps \\ 9.3.2. A simple heap in C++ \\ 9.4. ADT ordered set \\ 9.4.1. A simple C++ binary search tree \\ 9.4.2. Balancing binary trees \\ 9.5. Pointer arithmetic, aerators and templates \\ 9.5.1. Iterators \\ 9.5.2. A linked list template class \\ 9.6. Exercises \\ 10.1. Introduction \\ 10.2. Container basics \\ 10.3. Vector and deque \\ 10.3.1. Streaming data \\ 10.3.2. Flexible data input \\ 10.3.3. Guess5 revisited \\ 10.4. The C++ list container \\ 10.4.1. An example \\ 10.4.2. A chaining hash table \\ 10.5. Queues \\ 10.6. The map and set containers \\ 10.7. Algorithm basics \\ 10.8. Exercises \\ 11.1. Introduction \\ 11.2. OpenMP \\ 11.3. Basic MPI commands for C++ \\ 11.4. Parallel processing in R \\ 11.5. Parallel random number generation \\ 11.6. Exercises \\ A.1. Getting around and finding things \\ A.2. Seeing what's there \\ A.3. Creating and destroying things \\ A.4. Things that are running and how to stop them \\ B.1. R as a calculator \\ B.2. R as a graphics engine \\ B.3. R for statistical analysis \\ C.1. Pseudo-random numbers \\ C.2. Hash tables \\ C.3. Tuples", } @Article{Gander:2012:ERG, author = "Martin J. Gander and Gerhard Wanner", title = "From {Euler}, {Ritz}, and {Galerkin} to Modern Computing", journal = j-SIAM-REVIEW, volume = "54", number = "4", pages = "627--666", month = "????", year = "2012", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/100804036", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Fri Jun 21 11:25:02 MDT 2013", bibsource = "http://epubs.siam.org/toc/siread/54/4; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "January 2012", } @Book{Griffiths:2012:TWA, author = "Graham W. Griffiths and W. E. Schiesser", title = "Traveling wave analysis of partial differential equations: numerical and analytical methods with {MATLAB} and {Maple}", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "xiii + 447", year = "2012", ISBN = "0-12-384652-8 (hardcover)", ISBN-13 = "978-0-12-384652-5 (hardcover)", LCCN = "QA374 .G75 2012", bibdate = "Tue Jun 19 15:02:49 MDT 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/maple-extract.bib; http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "Differential equations, Partial; Numerical analysis; Computer programs; MATLAB; Maple (Computer file)", tableofcontents = "Introduction to traveling wave analysis \\ Linear advection equation \\ Linear diffusion equation \\ A linear convection diffusion reaction equation \\ Diffusion equation with nonlinear source terms \\ Burgers-Huxley equation \\ Burgers-Fisher equation \\ Fisher-Kolmogorov equation \\ Fitzhugh-Nagumo equation \\ Kolmogorov-Petrovskii-Piskunov equation \\ Kuramoto-Sivashinsky equation \\ Kawahara equation \\ Regularized long wave equation \\ Extended Bernoulli equation \\ Hyperbolic Liouville equation \\ Sine-Gordon equation \\ Mth-Oder Klein-Gordon equation \\ Boussinesq equation \\ Modified wave equation \\ Appendix: Analytical solution methods for traveling wave problems", } @Book{Hamming:2012:IAN, author = "R. W. (Richard Wesley) Hamming", title = "Introduction to Applied Numerical Analysis", publisher = pub-DOVER, address = pub-DOVER:adr, pages = "x + 331", year = "2012", ISBN = "0-486-48590-0 (paperback)", ISBN-13 = "978-0-486-48590-4 (paperback)", LCCN = "QA297 .H275 2012", bibdate = "Mon Aug 6 08:42:33 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Dover books on mathematics", abstract = "This book is appropriate for an applied numerical analysis course for upper-level undergraduate and graduate students as well as computer science students. Actual programming is not covered, but an extensive range of topics includes round-off and function evaluation, real zeros of a function, integration, ordinary differential equations, optimization, orthogonal functions, Fourier series, and much more.", acknowledgement = ack-nhfb, author-dates = "1915--1998", remark = "Originally published as \cite{Hamming:1989:IAN}.", subject = "Numerical analysis; Data processing", tableofcontents = "Preface \\ 1. Roundoff and Function Evaluation \\ 2. Real Zeros of a Function \\ 3. Complex Zeros \\ 4. Zeros of Polynomials \\ 5. Simultaneous Linear Equations and Matrices \\ 6. Interpolation and Roundoff Estimation \\ 7. Integration \\ 8. Ordinary Differential Equations \\ 9. Optimization \\ 10. Least Squares \\ 11. Orthogonal Functions \\ 12. Fourier Series \\ 13. Chebyshev Approximation \\ 14. Random Processes \\ 15. Design of a Library \\ Index", } @Book{Horn:2012:MA, author = "Roger A. Horn and Charles R. (Charles Royal) Johnson", title = "Matrix Analysis", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, edition = "Second", pages = "xviii + 643", year = "2012", DOI = "https://doi.org/10.1017/CBO9781139020411", ISBN = "0-521-83940-8 (hardcover), 0-521-54823-3 (paperback), 1-283-74139-3, 1-139-77904-4, 1-139-77600-2 (e-book), 1-139-02041-2 (e-book)", ISBN-13 = "978-0-521-83940-2 (hardcover), 978-0-521-54823-6 (paperback), 978-1-283-74139-2, 978-1-139-77904-3, 978-1-139-77600-4 (e-book), 978-1-139-02041-1 (e-book)", LCCN = "QA188 .H66 2012", bibdate = "Thu Nov 20 09:13:05 MST 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/linala2010.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", abstract = "The thoroughly revised and updated second edition of this acclaimed text has several new and expanded sections and more than 1,100 exercises.", acknowledgement = ack-nhfb, subject = "Matrices; MATHEMATICS; Algebra; Abstract; Matrices", tableofcontents = "Frontmatter / i--vi \\ Contents / vii--x \\ Preface to the Second Edition / xi--xiv \\ Preface to the First Edition / xv--xviii \\ 0. Review and Miscellanea / 1--42 \\ 1. Eigenvalues, Eigenvectors, and Similarity / 43--82 \\ 2. Unitary Similarity and Unitary Equivalence / 83--162 \\ 3. Canonical Forms for Similarity and Triangular Factorizations / 163--224 \\ 4. Hermitian Matrices, Symmetric Matrices, and Congruences / 225--312 \\ 5. Norms for Vectors and Matrices / 313--386 \\ 6. Location and Perturbation of Eigenvalues / 387--424 \\ 7. Positive Definite and Semidefinite Matrices / 425--516 \\ 8. Positive and Nonnegative Matrices / 517--554 \\ Appendix A. Complex Numbers / 555--556 \\ Appendix B. Convex Sets and Functions / 557--560 \\ Appendix C. The Fundamental Theorem of Algebra / 561--562 \\ Appendix D. Continuity of Polynomial Zeroes and Matrix Eigenvalues / 563--564 \\ Appendix E. Continuity, Compactness, and Weierstrass's Theorem / 565--566 \\ Appendix F. Canonical Pairs / 567--570 \\ References / 571--574 \\ Notation / 575--578 \\ Hints for Problems / 579--606 \\ Index / 607--643", } @Book{Kharab:2012:INM, author = "Abdelwahab Kharab and Ronald B. Guenther", title = "An introduction to numerical methods: a {MATLAB} approach", publisher = pub-CHAPMAN-HALL-CRC, address = pub-CHAPMAN-HALL-CRC:adr, edition = "Third", pages = "14 + 567", year = "2012", ISBN = "1-4398-6899-9 (hardback), 1-4398-6900-6 (e-book)", ISBN-13 = "978-1-4398-6899-7 (hardback), 978-1-4398-6900-0 (e-book)", LCCN = "QA297 .K52 2012", bibdate = "Fri Nov 16 06:29:40 MST 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "Numerical analysis; Data processing; MATLAB", tableofcontents = "Introduction \\ Number system and errors \\ Roots of equations \\ System of linear equations \\ Interpolation \\ Interpolation with spline functions \\ The method of least-squares \\ Numerical optimization \\ Numerical differentiation \\ Numerical integration \\ Numerical methods for linear integral equations \\ Numerical methods for differential equations \\ Boundary-value problems \\ Eigenvalues and eigenvectors \\ Partial differential equations", } @Book{Kugler:2012:AMB, author = "Philipp K{\"u}gler and Wolfgang Windsteiger", title = "Algorithmische {Methoden}. {Band} 2", publisher = "Birkh{\"a}user/Springer Basel AG, Basel", pages = "viii + 159", year = "2012", DOI = "https://doi.org/10.1007/978-3-7643-8516-3", ISBN = "3-7643-8515-4; 3-7643-8516-2", ISBN-13 = "978-3-7643-8515-6; 978-3-7643-8516-3", MRclass = "65-01 (68-01)", MRnumber = "3086486", bibdate = "Tue May 27 11:24:21 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib", note = "Funktionen, Matrizen, multivariate Polynome. [Functions, matrices, multivariate polynomials]", series = "Mathematik Kompakt. [Compact Mathematics]", acknowledgement = ack-nhfb, } @Book{Langtangen:2012:PSP, author = "Hans Petter Langtangen", title = "A primer on scientific programming with {Python}", volume = "6", publisher = pub-SV, address = pub-SV:adr, edition = "Third", year = "2012", DOI = "https://doi.org/10.1007/978-3-642-30293-0", ISBN = "3-642-30292-0, 3-642-30293-9 (e-book)", ISBN-13 = "978-3-642-30292-3, 978-3-642-30293-0 (e-book)", ISSN = "1611-0994", LCCN = "QA76.73.P98 L36 2012", bibdate = "Fri Nov 29 07:00:01 MST 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/python.bib", series = "Texts in computational science and engineering", URL = "http://site.ebrary.com/id/10650410", abstract = "The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example- and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology, and finance. The book teaches ``Matlab-style'' and procedural programming as well as object-oriented programming. High school mathematics is a required background, and it is advantageous to study classical and numerical one-variable calculus in parallel with reading this book. Besides learning how to program computers.", acknowledgement = ack-nhfb, subject = "Python (Computer program language); Computer programming; Science; Data processing", tableofcontents = "Computing with Formulas \\ Loops and Lists \\ Functions and Branching \\ Input Data and Error Handling \\ Array Computing and Curve Plotting \\ Files, Strings, and Dictionaries \\ Introduction to Classes \\ Random Numbers and Simple Games \\ Object-Oriented Programming", } @Book{Laub:2012:CMA, author = "Alan J. Laub", title = "Computational matrix analysis", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xiii + 154", year = "2012", ISBN = "1-61197-220-5 (paperback), 1-61197-221-3 (e-book)", ISBN-13 = "978-1-61197-220-7 (paperback), 978-1-61197-221-4 (e-book)", LCCN = "QA274.2 .L38 2012", MRclass = "65-01 (65Fxx)", MRnumber = "2934576", MRreviewer = "Petko Petkov", bibdate = "Tue May 27 12:02:28 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Other titles in applied mathematics", URL = "http://www.loc.gov/catdir/enhancements/fy1211/2011050702-b.html; http://www.loc.gov/catdir/enhancements/fy1211/2011050702-d.html; http://www.loc.gov/catdir/enhancements/fy1211/2011050702-t.html", acknowledgement = ack-nhfb, subject = "Matrix analytic methods; Data processing", } @Book{Layton:2012:ADM, author = "William J. Layton and Leo G. Rebholz", title = "Approximate Deconvolution Models of Turbulence: Analysis, Phenomenology and Numerical Analysis", volume = "2042", publisher = pub-SV, address = pub-SV:adr, pages = "viii + 184", year = "2012", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/978-3-642-24409-4", ISBN = "3-642-24408-4 (print), 3-642-24409-2 (e-book)", ISBN-13 = "978-3-642-24408-7 (print), 978-3-642-24409-4 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", LCCN = "QA3 .L28 no. 2042", MRclass = "76-02 (76D03 76D05 76F65)", MRnumber = "2934085", MRreviewer = "Peter Bernard Weichman", bibdate = "Tue May 6 14:56:41 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/lnm2010.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = ser-LECT-NOTES-MATH, URL = "http://link.springer.com/book/10.1007/978-3-642-24409-4; http://www.springerlink.com/content/978-3-642-24409-4", acknowledgement = ack-nhfb, series-URL = "http://link.springer.com/bookseries/304", } @Book{Molitierno:2012:ACM, author = "Jason J. Molitierno", title = "Applications of combinatorial matrix theory to {Laplacian} matrices of graphs", publisher = pub-CRC, address = pub-CRC:adr, pages = "405", year = "2012", ISBN = "1-4398-6337-7 (hardcover)", ISBN-13 = "978-1-4398-6337-4 (hardcover)", LCCN = "QA166.243 .M65 2012", bibdate = "Tue May 5 16:13:52 MDT 2015", bibsource = "http://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Discrete mathematics and its applications", abstract = "On the surface, matrix theory and graph theory are seemingly very different branches of mathematics. However, these two branches of mathematics interact since it is often convenient to represent a graph as a matrix. Adjacency, Laplacian, and incidence matrices are commonly used to represent graphs. In 1973, Fiedler published his first paper on Laplacian matrices of graphs and showed how many properties of the Laplacian matrix, especially the eigenvalues, can give us useful information about the structure of the graph. Since then, many papers have been published on Laplacian matrices. This book is a compilation of many of the exciting results concerning Laplacian matrices that have been developed since the mid 1970's. Papers written by well-known mathematicians such as (alphabetically) Fallat, Fiedler, Grone, Kirkland, Merris, Mohar, Neumann, Shader, Sunder, and several others are consolidated here. Each theorem is referenced to its appropriate paper so that the reader can easily do more in-depth research on any topic of interest. However, the style of presentation in this book is not meant to be that of a journal but rather a reference textbook. Therefore, more examples and more detailed calculations are presented in this book than would be in a journal article. Additionally, most sections are followed by exercises to aid the reader in gaining a deeper understanding of the material. Some exercises are routine calculations that involve applying the theorems presented in the section. Other exercises require a more in-depth analysis of the theorems and require the reader to prove theorems that go beyond what was presented in the section. Many of these exercises are taken from relevant papers and they are referenced accordingly.", acknowledgement = ack-nhfb, subject = "Graph connectivity; Laplacian matrices; COMPUTERS / Operating Systems / General.; COMPUTERS / Programming / Algorithms.; MATHEMATICS / Combinatorics.", } @Book{Pont:2012:DDW, author = "Jean-Claude Pont and Christophe Rossel", title = "Le destin douloureux de {Walther Ritz} (1878--1909), physicien th{\'e}oricien de g{\'e}nie", volume = "24", publisher = "Archives de l'{\'e}tat du Valais", address = "Vallesia, France", pages = "264 + 41", year = "2012", ISBN = "2-9700636-5-4 (hardcover)", ISBN-13 = "978-2-9700636-5-0 (hardcover)", LCCN = "????", bibdate = "Mon Apr 21 12:49:54 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/histmath.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Cahiers de Vallesia", acknowledgement = ack-nhfb, author-dates = "(1941--\ldots{}.).", remark = "Contributions en fran{\c{c}}ais et en anglais.", subject = "Ritz, Walther; Biographies.; Physique math{\'e}matique; Histoire.; Sciences", subject-dates = "(1878--1909)", tableofcontents = "Aspects de la vie et de l'oeuvre de Walther Ritz, physicien th{\'e}oricien valaisan / Jean-Claude Pont \\ Walther Ritz et ses correspondants / Jean-Claude Pont \\ Walther Ritz, quelques dates / Jean-Claude Pont \\ Sion au temps de Walther Ritz / Patrice Tschopp \\ Ritz face {\`a} la physique de son temps / Jan Lacki \\ Walther Ritz exp{\'e}rimentateur / Nicolas Produit \\ Walther Ritz's theoretical work in spectroscopy, focussing on series formulas / Klaus Hentschel \\ From Euler, Ritz and Galerkin to modern computing / Martin J. Gander and Gerhard Wanner \\ Electrodynamics in the physics of Walther Ritz / Olivier Darrigol \\ Manifestations {\`a} l'occasion du centenaire de la mort de Walther Ritz, Sion, 17--19 septembre 2009 \\ Bibliographie des {\'e}crits de Walther Ritz / Jean-Claude Pont and Nicolas Produit", } @Book{Rebaza:2012:FCA, author = "Jorge Rebaza", title = "A first course in applied mathematics", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xvi + 439", year = "2012", ISBN = "1-118-22962-2", ISBN-13 = "978-1-118-22962-0", LCCN = "TA342 .R43 2012", bibdate = "Tue May 5 16:13:00 MDT 2015", bibsource = "http://www.math.utah.edu/pub/tex/bib/datacompression.bib; http://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/enhancements/fy1201/2011043340-d.html; http://www.loc.gov/catdir/enhancements/fy1201/2011043340-t.html; http://www.loc.gov/catdir/enhancements/fy1210/2011043340-b.html", abstract = "This book details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world problems. Due to the broad range of applications, mathematical concepts and techniques and reviewed throughout, especially those in linear algebra, matrix analysis, and differential equations. Some classical definitions and results from analysis are also discussed and used. Some applications (postscript fonts, information retrieval, etc.) are presented at the end of a chapter as an immediate application of the theory just covered, while those applications that are discussed in more detail (ranking web pages, compression, etc.) are presented in dedicated chapters. A collection of mathematical models of a slightly different nature, such as basic discrete mathematics and optimization, is also provided. Clear proofs of the main theorems ultimately help to make the statements of the theorems more understandable, and a multitude of examples follow important theorems and concepts. In addition, the author builds material from scratch and thoroughly covers the theory needed to explain the applications in full detail, while not overwhelming readers with unnecessary topics or discussions. In terms of exercises, the author continuously refers to the real numbers and results in calculus when introducing a new topic so readers can grasp the concept of the otherwise intimidating expressions. By doing this, the author is able to focus on the concepts rather than the rigor. The quality, quantity, and varying level of difficulty of the exercises provides instructors more classroom flexibility. Topical coverage includes linear algebra; ranking web pages; matrix factorizations; least squares; image compression; ordinary differential equations; dynamical systems; and mathematical models.", acknowledgement = ack-nhfb, author-dates = "1962--", subject = "Mathematical models; Computer simulation; Mathematics / Applied", tableofcontents = "Preface / xi \\ 1. Basics of Linear Algebra / 1 \\ 1.1 Notation and Terminology / 1 \\ 1.2 Vector and Matrix Norms / 4 \\ 1.3 Dot Product and Orthogonality / 8 \\ 1.4 Special Matrices / 9 \\ 1.5 Vector Spaces / 21 \\ 1.6 Linear Independence and Basis / 24 \\ 1.7 Orthogonalization and Direct Sums / 30 \\ 1.8 Column Space, Row Space and Null Space / 34 \\ 1.9 Orthogonal Projections / 43 \\ 1.10 Eigenvalues and Eigenvectors / 47 \\ 1.11 Similarity / 56 \\ 1.12 Bezier Curves Postscripts Fonts / 59 \\ 1.13 Final Remarks and Further Reading / 68 \\ 2. Ranking Web Pages / 79 \\ 2.1 The Power Method / 80 \\ 2.2 Stochastic, Irreducible and Primitive Matrices / 84 \\ 2.3 Google's PageRank Algorithm / 92 \\ 2.4 Alternatives to Power Method / 106 \\ 2.5 Final Remarks and Further Reading / 120 \\ 3. Matrix Factorizations / 131 \\ 3.1 LU Factorization / 132 \\ 3.2 QR Factorization / 142 \\ 3.3 Singular Value Decomposition (SVD) / 155 \\ 3.4 Schur Factorization / 166 \\ 3.5 Information Retrieval / 186 \\ 3.6 Partition of Simple Substitution Cryptograms / 194 \\ 3.7 Final Remarks and Further Reading / 203 \\ 4. Least Squares / 215 \\ 4.1 Projections and Normal Equations / 215 \\ 4.2 Least Squares and QR Factorization / 224 \\ 4.3 Lagrange Multipliers / 228 \\ 4.4 Final Remarks and Further Reading / 231 \\ 5. Image Compression / 235 \\ 5.1 Compressing with Discrete Cosine Transform / 236 \\ 5.2 Huffman Coding / 260 \\ 5.3 Compression with SVD / 267 \\ 5.4 Final Remarks and Further Reading / 271 \\ 6. Ordinary Differential Equations / 277 \\ 6.1 One-Dimensional Differential Equations / 278 \\ 6.2 Linear Systems of Differential Equations / 307 \\ 6.3 Solutions via Eigenvalues and Eigenvectors / 308 \\ 6.4 Fundamentals Matrix Solution / 312 \\ 6.5 Final Remarks and Further Reading / 316 \\ 7. Dynamical Systems / 325 \\ 7.1 Linear Dynamical Systems / 326 \\ 7.2 Nonlinear Dynamical Systems / 340 \\ 7.3 Predator--Prey Models with Harvesting / 374 \\ 7.4 Final Remarks and Further Reading / 385 \\ 8. Mathematical Models / 395 \\ 8.1 Optimization of a Waste Management System / 396 \\ 8.2 Grouping Problem in Networks / 404 \\ 8.3 American Cutaneous Leishmaniasis / 410 \\ 8.4 Variable Population Interactions / 420 \\ References / 431 \\ Index / 435", } @Book{Rizopoulos:2012:JML, author = "Dimitris Rizopoulos", title = "Joint models for longitudinal and time-to-event data: with applications in {R}", volume = "6", publisher = pub-CRC, address = pub-CRC:adr, pages = "xiv + 261", year = "2012", ISBN = "1-4398-7286-4 (hardcover)", ISBN-13 = "978-1-4398-7286-4 (hardcover)", LCCN = "QA279 .R59 2012", bibdate = "Thu Jul 21 05:59:33 MDT 2016", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/s-plus.bib; z3950.loc.gov:7090/Voyager", series = "Chapman and Hall/CRC biostatistics series", abstract = "Joint models for longitudinal and time-to-event data have become a valuable tool in the analysis of follow-up data. These models are applicable mainly in two settings: First, when focus is in the survival outcome and we wish to account for the effect of an endogenous time-dependent covariate measured with error, and second, when focus is in the longitudinal outcome and we wish to correct for nonrandom dropout. Due to their capability to provide valid inferences in settings where simpler statistical tools fail to do so, and their wide range of applications, the last 25 years have seen many advances in the joint modeling field. Even though interest and developments in joint models have been widespread, information about them has been equally scattered in articles, presenting recent advances in the field, and in book chapters in a few texts dedicated either to longitudinal or survival data analysis. However, no single monograph or text dedicated to this type of models seems to be available. The purpose in writing this book, therefore, is to provide an overview of the theory and application of joint models for longitudinal and survival data. In the literature two main frameworks have been proposed, namely the random effects joint model that uses latent variables to capture the associations between the two outcomes (Tsiatis and Davidian, 2004), and the marginal structural joint models based on G estimators (Robins et al., 1999, 2000). In this book we focus in the former. Both subfields of joint modeling, i.e., handling of endogenous time-varying covariates and nonrandom dropout, are equally covered and presented in real datasets.", acknowledgement = ack-nhfb, shorttableofcontents = "1. Introduction \\ 2. Longitudinal data analysis \\ 3. Analysis of event time data \\ 4. Joint models for longitudinal and time-to-event data \\ 5. Extensions of the standard joint model \\ 6. Joint model diagnostics \\ 7. Prediction and accuracy in joint models", subject = "Numerical analysis; Data processing; R (Computer program language); MATHEMATICS / Probability and Statistics / General; MEDICAL / Epidemiology", tableofcontents = "Preface \\ 1: Introduction \\ 1.1: Goals \\ 1.2: Motivating Studies \\ 1.2.1: Primary Biliary Cirrhosis Data \\ 1.2.2: AIDS Data \\ 1.2.3: Liver Cirrhosis Data \\ 1.2.4: Aortic Valve Data \\ 1.2.5: Other Applications \\ 1.3: Inferential Objectives in Longitudinal Studies \\ 1.3.1: Effect of Covariates on a Single Outcome \\ 1.3.2: Association between Outcomes \\ 1.3.3: Complex Hypothesis Testing \\ 1.3.4: Prediction \\ 1.3.5: Statistical Analysis with Implicit Outcomes \\ 1.4: Overview \\ 2: Longitudinal Data Analysis \\ 2.1: Features of Longitudinal Data \\ 2.2: Linear Mixed-Effects Models \\ 2.2.1: Estimation \\ 2.2.2: Implementation in R \\ 2.3: Missing Data in Longitudinal Studies \\ 2.3.1: Missing Data Mechanisms \\ 2.3.2: Missing Not at Random Model Families \\ 2.4: Further Reading \\ 3: Analysis of Event Time Data \\ 3.1: Features of Event Time Data \\ 3.2: Basic Functions in Survival Analysis \\ 3.2.1: Likelihood Construction for Censored Data \\ 3.3: Relative Risk Regression Models \\ 3.3.1: Implementation in R \\ 3.4: Time-Dependent Covariates \\ 3.5: Extended Cox Model \\ 3.6: Further Reading \\ 4: Joint Models for Longitudinal and Time-to-Event Data \\ 4.1: The Basic Joint Model \\ 4.1.1: The Survival Submodel \\ 4.1.2: The Longitudinal Submodel \\ 4.2: Joint Modeling in R: A Comparison with the Extended Cox Model \\ 4.3: Estimation of Joint Models \\ 4.3.1: Two-Stage Approaches \\ 4.3.2: Joint Likelihood Formulation \\ 4.3.3: Standard Errors with an Unspecified Baseline Risk Function \\ 4.3.4: Optimization Control in JM \\ 4.3.5: Numerical Integration \\ 4.3.6: Numerical Integration Control in JM \\ 4.3.7: Convergence Problems \\ 4.4: Asymptotic Inference for Joint Models \\ 4.4.1: Hypothesis Testing \\ 4.4.2: Confidence Intervals \\ 4.4.3: Design Considerations \\ 4.5: Estimation of the Random Effects \\ 4.6: Connection with the Missing Data Framework \\ 4.7: Sensitivity Analysis under Joint Models \\ 5: Extensions of the Standard Joint Model \\ 5.1: Parameterizations \\ 5.1.1: Interaction Effects \\ 5.1.2: Lagged Effects \\ 5.1.3: Time-Dependent Slopes Parameterization \\ 5.1.4: Cumulative Effects Parameterization \\ 5.1.5: Random-Effects Parameterization \\ 5.2: Handling Exogenous Time-Dependent Covariates \\ 5.3: Stratified Relative Risk Models \\ 5.4: Latent Class Joint Models \\ 5.5: Multiple Failure Times \\ 5.5.1: Competing Risks \\ 5.5.2: Recurrent Events \\ 5.6: Accelerated Failure Time Models \\ 5.7: Joint Models for Categorical Longitudinal Outcomes \\ 5.7.1: The Generalized Linear Mixed Model (GLMM) \\ 5.7.2: Combining Discrete Repeated Measures with Survival \\ 5.8: Joint Models for Multiple Longitudinal Outcomes \\ 6: Joint Model Diagnostics \\ 6.1: Residuals for Joint Models \\ 6.1.1: Residuals for the Longitudinal Part \\ 6.1.2: Residuals for the Survival Part \\ 6.2: Dropout and Residuals \\ 6.3: Multiple Imputation Residuals \\ 6.3.1: Fixed Visit Times \\ 6.3.2: Random Visit Times \\ 6.4: Random-Effects Distribution \\ 7: Prediction and Accuracy in Joint Models \\ 7.1: Dynamic Predictions of Survival Probabilities \\ 7.1.1: Definition \\ 7.1.2: Estimation \\ 7.1.3: Implementation in R \\ 7.2: Dynamic Predictions for the Longitudinal Outcome \\ 7.3: Effect of Parameterization on Predictions \\ 7.4: Prospective Accuracy for Joint Models \\ 7.4.1: Discrimination Measures for Binary Outcomes \\ 7.4.2: Discrimination Measures for Survival Outcomes \\ 7.4.3: Prediction Rules for Longitudinal Markers \\ 7.4.4: Discrimination Indices \\ 7.4.5: Estimation under the Joint Modeling Framework \\ 7.4.6: Implementation in R \\ A: A Brief Introduction to R \\ A.1: Obtaining and Installing R and R Packages \\ A.2: Simple Manipulations \\ A.2.1: Basic R Objects \\ A.2.2: Indexing \\ A.3: Import and Manipulate Data Frames \\ A.4: The Formula Interface \\ B: The EM Algorithm for Joint Models \\ B.1: A Short Description of the EM Algorithm \\ B.2: The E-step for Joint Models \\ B.3: The M-step for Joint Models \\ C: Structure of the JM Package \\ C.1: Methods for Standard Generic Functions \\ C.2: Additional Functions \\ References \\ Index", } @Book{Shapira:2012:SPC, author = "Yair Shapira", title = "Solving {PDEs} in {C++}: numerical methods in a unified object-oriented approach", publisher = pub-SIAM, address = pub-SIAM:adr, edition = "Second", pages = "xxxii + 776", year = "2012", DOI = "https://doi.org/10.1137/9781611972177", ISBN = "1-61197-216-7 (paperback)", ISBN-13 = "978-1-61197-216-0 (paperback)", LCCN = "QA377 .S466 2012", bibdate = "Thu Aug 28 08:20:59 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Computational science and engineering series", acknowledgement = ack-nhfb, author-dates = "1960--", subject = "Differential equations, Partial; C++ (Computer program language); Object-oriented programming (Computer science)", tableofcontents = "Part I. Elementary background in programming \\ 1. Concise introduction to C \\ 2. Concise introduction to C++ \\ 3. Data structures used in the present algorithms \\ Part II. Object-oriented programming \\ 4. From Wittgenstein--Lacan's theory to the object-oriented implementation of graphs and matrices \\ 5. FFT and other algorithms in numerics and cryptography \\ 6. Object-oriented analysis of nonlinear ordinary differential equations \\ Part III. Partial differential equations and their discretization \\ 7. The convection--diffusion equation \\ 8. Some stability analysis \\ 9. About nonlinear conservation laws \\ 10. Application in image processing \\ Part IV. Finite elements \\ 11. About the weak formulation \\ 12. Some background in linear finite elements \\ 13. Unstructured finite-element meshes \\ 14. Adaptive mesh refinement \\ 15. Towards high-order finite elements\\ Part V. The numerical solution of large sparse linear systems of algebraic equations \\ 16. Sparse matrices and their object-oriented implementation \\ 17. Iterative methods for the numerical solution of large sparse linear systems of algebraic equations \\ 18. Towards parallelism\\ Part VI. Applications in two spatial dimensions \\ 19. Diffusion equations \\ 20. The linear elasticity equations \\ 21. The Stokes equations \\ 22. Application in electromagnetic waves \\ 23. Multigrid for nonlinear equations and for the fusion problem in image processing \\ Part VII. Applications in three spatial dimensions \\ 24. Polynomials in three independent variables \\ 25. The Helmholtz equation : error estimate \\ 26. Adaptive finite elements in three spatial dimensions \\ 27. Application in nonlinear optics : the nonlinear Helmholtz equation in three spatial dimensions \\ 28. High-order finite elements in three spatial dimensions \\ 29. Application in the nonlinear Maxwell equations \\ 30. Towards inverse problems \\ 31. Application in the Navier--Stokes equations \\ Appendix A. Solutions to selected exercises \\ Bibliography \\ Index", } @Book{Sirca:2012:CMP, author = "Simon {\v{S}}irca and Martin Horvat", title = "Computational methods for physicists", publisher = pub-SV, address = pub-SV:adr, pages = "xx + 715", year = "2012", DOI = "https://doi.org/10.1007/978-3-642-32478-9", ISBN = "3-642-32477-0; 3-642-32478-9", ISBN-13 = "978-3-642-32477-2; 978-3-642-32478-9", MRclass = "65-01", MRnumber = "3013260", bibdate = "Tue May 27 11:24:21 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib", note = "Compendium for students", series = "Graduate Texts in Physics", acknowledgement = ack-nhfb, } @Book{Soetaert:2012:SDE, author = "Karline Soetaert and Jeff Cash and Francesca Mazzia", title = "Solving differential equations in {R}", publisher = pub-SV, address = pub-SV:adr, pages = "xvi + 248", year = "2012", DOI = "https://doi.org/10.1007/978-3-642-28070-2", ISBN = "3-642-28069-2 (hardcover), 3-642-28070-6 (e-book)", ISBN-13 = "978-3-642-28069-6 (hardcover), 978-3-642-28070-2 (e-book)", LCCN = "QA371.5.D37 S64 2012", MRclass = "68N15 65Lxx", bibdate = "Tue Mar 13 16:56:48 MDT 2018", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/s-plus.bib; z3950.loc.gov:7090/Voyager", series = "Use R!", abstract = "Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.", acknowledgement = ack-nhfb, subject = "Statistics; Computer simulation; Differential equations; Differential equations, Partial; Computer science; Mathematics; Mathematical statistics; Statistics and Computing/Statistics Programs; Ordinary Differential Equations; Partial Differential Equations; Computational Mathematics and Numerical Analysis; Simulation and Modeling; Mathematics.; Computer simulation.; Differential equations.; Differential equations, Partial.; Mathematical statistics.; Statistics.", tableofcontents = "1 Differential Equations / 1 \\ 1.1 Basic Theory of Ordinary Differential Equations / 1 \\ 1.1.1 First Order Differential Equations / 1 \\ 1.1.2 Analytic and Numerical Solutions / 2 \\ 1.1.3 Higher Order Ordinary Differential Equations / 3 \\ 1.1.4 Initial and Boundary Values / 4 \\ 1.1.5 Existence and Uniqueness of Analytic Solutions / 5 \\ 1.2 Numerical Methods / 6 \\ 1.2.1 The Euler Method / 6 \\ 1.2.2 Implicit Methods / 7 \\ 1.2.3 Accuracy and Convergence of Numerical Methods / 8 \\ 1.2.4 Stability and Conditioning / 9 \\ 1.3 Other Types of Differential Equations / 11 \\ 1.3.1 Partial Differential Equations / 11 \\ 1.3.2 Differential Algebraic Equations / 12 \\ 1.3.3 Delay Differential Equations / 13 \\ References / 13 \\ 2 Initial Value Problems / 15 \\ 2.1 Runge--Kutta Methods / 15 \\ 2.1.1 Explicit Runge--Kutta Formulae / 15 \\ 2.1.2 Deriving a Runge--Kutta Formula / 17 \\ 2.1.3 Implicit Runge--Kutta Formulae / 22 \\ 2.2 Linear Multistep methods / 22 \\ 2.2.1 Convergence, Stability and Consistency / 23 \\ 2.2.2 Adams Methods / 25 \\ 2.2.3 Backward Differentiation Formulae / 27 \\ 2.2.4 Variable Order--Variable Coefficient Formulae for Linear Multistep Methods / 29 \\ 2.3 Boundary Value Methods / 30 \\ 2.4 Modified Extended Backward Differentiation Formulae / 31 \\ 2.5 Stiff Problems / 32 \\ 2.5.1 Stiffness Detection / 33 \\ 2.5.2 Non-stiffness Test / 34 \\ 2.6 Implementing Implicit Methods / 34 \\ 2.6.1 Fixed-Point Iteration to Convergence / 34 \\ 2.6.2 Chord Iteration / 35 \\ 2.6.3 Predictor--Corrector Methods / 36 \\ 2.6.4 Newton Iteration for Implicit Runge--Kutta Methods / 36 \\ 2.7 Codes to Solve Initial Value Problems / 37 \\ 2.7.1 Codes to Solve Non-stiff Problems / 38 \\ 2.7.2 Codes to Solve Stiff Problems / 38 \\ 2.7.3 Codes that Switch Between Stiff and Non-stiff Solvers / 38 \\ References / 39 \\ 3 Solving Ordinary Differential Equations in R / 41 \\ 3.1 Implementing Initial Value Problems in R / 41 \\ 3.1.1 A Differential Equation Comprising One Variable / 42 \\ 3.1.2 Multiple Variables: The Lorenz Model / 44 \\ 3.2 Runge--Kutta Methods / 45 \\ 3.2.1 Rigid Body Equations / 47 \\ 3.2.2 Arenstorf Orbits / 49 \\ 3.3 Linear Multistep Methods / 51 \\ 3.3.1 Seven Moving Stars / 52 \\ 3.3.2 A Stiff Chemical Example / 56 \\ 3.4 Discontinuous Equations, Events / 59 \\ 3.4.1 Pharmacokinetic Models / 60 \\ 3.4.2 A Bouncing Ball / 64 \\ 3.4.3 Temperature in a Climate-Controlled Room / 66 \\ 3.5 Method Selection / 68 \\ 3.5.1 The van der Pol Equation / 70 \\ 3.6 Exercises / 75 \\ 3.6.1 Getting Started with IVP / 75 \\ 3.6.2 The Robertson Problem / 76 \\ 3.6.3 Displaying Results in a Phase-Plane Graph / 76 \\ 3.6.4 Events and Roots / 78 \\ 3.6.5 Stiff Problems / 79 \\ References / 79 \\ 4 Differential Algebraic Equations / 81 \\ 4.1 Introduction / 81 \\ 4.1.1 The Index of a DAE / 82 \\ 4.1.2 A Simple Example / 83 \\ 4.1.3 DAEs in Hessenberg Form / 84 \\ 4.1.4 Hidden Constraints and the Initial Conditions / 85 \\ 4.1.5 The Pendulum Problem / 86 \\ 4.2 Solving DAEs / 87 \\ 4.2.1 Semi-implicit DAEs of Index 1 / 87 \\ 4.2.2 General Implicit DAEs of Index 1 / 88 \\ 4.2.3 Discretization Algorithms / 89 \\ 4.2.4 DAEs of Higher Index / 90 \\ 4.2.5 Index of a DAE Variable / 93 \\ References / 94 \\ 5 Solving Differential Algebraic Equations in R / 95 \\ 5.1 Differential Algebraic Equation Solvers in R / 95 \\ 5.2 A Simple DAE of Index 2 / 96 \\ 5.2.1 Solving the DAEs in General Implicit Form / 97 \\ 5.2.2 Solving the DAEs in Linearly Implicit Form / 98 \\ 5.3 A Nonlinear Implicit ODE / 98 \\ 5.4 A DAE of Index 3: The Pendulum Problem / 100 \\ 5.5 Multibody Systems / 101 \\ 5.5.1 The Car Axis Problem / 102 \\ 5.6 Electrical Circuit Models / 106 \\ 5.6.1 The Transistor Amplifier / 107 \\ 5.7 Exercises / 111 \\ 5.7.1 A Simple DAE / 111 \\ 5.7.2 The Robertson Problem / 111 \\ 5.7.3 The Pendulum Problem Revisited / 111 \\ 5.7.4 The Akzo Nobel Problem / 112 \\ References / 115 \\ 6 Delay Differential Equations / 117 \\ 6.1 Delay Differential Equations / 117 \\ 6.1.1 DDEs with Delays of the Dependent Variables / 118 \\ 6.1.2 DDEs with Delays of the Derivatives / 118 \\ 6.2 Difficulties when Solving DDEs / 119 \\ 6.2.1 Discontinuities in DDEs / 119 \\ 6.2.2 Small and Vanishing Delays / 120 \\ 6.3 Numerical Methods for Solving DDEs / 121 \\ References / 121 \\ 7 Solving Delay Differential Equations in R / 123 \\ ,7.1 Delay Differential Equation Solvers in R / 123 \\ 7.2 Two Simple Examples / 124 \\ 7.2.1 DDEs Involving Solution Delay Terms / 124 \\ 7.2.2 DDEs Involving Derivative Delay Terms / 124 \\ 7.3 Chaotic Production of White Blood Cells / 125 \\ 7.4 A DDE Involving a Root Function / 127 \\ 7.5 Vanishing Time Delays / 128 \\ 7.6 Predator--Prey Dynamics with Harvesting / 130 \\ 7.7 Exercises / 132 \\ 7.7.1 The Lemming Model / 132 \\ 7.7.2 Oberle and Pesch / 132 \\ 7.7.3 An Epidemiological Model / 133 \\ 7.7.4 A Neutral DDE / 134 \\ 7.7.5 Delayed Cellular Neural Networks With Impulses / 134 \\ References / 135 \\ 8 Partial Differential Equations / 137 \\ 8.1 Partial Differential Equations / 137 \\ 8.1.1 Alternative Formulations / 138 \\ 8.1.2 Polar, Cylindrical and Spherical Coordinates / 140 \\ 8.1.3 Boundary Conditions / 141 \\ 8.2 Solving PDEs / 142 \\ 8.3 Discretising Derivatives / 143 \\ 8.3.1 Basic Diffusion Schemes / 144 \\ 8.3.2 Basic Advection Schemes / 145 \\ 8.3.3 Flux-Conservative Discretisations / 147 \\ 8.3.4 More Complex Advection Schemes / 148 \\ 8.4 The Method Of Lines / 152 \\ 8.5 The Finite Difference Method / 153 \\ References / 153 \\ 9 Solving Partial Differential Equations in R / 157 \\ 9.1 Methods for Solving PDEs in R / 157 \\ 9.1.1 Numerical Approximations / 157 \\ 9.1.2 Solution Methods / 159 \\ 9.2 Solving Parabolic, Elliptic and Hyperbolic PDEs in R / 160 \\ 9.2.1 The Heat Equation / 160 \\ 9.2.2 The Wave Equation / 163 \\ 9.2.3 Poisson and Laplace's Equation / 166 \\ 9.2.4 The Advection Equation / 168 \\ 9.3 More Complex Examples / 170 \\ 9.3.1 The Brusselator in One Dimension / 170 \\ 9.3.2 The Brusselator in Two Dimensions / 173 \\ 9.3.3 Laplace Equation in Polar Coordinates / 174 \\ 9.3.4 The Time-Dependent 2-D Sine-Gordon Equation / 176 \\ 9.3.5 The Nonlinear Schr{\"o}dinger Equation / 179 \\ 9.4 Exercises / 181 \\ 9.4.1 The Gray--Scott Equation / 181 \\ 9.4.2 A Macroscopic Model of Traffic / 182 \\ 9.4.3 A Vibrating String / 183 \\ 9.4.4 A Pebble in a Bucket of Water / 184 \\ 9.4.5 Combustion in 2-D / 184 \\ References / 185 \\ 10 Boundary Value Problems / 187 \\ 10.1 Two-Point Boundary Value Problems / 187 \\ 10.2 Characteristics of Boundary Value Problems / 188 \\ 10.2.1 Uniqueness of Solutions / 188 \\ 10.2.2 Isolation of Solutions / 189 \\ 10.2.3 Stiffness of Boundary Value Problems and Dichotomy / 189 \\ 10.2.4 Conditioning of Boundary Value Problems / 190 \\ 10.2.5 Singular Problems / 191 \\ 10.3 Boundary Conditions / 192 \\ 10.3.1 Separated Boundary Conditions / 192 \\ 10.3.2 Defining Good Boundary Conditions / 193 \\ 10.3.3 Problems Defined on an Infinite Interval / 193 \\ 10.4 Methods of Solution / 194 \\ 10.5 Shooting Methods for Two-Point BVPs / 194 \\ 10.5.1 The Linear Case / 194 \\ 10.5.2 The Nonlinear Case / 195 \\ 10.5.3 Multiple Shooting / 196 \\ 10.6 Finite Difference Methods / 197 \\ 10.6.1 A Low Order Method for Second Order Equations / 197 \\ 10.6.2 Other Low Order Methods / 198 \\ 10.6.3 Higher Order Methods Based on Collocation Runge--Kutta Schemes / 199 \\ 10.6.4 Higher Order Methods Based on Mono Implicit Runge--Kutta Formulae / 200 \\ 10.6.5 Higher Order Methods Based on Linear Multistep Formulae / 201 \\ 10.6.6 Deferred Correction / 202 \\ 10.7 Codes for the Numerical Solution of Boundary Value Problems / 203 \\ References / 203 \\ 11 Solving Boundary Value Problems in R / 207 \\ 11.1 Boundary Value Problem Solvers in R / 207 \\ 11.2 A Simple BVP Example / 208 \\ 11.2.1 Implementing the BVP in First Order Form / 208 \\ 11.2.2 Implementing the BVP in Second Order Form / 209 \\ 11.3 A More Complex BVP Example / 210 \\ 11.4 More Complex Initial or End Conditions / 214 \\ 11.5 Solving a Boundary Value Problem Using Continuation / 216 \\ 11.5.1 Manual Continuation / 216 \\ 11.5.2 Automatic Continuation / 219 \\ 11.6 BVPs with Unknown Constants / 220 \\ 11.6.1 The Elastica Problem / 221 \\ 11.6.2 Non-separated Boundary Conditions / 222 \\ 11.6.3 An Unknown Integration Interval / 225 \\ 11.7 Integral Constraints / 228 \\ 11.8 Sturm--Liouville Problems / 229 \\ 11.9 A Reaction Transport Problem / 230 \\ 11.10 Exercises / 233 \\ 11.10.1 A Stiff Boundary Value Problem / 233 \\ 11.10.2 The Mathieu Equation / 234 \\ 11.10.3 Another Swirling Flow Problem / 234 \\ 11.10.4 Another Reaction Transport Problem / 236 \\ References / 237 \\ A Appendix / 239 \\ A. 1 Butcher Tableaux for Some Runge--Kutta Methods : / 239 \\ A.2 Coefficients for Some Linear Multistep Formulae / 239 \\ A.3 Implemented Integration Methods for Solving Initial Value Problems in R / 241 \\ A.4 Other Integration Methods in R / 242 \\ References / 242 \\ Index / 245", } @Book{Wulf:2012:CVR, author = "Andrea Wulf", title = "Chasing {Venus}: the race to measure the heavens", publisher = pub-KNOPF, address = pub-KNOPF:adr, pages = "xxvi + 304", year = "2012", ISBN = "0-307-70017-8 (hardcover), 0-307-95861-2 (e-book)", ISBN-13 = "978-0-307-70017-9 (hardcover), 978-0-307-95861-7 (e-book)", LCCN = "QB205.A2 W85 2012", bibdate = "Mon Jun 18 14:33:26 MDT 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", abstract = "The author of the highly acclaimed Founding Gardeners now gives us an enlightening chronicle of the first truly international scientific endeavor --- the eighteenth-century quest to observe the transit of Venus and measure the solar system. On June 6, 1761, the world paused to observe a momentous occasion: the first transit of Venus between the earth and the sun in more than a century. Through that observation, astronomers could calculate the size of the solar system --- but only if the transit could be viewed at the same time from many locations. Overcoming incredible odds and political strife, astronomers from Britain, France, Russia, Germany, Sweden, and the American colonies set up observatories in remote corners of the world only to have their efforts thwarted by unpredictable weather and warring armies. Fortunately, transits of Venus occur in pairs: eight years later, the scientists were given a second chance to get it right. Chasing Venus brings to life this extraordinary endeavor: the personalities of eighteenth-century astronomy, the collaborations, discoveries, personal rivalries, volatile international politics, and the race to be first to measure the distances between the planets.\par On June 6, 1761, the world paused to observe a momentous occasion: the first transit of Venus between the Earth and the sun in more than a century. Through that observation, astronomers could calculate the size of the solar system --- but only if the transit could be viewed at the same time from many locations. Overcoming incredible odds and political strife, astronomers from Britain, France, Russia, Germany, Sweden, and the American colonies set up observatories in remote corners of the world only to have their efforts thwarted by unpredictable weather and warring armies. Fortunately, transits of Venus occur in pairs: eight years later, the scientists were given a second chance to get it right. Chasing Venus brings to life this extraordinary endeavor: the personalities of eighteenth-century astronomy, the collaborations, discoveries, personal rivalries, volatile international politics, and the race to be first to measure the distances between the planets.", acknowledgement = ack-nhfb, remark = "The Venus solar transit of Tuesday 5 June 2012 was expected to be visible in Salt Lake City, which normally enjoys clear skies during much of the year. Alas, heavy clouds hung low in the valley on that single day, obscuring the event. Only near sundown was the final part of the six-hour transit partly visible through the clouds, by which time, most observers (including me) had given up.", subject = "geodetic astronomy; history; 18th century; astronomy; Venus (planet); transit", tableofcontents = "The gauntlet \\ Transit 1761. Call to action; The French are first; Britain enters the race; To Siberia; Getting ready for Venus; Day of transit, 6 June 1761; How far to the sun? \\ Transit 1769. A second change; Russia enters the race; The most daring voyage of all; Scandinavia, or, The Land of the Midnight Sun; The North American continent; Racing to the four corners of the globe; Day of transit, 3 June 1769; After the transit \\ A new dawn \\ List of observers, 1761 \\ List of observers, 1769", } @Book{Bailey:2013:CAM, editor = "David H. Bailey and Heinz H. Bauschke and Peter Borwein and Frank Garvan and Michel Th{\'e}ra and Jon D. Vanderwerff and Henry Wolkowicz", booktitle = "Computational and analytical mathematics: in honor of {Jonathan Borwein}'s 60th Birthday", title = "Computational and analytical mathematics: in honor of {Jonathan Borwein}'s 60th Birthday", volume = "50", publisher = pub-SV, address = pub-SV:adr, pages = "xv + 701", year = "2013", DOI = "https://doi.org/10.1007/978-1-4614-7621-4", ISBN = "1-4614-7620-8, 1-4614-7621-6 (e-book)", ISBN-13 = "978-1-4614-7620-7, 978-1-4614-7621-4 (e-book)", ISSN = "2194-1009", LCCN = "QA241", bibdate = "Thu Aug 11 13:32:34 MDT 2016", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib; http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/prng.bib", series = "Springer proceedings in mathematics and statistics", URL = "http://public.eblib.com/choice/publicfullrecord.aspx?p=1466708; http://swb.eblib.com/patron/FullRecord.aspx?p=1466708; http://www.myilibrary.com?id=547562", abstract = "The research of Jonathan Borwein has had a profound impact on optimization, functional analysis, operations research, mathematical programming, number theory, and experimental mathematics. Having authored more than a dozen books and more than 300 publications, Dr. Borwein is one of the most productive Canadian mathematicians ever. His research spans pure, applied, and computational mathematics as well as high performance computing, and continues to have an enormous impact: MathSciNet lists more than 2500 citations by more than 1250 authors, and Borwein is one of the 250 most cited mathematicians of the period 1980--1999. He has served the Canadian Mathematics Community through his presidency (2000--2002) as well as his 15 years of editing the CMS book series. Jonathan Borwein's vision and initiative have been crucial in initiating and developing several institutions that provide support for researchers with a wide range of scientific interests. A few notable examples include the Centre for Experimental and Constructive Mathematics and the IRMACS Centre at Simon Fraser University, the Dalhousie Distributed Research Institute at Dalhousie University, the Western Canada Research Grid, and the Centre for Computer Assisted Research Mathematics and its Applications, University of Newcastle. The workshops that were held over the years in Dr. Borwein's honor attracted high-caliber scientists from a wide range of mathematical fields. This present volume is an outgrowth of the workshop entitled Computational and Analytical Mathematics, held in May 2011 in celebration of Jonathan Borwein's 60th Birthday. The collection contains various state-of-the-art research manuscripts and surveys presenting contributions that have risen from the conference, and is an excellent opportunity to survey state-of-the-art research and discuss promising research directions and approaches.", acknowledgement = ack-nhfb, subject = "Number theory; Mathematical analysis; Mathematics; Functional Analysis; Operator Theory; Operations Research, Management Science; Algebra; Intermediate.; Mathematical analysis.; Number theory.", tableofcontents = "Normal Numbers and Pseudorandom Generators / David H. Bailey and Jonathan M. Borwein / 1--18 \\ New Demiclosedness Principles for (Firmly) Nonexpansive Operators / Heinz H. Bauschke / 19--28 \\ Champernowne's Number, Strong Normality, and the X Chromosome / Adrian Belshaw and Peter B. Borwein / 29--44 \\ Optimality Conditions for Semivectorial Bilevel Convex Optimal Control Problems / Henri Bonnel and Jacqueline Morgan / 45--78 \\ Monotone Operators Without Enlargements / Jonathan M. Borwein and Regina S. Burachik / 79--103 \\ A Br{\o}ndsted--Rockafellar Theorem for Diagonal Subdifferential Operators / Radu Ioan Bo{\c{t}} and Ern{\"o} Robert Csetnek / 105--112 \\ A $q$-Analog of Euler's Reduction Formula for the Double Zeta Function / David M. Bradley and Xia Zhou / 113--126 \\ Fast Computation of Bernoulli, Tangent and Secant Numbers / Richard P. Brent and David Harvey / 127--142 \\ Monotone Operator Methods for Nash Equilibria in Non-potential Games / Luis M. Brice{\"a}no-Arias and Patrick L. Combettes / 143--159 \\ Compactness, Optimality, and Risk / B. Cascales, J. Orihuela and M. Ruiz Gal{\'a}n / 161--218 \\ Logarithmic and Complex Constant Term Identities / Tom Chappell, Alain Lascoux and S. Ole Warnaar / 219--250\\ Preprocessing and Regularization for Degenerate Semidefinite Programs / Yuen-Lam Cheung, Simon Schurr and Henry Wolkowicz / 251--303 \\ The Largest Roots of the Mandelbrot Polynomials / Robert M. Corless and Piers W. Lawrence / 305--324 \\ On the Fractal Distribution of Brain Synapses / Richard Crandall / 325--348 \\ Visible Points in Convex Sets and Best Approximation / Frank Deutsch, Hein Hundal and Ludmil Zikatanov / 349--364 \\ On Derivative Criteria for Metric Regularity / Asen L. Dontchev and H{\'e}l{\`e}ne Frankowska / 365--374 \\ Five Classes of Monotone Linear Relations and Operators / Mclean R. Edwards / 375--400 \\ Upper Semicontinuity of Duality and Preduality Mappings / J. R. Giles / 401--410 \\ Convexity and Variational Analysis / A. D. Ioffe / 411--444 \\ Generic Existence of Solutions and Generic Well-Posedness of Optimization Problems / P. S. Kenderov and J. P. Revalski / 445--453 \\ Legendre Functions Whose Gradients Map Convex Sets to Convex Sets / Alexander Knecht and Jon Vanderwerff / 455--462\\ On the Convergence of Iteration Processes for Semigroups of Nonlinear Mappings in Banach Spaces / W. M. Kozlowski and Brailey Sims / 463--484 \\ Techniques and Open Questions in Computational Convex Analysis / Yves Lucet / 485--500 \\ Existence and Approximation of Fixed Points of Right Bregman Nonexpansive Operators / Victoria Mart{\'i}n-M{\'a}rquez and Simeon Reich / 501--520 \\ Primal Lower Nice Functions and Their Moreau Envelopes / Marc Mazade and Lionel Thibault / 521--553 \\ Bundle Method for Non-Convex Minimization with Inexact Subgradients and Function Values / Dominikus Noll / 555--592 \\ Convergence of Linesearch and Trust-Region Methods Using the Kurdyka--{\L}ojasiewicz Inequality / Dominikus Noll and Aude Rondepierre / 593--611 \\ Strong Duality in Conic Linear Programming: Facial Reduction and Extended Duals / G{\'a}bor Pataki / 613--634 \\ Towards a New Era in Subdifferential Analysis? / Jean-Paul Penot /635--665 \\ Modular Equations and Lattice Sums / Mathew Rogers and Boonrod Yuttanan / 667--680 \\ An Epigraph-Based Approach to Sensitivity Analysis in Set-Valued Optimization / Douglas E. Ward and Stephen E. Wright / 681--701", } @Book{Corless:2013:GIN, author = "Robert M. Corless and Nicolas Fillion", title = "A Graduate Introduction to Numerical Methods: from the Viewpoint of Backward Error Analysis", publisher = pub-SV, address = pub-SV:adr, pages = "xxxix + 868", year = "2013", ISBN = "1-4614-8452-9 (hardcover), 1-4614-8453-7 (e-book)", ISBN-13 = "978-1-4614-8452-3 (hardcover), 978-1-4614-8453-0 (e-book)", LCCN = "QA297 .C665 2013", bibdate = "Sat Oct 6 08:53:42 MDT 2018", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "Numerical analysis; Textbooks; Error analysis (Mathematics); Mathematics; Methodology; Study and teaching (Graduate)", tableofcontents = "Computer Arithmetic and Fundamental Concepts of Computation \\ Polynomials and Series \\ Rootfinding and Function Evaluation \\ Solving $ A x = b$ \\ Solving $A x = \lambda x$ \\ Structured Linear Systems \\ Iterative Methods \\ Polynomial and Rational Interpolation \\ The Discrete Fourier Transform \\ Numerical Integration \\ Numerical Differentiation and Finite Differences \\ Numerical Solution of ODEs \\ Numerical Methods for ODEs \\ Numerical Solutions of Boundary Value Problems \\ Numerical Solution of Delay DEs \\ Numerical Solution of PDEs", } @Book{Dennis:2013:RSC, author = "Brian Dennis", title = "The {R} student companion", publisher = "CRC Press, Taylor and Francis Group", address = "Boca Raton, FL, USA", pages = "xvii + 339", year = "2013", ISBN = "1-4398-7540-5 (paperback)", ISBN-13 = "978-1-4398-7540-7 (paperback)", LCCN = "QA276.45.R3 D46 2013", bibdate = "Thu Jul 10 12:58:52 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/s-plus.bib; z3950.loc.gov:7090/Voyager", URL = "http://jacketsearch.tandf.co.uk/common/jackets/covers/websmall/978143987/9781439875407.jpg", abstract = "R is a computer package for scientific graphs and calculations. It is written and maintained by statisticians and scientists, for scientists to use in their work. It is easy to use, yet is extraordinarily powerful. R is spreading rapidly throughout the science and technology world, and it is setting the standards for graphical data displays in science publications. R is free. It is an open-source product that is easy to install on most computers. It is available for Windows, Mac, and Unix/Linux operating systems. One simply downloads and installs it from the R website (http:// www.r-project.org/). This book is for high school and college students, and anyone else, who wants to learn to use R. With this book, you can put your computer to work in powerful fashion, in any subject that uses applied mathematics. In particular, physics, life sciences, chemistry, earth science, economics, engineering, and business involve much analysis, modeling, simulation, statistics, and graphing. These quantitative applications become remarkably straightforward and understandable when performed with R. Difficult concepts in mathematics and statistics become clear when illustrated with R. The book starts from the beginning and assumes the reader has no computer programming background. The mathematical material in the book requires only a moderate amount of high school algebra. R makes graphing calculators seem awkward and obsolete. The calculators are hard to learn, cumbersome to use for anything but tiny problems, and the graphs are small and have poor resolution. Calculating in R by comparison is intuitive, even fun. Fantastic, publication-quality graphs of data, equations, or both can be produced with little effort.", acknowledgement = ack-nhfb, author-dates = "1952--", subject = "R (Computer program language); Probabilities; Mathematical statistics; Data processing; MATHEMATICS / General.; MATHEMATICS / Probability and Statistics / General.", tableofcontents = "1. Introduction: Getting started with R \\ 2. R scripts \\ 3. Functions \\ 4. Basic graphs \\ 5. Data input and output \\ 6. Loops \\ 7. Logic and control \\ 8. Quadratic functions \\ 9. Trigonometric functions \\ 10. Exponential and logarithmic functions \\ 11. Matrix arithmetic \\ 12. Systems of linear equations \\ 13. Advanced graphs \\ 14. Probability and simulation \\ 15. Fitting models to data \\ 16. Conclusion: It doesn't take a rocket scientist \\ Appendix A Installing R \\ Appendix B: Getting help \\ Appendix C: Common R expressions", } @Book{Golub:2013:MC, author = "Gene H. Golub and Charles F. {Van Loan}", title = "Matrix Computations", publisher = pub-JOHNS-HOPKINS, address = pub-JOHNS-HOPKINS:adr, edition = "Fourth", pages = "xxi + 756", year = "2013", ISBN = "1-4214-0794-9 (hardcover), 1-4214-0859-7 (e-book)", ISBN-13 = "978-1-4214-0794-4 (hardcover), 978-1-4214-0859-0 (e-book)", LCCN = "QA188 .G65 2013", bibdate = "Fri Nov 21 06:49:56 2014", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Johns Hopkins Studies in the Mathematical Sciences", URL = "https://jhupbooks.press.jhu.edu/title/matrix-computations", abstract = "This revised edition provides the mathematical background and algorithmic skills required for the production of numerical software. It includes rewritten and clarified proofs and derivations, as well as new topics such as Arnoldi iteration, and domain decomposition methods.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", shorttableofcontents = "1: Matrix multiplication \\ 2: Matrix analysis \\ 3: General linear systems \\ 4: Special linear systems \\ 5: Orthogonalization and least squares \\ 6: Modified least squares problems and methods \\ 7: Unsymmetric eigenvalue problems \\ 8: Symmetric eigenvalue problems \\ 9: Functions of matrices \\ 10: Large sparse eigenvalue problems \\ 11: Large sparse linear system problems \\ 12: Special topics", subject = "Matrices; Data processing; Data processing.; Matrix.; Matrizenrechnung.; Matrizentheorie.; Numerische Mathematik.", tableofcontents = "Preface \\ Global References \\ Other Books \\ Useful URLs \\ Common Notation \\ 1: Matrix Multiplication \\ 1.1 Basic Algorithms and Notation \\ 1.2 Structure and Efficiency \\ 1.3 Block Matrices and Algorithms \\ 1.4 Fast Matrix--Vector Products \\ 1.5 Vectorization and Locality \\ 1.6 Parallel Matrix Multiplication \\ 2: Matrix Analysis \\ 2.1 Basic Ideas from Linear Algebra \\ 2.2 Vector Norms \\ 2.3 Matrix Norms \\ 2.4 The Singular Value Decomposition \\ 2.5 Subspace Metrics \\ 2.6 The Sensitivity of Square Systems \\ 2.7 Finite Precision Matrix Computations \\ 3: General Linear Systems \\ 3.1 Triangular Systems \\ 3.2 The $L U$ Factorization \\ 3.3 Roundoff Error in Gaussian Elimination \\ 3.4 Pivoting \\ 3.5 Improving and Estimating Accuracy \\ 3.6 Parallel $L U$ \\ 4: Special Linear Systems \\ 4.1 Diagonal Dominance and Symmetry \\ 4.2 Positive Definite Systems \\ 4.3 Banded Systems \\ 4.4 Symmetric Indefinite Systems \\ 4.5 Block Tridiagonal Systems \\ 4.6 Vandermonde Systems \\ 4.7 Classical Methods for Toeplitz Systems \\ 4.8 Circulant and Discrete Poisson Systems \\ 5: Orthogonalization and Least Squares \\ 5.1 Householder and Givens Transformations \\ 5.2 The $Q R$ Factorization \\ 5.3 The Full-Rank Least Squares Problem \\ 5.4 Other Orthogonal Factorizations \\ 5.5 The Rank-Deficient Least Squares Problem \\ 5.6 Square and Underdetermined Systems \\ 6: Modified Least Squares Problems and Methods \\ 6.1 Weighting and Regularization \\ 6.2 Constrained Least Squares \\ 6.3 Total Least Squares \\ 6.4 Subspace Computations with the SVD \\ 6.5 Updating Matrix Factorizations \\ 7: Unsymmetric Eigenvalue Problems \\ 7.1 Properties and Decompositions \\ 7.2 Perturbation Theory \\ 7.3 Power Iterations \\ 7.4 The Hessenberg and Real Schur Forms \\ 7.5 The Practical $Q R$ Algorithm \\ 7.6 Invariant Subspace Computations \\ 7.7 The Generalized Eigenvalue Problem \\ 7.8 Hamiltonian and Product Eigenvalue Problems \\ 7.9 Pseudospectra \\ 8: Symmetric Eigenvalue Problems \\ 8.1 Properties and Decompositions \\ 8.2 Power Iterations \\ 8.3 The Symmetric $Q R$ Algorithm \\ 8.4 More Methods for Tridiagonal Problems \\ 8.5 Jacobi Methods \\ 8.6 Computing the SVD \\ 8.7 Generalized Eigenvalue Problems with Symmetry \\ 9: Functions of Matrices \\ 9.1 Eigenvalue Methods \\ 9.2 Approximation Methods \\ 9.3 The Matrix Exponential \\ 9.4 The Sign, Square Root, and Log of a Matrix \\ 10: Large Sparse Eigenvalue Problems \\ 10.1 The Symmetric Lanczos Process \\ 10.2 Lanczos, Quadrature, and Approximation \\ 10.3 Practical Lanczos Procedures \\ 10.4 Large Sparse SVD Frameworks \\ 10.5 Krylov Methods for Unsymmetric Problems \\ 10.6 Jacobi--Davidson and Related Methods \\ 11: Large Sparse Linear System Problems \\ 11.1 Direct Methods \\ 11.2 The Classical Iterations \\ 11.3 The Conjugate Gradient Method \\ 11.4 Other Krylov Methods \\ 11.5 Preconditioning \\ 11.6 The Multigrid Framework \\ 12: Special Topics \\ 12.1 Linear Systems with Displacement Structure \\ 12.2 Structured-Rank Problems \\ 12.3 Kronecker Product Computations \\ 12.4 Tensor Unfoldings and Contractions \\ 12.5 Tensor Decompositions and Iterations \\ Index", } @Book{Graham:2013:SSM, author = "C. (Carl) Graham and D. (Denis) Talay", title = "Stochastic Simulation and {Monte Carlo} Methods: Mathematical Foundations of Stochastic Simulation", volume = "68", publisher = pub-SV, address = pub-SV:adr, pages = "xvi + 260 + 4", year = "2013", DOI = "https://doi.org/10.1007/978-3-642-39363-1", ISBN = "3-642-39362-4", ISBN-13 = "978-3-642-39362-4", ISSN = "0172-4568", ISSN-L = "0172-4568", LCCN = "QA273.A1-274.9; QA274-274.9", bibdate = "Tue Apr 29 18:44:55 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/probstat2010.bib; prodorbis.library.yale.edu:7090/voyager", series = "Stochastic Modelling and Applied Probability", abstract = "In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners and \#x2019; aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of {It{\^o}} integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view. and The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations. and .", acknowledgement = ack-nhfb, subject = "Mathematics; Finance; Numerical analysis; Distribution (Probability theory)", tableofcontents = "Part I:Principles of Monte Carlo Methods \\ 1.Introduction \\ 2.Strong Law of Large Numbers and Monte Carlo Methods \\ 3.Non Asymptotic Error Estimates for Monte Carlo Methods \\ Part II:Exact and Approximate Simulation of Markov Processes \\ 4.Poisson Processes \\ 5.Discrete-Space Markov Processes \\ 6.Continuous-Space Markov Processes with Jumps \\ 7.Discretization of Stochastic Differential Equations \\ Part III:Variance Reduction, Girsanov and \#x2019;s Theorem, and Stochastic Algorithms \\ 8.Variance Reduction and Stochastic Differential Equations \\ 9.Stochastic Algorithms \\ References \\ Index", } @Book{Hansen:2013:LSD, author = "Per Christian Hansen and V. (V{\'\i}ctor) Pereyra and Godela Scherer", title = "Least Squares Data Fitting with Applications", publisher = pub-JOHNS-HOPKINS, address = pub-JOHNS-HOPKINS:adr, pages = "xv + 305", year = "2013", ISBN = "1-4214-0786-8 (hardcover), 1-4214-0858-9 (e-book)", ISBN-13 = "978-1-4214-0786-9 (hardcover), 978-1-4214-0858-3 (e-book)", LCCN = "QA275 .H26 2013", MRclass = "65-01 (62J05 65Fxx)", MRnumber = "3012616", bibdate = "Sat Feb 2 09:11:29 MST 2019", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; prodorbis.library.yale.edu:7090/voyager; z3950.loc.gov:7090/Voyager http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://muse.jhu.edu/books/9781421408583/", abstract = "As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data predictively. The main concern of Least Squares Data Fitting with Applications is how to do this on a computer with efficient and robust computational methods for linear and nonlinear relationships. The presentation also establishes a link between the statistical setting and the computational issues. In a number of applications, the accuracy and efficiency of the least squares fit is central, and Per Christian Hansen, V{\'i}ctor Pereyra, and Godela Scherer survey modern computational methods and illustrate them in fields ranging from engineering and environmental sciences to geophysics. Anyone working with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems.", acknowledgement = ack-nhfb, remark = "In his interview \cite[page 44]{Haigh:2005:IGG}, Gene Golub notes that he was working on a book with V{\'\i}ctor Pereyra. This is the further development of that book, as the preface reports on page xi: ``Prior to his untimely death in November 2007, Professor Gene Golub had been an integral part of the project team. Although the book has changed significantly since then, it has greatly benefitted from his insight and knowledge. He was an aspiring mentor and great friend, and we miss him dearly.''", subject = "Least squares; Mathematical models; MATHEMATICS; General.; Least squares.; Mathematical models.", tableofcontents = "Preface / ix \\ Symbols and Acronyms / xiii \\ 1 The Linear Data Fitting Problem / 1 \\ 1.1 Parameter estimation, data approximation / 1 \\ 1.2 Formulation of the data fitting problem / 4 \\ 1.3 Maximum likelihood estimation / 9 \\ 1.4 The residuals and their properties / 13 \\ 1.5 Robust regression / 19 \\ 2 The Linear Least Squares Problem / 25 \\ 2.1 Linear least squares problem formulation / 25 \\ 2.2 The QR factorization and its role / 33 \\ 2.3 Permuted QR factorization / 39 \\ 3 Analysis of Least Squares Problems / 47 \\ 3.1 The pseudoinverse / 47 \\ 3.2 The singular value decomposition / 50 \\ 3.3 Generalized singular value decomposition / 54 \\ 3.4 Condition number and column scaling / 55 \\ 3.5 Perturbation analysis / 58 \\ 4 Direct Methods for Full-Rank Problems / 65 \\ 4.1 Normal equations / 65 \\ 4.2 LU factorization / 68 \\ 4.3 QR factorization / 70 \\ 4.4 Modifying least squares problems / 80 \\ 4.5 Iterative refinement / 85 \\ 4.6 Stability and condition number estimation / 88 \\ 4.7 Comparison of the methods / 89 \\ 5 Direct Methods for Rank-Deficient Problems / 91 \\ 5.1 Numerical rank / 92 \\ 5.2 Peters-Wilkinson LU factorization / 93 \\ 5.3 QR factorization with column permutations / 94 \\ 5.4 UTV and VSV decompositions / 98 \\ 5.5 Bidiagonalization / 99 \\ 5.6 SVD computations / 101 \\ 6 Methods for Large-Scale Problems / 105 \\ 6.1 Iterative versus direct methods / 105 \\ 6.2 Classical stationary methods / 107 \\ 6.3 Non-stationary methods, Krylov methods / 108 \\ 6.4 Practicalities: preconditioning and stopping criteria / 114 \\ 6.5 Block methods / 117 \\ 7 Additional Topics in Least Squares / 121 \\ 7.1 Constrained linear least squares problems / 121 \\ 7.2 Missing data problems / 131 \\ 7.3 Total least squares (TLS) / 136 \\ 7.4 Convex optimization / 143 \\ 7.5 Compressed sensing / 144 \\ 8 Nonlinear Least Squares Problems / 147 \\ 8.1 Introduction / 147 \\ 8.2 Unconstrained problems / 150 \\ 8.3 Optimality conditions for constrained problems / 156 \\ 8.4 Separable nonlinear least squares problems / 158 \\ 8.5 Multiobjective optimization / 160 \\ 9 Algorithms for Solving Nonlinear LSQ Problems / 163 \\ 9.1 Newton's method / 164 \\ 9.2 The Gauss-Newton method / 166 \\ 9.3 The Levenberg-Marquardt method / 170 \\ 9.4 Additional considerations and software / 176 \\ 9.5 Iteratively reweighted LSQ algorithms for robust data fitting problems / 178 \\ 9.6 Variable projection algorithm / 181 \\ 9.7 Block methods for large-scale problems / 186 \\ 10 Ill-Conditioned Problems / 191 \\ 10.1 Characterization / 191 \\ 10.2 Regularization methods / 192 \\ 10.3 Parameter selection techniques / 195 \\ 10.4 Extensions of Tikhonov regularization / 198 \\ 10.5 Ill-conditioned NLLSQ problems / 201 \\ 11 Linear Least Squares Applications / 203 \\ 11.1 Splines in approximation / 203 \\ 11.2 Global temperatures data fitting / 212 \\ 11.3 Geological surface modeling / 221 \\ 12 Nonlinear Least Squares Applications / 231 \\ 12.1 Neural networks training / 231 \\ 12.2 Response surfaces, surrogates or proxies / 238 \\ 12.3 Optimal design of a supersonic aircraft / 241 \\ 12.4 NMR spectroscopy / 248 \\ 12.5 Piezoelectric crystal identification / 251 \\ 12.6 Travel time inversion of seismic data / 258 \\ Appendix A Sensitivity Analysis / 263 \\ A.l Floating-point arithmetic / 263 \\ A.2 Stability, conditioning and accuracy / 264 \\ Appendix B Linear Algebra Background / 267 \\ B.l Norms / 267 \\ B.2 Condition number / 268 \\ B.3 Orthogonality / 269 \\ B.4 Some additional matrix properties / 270 \\ Appendix C Advanced Calculus Background / 271 \\ C.l Convergence rates / 271 \\ C.2 Multivariable calculus / 272 \\ Appendix D Statistics / 275 \\ D.l Definitions / 275 \\ D.2 Hypothesis testing / 280 \\ References / 281 \\ Index / 301", } @Book{Hilber:2013:CMQ, author = "Norbert Hilber and Oleg Reichmann and Ch. (Christoph) Schwab and Christoph Winter", title = "Computational Methods for Quantitative Finance: Finite Element Methods for Derivative Pricing", publisher = pub-SV, address = pub-SV:adr, pages = "xiii + 299 + 57", year = "2013", DOI = "https://doi.org/10.1007/978-3-642-35401-4", ISBN = "3-642-35400-9", ISBN-13 = "978-3-642-35400-7", ISSN = "1616-0533", ISSN-L = "1616-0533", LCCN = "QA273.A1-274.9; QA274-274.9", bibdate = "Tue Apr 29 18:44:55 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/probstat2010.bib; prodorbis.library.yale.edu:7090/voyager", series = "Springer Finance", abstract = "Many mathematical assumptions on which classical derivative pricing methods are based have come under scrutiny in recent years. The present volume offers an introduction to deterministic algorithms for the fast and accurate pricing of derivative contracts in modern finance. This unified, non-Monte-Carlo computational pricing methodology is capable of handling rather general classes of stochastic market models with jumps, including, in particular, all currently used L{\'e}vy and stochastic volatility models. It allows us e.g. to quantify model risk in computed prices on plain vanilla, as well as on various types of exotic contracts. The algorithms are developed in classical Black-Scholes markets, and then extended to market models based on multiscale stochastic volatility, to L{\'e}vy, additive and certain classes of Feller processes. and The volume is intended for graduate students and researchers, as well as for practitioners in the fields of quantitative finance and applied and computational mathematics with a solid background in mathematics, statistics or economics.", acknowledgement = ack-nhfb, subject = "Mathematics; Finance; Numerical analysis; Distribution (Probability theory)", tableofcontents = "Part I. Basic techniques and models: \\ 1. Introduction \\ 2. Notions of mathematical finance \\ 3. Elements of numerical methods for PDEs \\ 4. Finite element methods for parabolic problems \\ 5. European options in BS markets \\ 6. American options \\ 7. Exotic options \\ 8. Interest rate models \\ 9. Multi-asset options \\ 10. Stochastic volatility models \\ 11. L{\'e}vy models \\ 12. Sensitivities and Greeks \\ Part II. Advanced techniques and models 13. Wavelet methods \\ 14. Multidimensional diffusion models \\ 15. Multidimensional L{\'e}vy models \\ 16. Stochastic volatility models with jumps \\ 17. Multidimensional Feller processes \\ Appendices: \\ A. Elliptic variational inequalities \\ B. Parabolic variational inequalities \\ References \\ Index", } @Book{Hollig:2013:AMB, author = "Klaus H{\"o}llig and J{\"o}rg H{\"o}rner", title = "Approximation and modeling with {B}-splines", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xiii + 214", year = "2013", ISBN = "1-61197-294-9", ISBN-13 = "978-1-61197-294-8", LCCN = "QA224 .H645 2013", bibdate = "Tue Aug 12 15:33:22 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Applied mathematics", acknowledgement = ack-nhfb, subject = "Spline theory; Approximation theory; Numerical analysis; Mathematical models; Engineering; Computer science; Mathematics; Algorithms; Industrial applications", tableofcontents = "Polynomials \\ B\'ezier Curves \\ Rational B\'ezier Curves \\ B-Splines \\ Approximation \\ Spline Curves \\ Multivariate Splines \\ Surfaces and Solids \\ Finite Elements \\ Appendix \\ Notation and Symbols", } @Book{Kiusalaas:2013:NME, author = "Jaan Kiusalaas", title = "Numerical methods in engineering with {Python 3}", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "xi + 423", year = "2013", ISBN = "1-107-03385-3", ISBN-13 = "978-1-107-03385-6", LCCN = "TA345 .K584 2013", MRclass = "65-01", MRnumber = "3026375", bibdate = "Tue May 27 12:31:32 MDT 2014", bibsource = "clas.caltech.edu:210/INNOPAC; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/python.bib", abstract = "This book is an introduction to numerical methods for students in engineering. It covers solution of equations, interpolation and data fitting, solution of differential equations, eigenvalue problems and optimisation. The algorithms are implemented in Python 3, a high-level programming language that rivals MATLAB in readability and ease of use. All methods include programs showing how the computer code is utilised in the solution of problems. The book is based on Numerical Methods in Engineering with Python, which used Python 2. This new edition demonstrates the use of Python 3 and includes an introduction to the Python plotting package Matplotlib. This comprehensive book is enhanced by the addition of numerous examples and problems throughout.", acknowledgement = ack-nhfb, subject = "Engineering mathematics; Data processing; Python (Computer program language)", tableofcontents = "1. Introduction to Python \\ 2. Systems of linear algebraic equations \\ 3. Interpolation and curve fitting \\ 4. Roots of equations \\ 5. Numerical differentiation \\ 6. Numerical integration \\ 7. Initial value problems \\ 8. Two-point boundary value problems \\ 9. Symmetric matrix eigenvalue problems \\ 10. Introduction to optimization", } @Book{Kutz:2013:DDM, author = "Jose Nathan Kutz", title = "Data-driven modeling and scientific computation: methods for complex systems and big data", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "xvii + 638", year = "2013", ISBN = "0-19-966033-6 (hardcover), 0-19-966034-4 (paperback)", ISBN-13 = "978-0-19-966033-9 (hardcover), 978-0-19-966034-6 (paperback)", LCCN = "Q183.9 .K88 2013", bibdate = "Tue Jan 12 16:17:35 MST 2016", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/s-plus.bib; z3950.loc.gov:7090/Voyager", abstract = "The burgeoning field of data analysis is expanding at an incredible pace due to the proliferation of data collection in almost every area of science. The enormous data sets now routinely encountered in the sciences provide an incentive to develop mathematical techniques and computational algorithms that help synthesize, interpret and give meaning to the data in the context of its scientific setting. A specific aim of this book is to integrate standard scientific computing methods with data analysis. By doing so, it brings together, in a self-consistent fashion, the key ideas from: statistics, \ldots{}", abstract = "Prolegomenon \\ How to Use This Book \\ About MATLAB \\ PART I: Basic Computations and Visualization \\ 1 MATLAB Introduction \\ 1.1 Vectors and Matrices \\ 1.2 Logic, Loops and Iterations \\ 1.3 Iteration: The Newton-Raphson Method \\ 1.4 Function Calls, Input/Output Interactions and Debugging \\ 1.5 Plotting and Importing/Exporting Data \\ 2 Linear Systems \\ 2.1 Direct Solution Methods for $ A x = b $ \\ 2.2 Iterative Solution Methods for $ A x = b $ \\ 2.3 Gradient (Steepest) Descent for $ A x = b $ \\ 2.4 Eigenvalues, Eigenvectors and Solvability \\ 2.5 Eigenvalues and Eigenvectors for Face Recognition. 2.6 Nonlinear Systems \\ 3 Curve Fitting \\ 3.1 Least-Square Fitting Methods \\ 3.2 Polynomial Fits and Splines \\ 3.3 Data Fitting with MATLAB \\ 4 Numerical Differentiation and Integration \\ 4.1 Numerical Differentiation \\ 4.2 Numerical Integration \\ 4.3 Implementation of Differentiation and Integration \\ 5 Basic Optimization \\ 5.1 Unconstrained Optimization (Derivative-Free Methods) \\ 5.2 Unconstrained Optimization (Derivative Methods) \\ 5.3 Linear Programming \\ 5.4 Simplex Method \\ 5.5 Genetic Algorithms \\ 6 Visualization \\ 6.1 Customizing Plots and Basic 2D Plotting \\ 6.2 More 2D and 3D Plotting. 6.3 Movies and Animations \\ PART II: Differential and Partial Differential Equations \\ 7 Initial and Boundary Value Problems of Differential Equations \\ 7.1 Initial Value Problems: Euler, Runge-Kutta and Adams Methods \\ 7.2 Error Analysis for Time-Stepping Routines \\ 7.3 Advanced Time-Stepping Algorithms \\ 7.4 Boundary Value Problems: The Shooting Method \\ 7.5 Implementation of Shooting and Convergence Studies \\ 7.6 Boundary Value Problems: Direct Solve and Relaxation \\ 7.7 Implementing MATLAB for Boundary Value Problems \\ 7.8 Linear Operators and Computing Spectra \\ 8 Finite Difference Methods. 8.1 Finite Difference Discretization \\ 8.2 Advanced Iterative Solution Methods for $ A x = b $ \\ 8.3 Fast Poisson Solvers: The Fourier Transform \\ 8.4 Comparison of Solution Techniques for $ A x = b $: Rules of Thumb \\ 8.5 Overcoming Computational Difficulties \\ 9 Time and Space Stepping Schemes: Method of Lines \\ 9.1 Basic Time-Stepping Schemes \\ 9.2 Time-Stepping Schemes: Explicit and Implicit Methods \\ 9.3 Stability Analysis \\ 9.4 Comparison of Time-Stepping Schemes \\ 9.5 Operator Splitting Techniques \\ 9.6 Optimizing Computational Performance: Rules of Thumb \\ 10 Spectral Methods \\ 10.1 Fast Fourier Transforms and Cosine/Sine Transform \\ 10.2 Chebychev Polynomials and Transform \\ 10.3 Spectral Method Implementation \\ 10.4 Pseudo-Spectral Techniques with Filtering \\ 10.5 Boundary Conditions and the Chebychev Transform \\ 10.6 Implementing the Chebychev Transform \\ 10.7 Computing Spectra: The Floquet-Fourier-Hill Method \\ 11 Finite Element Methods \\ 11.1 Finite Element Basis \\ 11.2 Discretizing with Finite Elements and Boundaries \\ 11.3 MATLAB for Partial Differential Equations \\ 11.4 MATLAB Partial Differential Equations Toolbox \\ PART III: Computational Methods for Data Analysis. 12 Statistical Methods and Their Applications", acknowledgement = ack-nhfb, subject = "MATLAB; Science; Data processing; Numerical analysis; Differential equations", } @Book{Larson:2013:FEM, author = "Mats G. Larson and Fredrik Bengzon", title = "The finite element method: theory, implementation, and applications", volume = "10", publisher = pub-SV, address = pub-SV:adr, pages = "xviii + 385", year = "2013", DOI = "https://doi.org/10.1007/978-3-642-33287-6", ISBN = "3-642-33286-2, 3-642-33287-0 (e-book)", ISBN-13 = "978-3-642-33286-9, 978-3-642-33287-6 (e-book)", ISSN = "1611-0994", LCCN = "TA347.F5 L37 2013", MRclass = "65-01 (65M60 65N30)", MRnumber = "3015004", bibdate = "Tue May 27 12:31:33 MDT 2014", bibsource = "clas.caltech.edu:210/INNOPAC; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Texts in Computational Science and Engineering", acknowledgement = ack-nhfb, subject = "Finite element method", } @Book{Ochsner:2013:ODF, author = "Andreas {\"O}chsner and Markus Merkel", title = "One-dimensional finite elements: an introduction to the FE method", publisher = pub-SV, address = pub-SV:adr, pages = "xxiii + 398", year = "2013", DOI = "https://doi.org/10.1007/978-3-642-31797-2", ISBN = "3-642-31796-0 (hardcover); 3-642-31797-9 (e-book)", ISBN-13 = "978-3-642-31796-5 (hardcover); 978-3-642-31797-2 (e-book)", LCCN = "TA347.F5 O24 2013", MRclass = "65-01 (65M60 65N30 74S05)", MRnumber = "2985770", MRreviewer = "Alexandre L. Madureira", bibdate = "Tue May 27 12:31:35 MDT 2014", bibsource = "clas.caltech.edu:210/INNOPAC; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", note = "An introduction to the FE method", abstract = "``This textbook presents finite element methods using exclusively one-dimensional elements. The aim is to present the complex methodology in an easily understandable but mathematically correct fashion. The approach of one-dimensional elements enables the reader to focus on the understanding of the principles of basic and advanced mechanical problems. The reader easily understands the assumptions and limitations of mechanical modeling as well as the underlying physics without struggling with complex mathematics. But although the description is easy it remains scientifically correct.The approach using only one-dimensional elements covers not only standard problems but allows also for advanced topics like plasticity or the mechanics of composite materials. Many examples illustrate the concepts and problems at the end of every chapter help to familiarize with the topics.'' -- Publisher's description.", acknowledgement = ack-nhfb, subject = "Finite element method", tableofcontents = "Motivation for the finite element method \\ Bar element \\ Torsion bar \\ Bending element \\ General 1D element \\ Plane and spatial frame structures \\ Beam with shear contribution \\ Beams of composite materials \\ Nonlinear elasticity \\ Plasticity \\ Stability (buckling) \\ Dynamics", } @Book{Pozrikidis:2013:XSC, author = "C. Pozrikidis", title = "{XML} in scientific computing", publisher = pub-CRC, address = pub-CRC:adr, pages = "xv + 243 pages", year = "2013", ISBN = "1-4665-1227-X (hardback)", ISBN-13 = "978-1-4665-1227-6 (hardback)", LCCN = "Q183.9 .P69 2013", bibdate = "Fri Nov 16 06:32:54 MST 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/sgml2010.bib; http://www.math.utah.edu/pub/tex/bib/super.bib; z3950.loc.gov:7090/Voyager", series = "Chapman and Hall/CRC numerical analysis and scientific computing series", acknowledgement = ack-nhfb, subject = "XML (Document markup language); Science; Data processing; Numerical analysis; COMPUTERS / Internet / General.; MATHEMATICS / General.; MATHEMATICS / Number Systems.", } @Book{Rossant:2013:LII, author = "Cyrille Rossant", title = "Learning {IPython} for interactive computing and data visualization: Learn {IPython} for interactive {Python} programming, high-performance numerical computing, and data visualization", publisher = "Packt Publishing", address = "Birmingham, UK", pages = "iv + 123", year = "2013", ISBN = "1-78216-993-8 (paperback), 1-78216-994-6 (e-book), 1-299-54508-4 (e-book)", ISBN-13 = "978-1-78216-993-2 (paperback), 978-1-78216-994-9 (e-book), 978-1-299-54508-3 (e-book)", LCCN = "QA76.73.P98 .R677 2013", bibdate = "Sat Mar 21 07:03:35 MDT 2015", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/python.bib", series = "Open source: community experience distilled", acknowledgement = ack-nhfb, author-dates = "1985--", subject = "Python (langage de programmation).; Python (Computer program language); Python (Computer program language)", } @Book{Singh:2013:LAS, author = "Kuldeep Singh", title = "Linear Algebra: Step by Step", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "viii + 608", year = "2013", ISBN = "0-19-965444-1 (paperback), 0-19-150776-8 (e-book)", ISBN-13 = "978-0-19-965444-4 (paperback), 978-0-19-150776-2 (e-book)", LCCN = "QA184.2 .S56 2014", bibdate = "Mon Sep 15 18:07:52 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", abstract = "Linear algebra is a fundamental area of mathematics, and is arguably the most powerful mathematical tool ever developed. It is a core topic of study within fields as diverse as: business, economics, engineering, physics, computer science, ecology, sociology, demography and genetics. For an example of linear algebra at work, one needs to look no further than the Google search engine, which relies upon linear algebra to rank the results of a search with respect to relevance. The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced\ldots{}.", abstract = "Cover \\ Contents \\ 1 Linear Equations and Matrices \\ 1.1 Systems of Linear Equations \\ 1.2 Gaussian Elimination \\ 1.3 Vector Arithmetic \\ 1.4 Arithmetic of Matrices \\ 1.5 Matrix Algebra \\ 1.6 The Transpose and Inverse of a Matrix \\ 1.7 Types of Solutions \\ 1.8 The Inverse Matrix Method \\ Des Higham Interview \\ 2 Euclidean Space \\ 2.1 Properties of Vectors \\ 2.2 Further Properties of Vectors \\ 2.3 Linear Independence \\ 2.4 Basis and Spanning Set \\ Chao Yang Interview \\ 3 General Vector Spaces \\ 3.1 Introduction to General Vector Spaces \\ 3.2 Subspace of a Vector Space \\ 3.3 Linear Independence and Basis \\ 3.4 Dimension 3.5 Properties of a Matrix \\ 3.6 Linear Systems Revisited \\ Janet Drew Interview \\ 4 Inner Product Spaces \\ 4.1 Introduction to Inner Product Spaces \\ 4.2 Inequalities and Orthogonality \\ 4.3 Orthonormal Bases \\ 4.4 Orthogonal Matrices \\ Anshul Gupta Interview \\ 5 Linear Transformations \\ 5.1 Introduction to Linear Transformations \\ 5.2 Kernel and Range of a Linear Transformation \\ 5.3 Rank and Nullity \\ 5.4 Inverse Linear Transformations \\ 5.5 The Matrix of a Linear Transformation \\ 5.6 Composition and Inverse Linear Transformations \\ Petros Drineas Interview. \\ 6 Determinants and the Inverse Matrix \\ 6.1 Determinant of a Matrix \\ 6.2 Determinant of Other Matrices \\ 6.3 Properties of Determinants \\ 6.4 LU Factorization \\ Fran{\c{c}}oise Tisseur Interview \\ 7 Eigenvalues and Eigenvectors \\ 7.1 Introduction to Eigenvalues and Eigenvectors \\ 7.2 Properties of Eigenvalues and Eigenvectors \\ 7.3 Diagonalization \\ 7.4 Diagonalization of Symmetric Matrices \\ 7.5 Singular Value Decomposition \\ Brief Solutions \\ Index", acknowledgement = ack-nhfb, } @Book{Anastassiou:2014:IRI, author = "George A. Anastassiou and Iuliana F. Iatan", title = "Intelligent Routines {II}: Solving Linear Algebra and Differential Geometry with {Sage}", volume = "58", publisher = "Springer International Publishing", address = "Cham, Switzerland", pages = "xiv + 306", year = "2014", DOI = "https://doi.org/10.1007/978-3-319-01967-3", ISBN = "3-319-01966-X, 3-319-01967-8 (e-book)", ISBN-13 = "978-3-319-01966-6, 978-3-319-01967-3 (e-book)", ISSN = "1868-4394", LCCN = "QA614 .A63 2014", bibdate = "Mon Sep 15 18:20:07 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Intelligent systems reference library", URL = "http://d-nb.info/1045077038/34; http://nbn-resolving.de/urn:nbn:de:1111-201312062402; http://www.springerlink.com/content/978-3-319-01967-3", abstract = "This book contains numerous examples and problems as well as many unsolved problems. It applies the successful software Sage, used for mathematical computation.", acknowledgement = ack-nhfb, author-dates = "1952--", remark = "``ISSN: 1868-4394.''.", subject = "Engineering; Algebras, Linear; Geometry, Differential; Algebras, Linear.; Engineering.; Geometry, Differential.", tableofcontents = "1. Vector spaces \\ 2. Plane and straight line in E3 \\ 3. Linear transformations \\ 4. Euclidean vector spaces \\ 5. Bilinear and quadratic forms \\ 6. Differential geometry of curves and surfaces \\ 7. Conics and quadrics", } @Book{Anonymous:2014:NMO, author = "Eric Walter", title = "Numerical Methods and Optimization: a Consumer Guide", publisher = pub-SV, address = pub-SV:adr, pages = "xv + 476", year = "2014", DOI = "https://doi.org/10.1007/978-3-319-07671-3", ISBN = "3-319-07670-1, 3-319-07671-X (e-book)", ISBN-13 = "978-3-319-07670-6, 978-3-319-07671-3 (e-book)", LCCN = "QA402.5 .W358 2014eb", bibdate = "Tue Sep 9 14:27:31 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/enhancements/fy1411/2014940746-d.html; http://www.loc.gov/catdir/enhancements/fy1411/2014940746-t.html", acknowledgement = ack-nhfb, keywords = "interval arithmetic", tableofcontents = "From Calculus to Computation \\ Notation and Norms \\ Solving Systems of Linear Equations \\ Solving Other Problems in Linear Algebra \\ Interpolation and Extrapolation \\ Integrating and Differentiating Functions \\ Solving Systems of Nonlinear Equations \\ Introduction to Optimization \\ Optimizing Without Constraint \\ Optimizing Under Constraints \\ Combinatorial Optimization \\ Solving Ordinary Differential Equations \\ Solving Partial Differential Equations \\ Assessing Numerical Errors \\ WEB Resources to go Further \\ Problems", } @Book{Bloomfield:2014:URN, author = "Victor A. Bloomfield", title = "Using {R} for Numerical Analysis in Science and Engineering", publisher = "CRC Press, Taylor and Francis Group", address = "Boca Raton, FL, USA", pages = "xxii + 335", year = "2014", ISBN = "1-4398-8448-X (hardcover)", ISBN-13 = "978-1-4398-8448-5 (hardcover)", LCCN = "Q183.9 .B56 2014", bibdate = "Mon Sep 28 08:51:19 MDT 2015", bibsource = "http://www.math.utah.edu/pub/tex/bib/jrss-a-2010.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/s-plus.bib; z3950.loc.gov:7090/Voyager", series = "Chapman and Hall/CRC the R series", URL = "http://www.crcnetbase.com/isbn/9781439884492", abstract = "This book shows how the free and open-source R environment can be used as a powerful and comprehensive platform for the kinds of numerical analysis that are traditionally employed by MATLAB. With R code fully integrated, the book offers brief descriptions of basic approaches and emphasizes detailed worked examples. It covers functions in the base installation of R as well as those in contributed packages, which greatly enhance the numerical analysis capabilities of R''-- ``The complex mathematical problems faced by scientists and engineers rarely can be solved by analytical approaches, so numerical methods are often necessary. There are many books that deal with numerical methods for scientists and engineers; their content is fairly standardized: solution of systems of linear algebraic equations and nonlinear equations, finding eigenvalues and eigenfunctions, interpolation and curve fitting, numerical differentiation and integration, optimization, solution of ordinary differential equations and partial differential equations, and Fourier analysis. Sometimes statistical analysis of data is included, as it should be. As powerful personal computers have become virtually universal on the desks of scientists and engineers, computationally intensive Monte Carlo methods are joining the numerical analysis armamentarium. If there are many books on these well-established topics, why am I writing another one? The answer is to propose and demonstrate the use of a language relatively new to the field: R. My approach in this book is not to present the standard theoretical treatments that underlie the various numerical methods used by scientists and engineers. There are many fine books and online resources that do that, including one that uses R: Owen Jones, Robert Maillardet, and Andrew Robinson. Introduction to Scientific Programming and Simulation Using R. Chapman and Hall/CRC, Boca Raton, FL, 2009. Instead, I have tried to write a guide to the capabilities of R and its add-on packages in the realm of numerical methods, with simple but useful examples of how the most pertinent functions can be employed in practical situations.", acknowledgement = ack-nhfb, subject = "Science; Data processing; Engineering; Numerical analysis; R (Computer program language); MATHEMATICS / General.; MATHEMATICS / Number Systems.; MATHEMATICS / Probability and Statistics / General.", tableofcontents = "1. Introduction \\ 2. Calculating \\ 3. Graphing \\ 4. Programming and functions \\ 5. Solving systems of algebraic equations \\ 6. Numerical differentiation and integration \\ 7. Optimization \\ 8. Ordinary differential equations \\ 9. Partial differential equations \\ 10. Analyzing data \\ 11. Fitting models to data", } @Article{Borrelli:2014:BRB, author = "Arianna Borrelli", title = "Book Review: {{\booktitle{Le destin douloureux de Walther Ritz (1878--1909), physicien th{\'e}oricien de g{\'e}nie}}, Jean-Claude Pont (Ed.). Vallesia, Archive de l'{\'E}tat du Valais, Sion (2012), ISBN 978-2-9700636-5-0}", journal = j-HIST-MATH, volume = "41", number = "1", pages = "107--110", month = feb, year = "2014", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Mon Apr 21 12:33:22 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/histmath.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0315086013000396", acknowledgement = ack-nhfb, fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860/", } @Book{Boyd:2014:STE, author = "John P. (John Philip) Boyd", title = "Solving transcendental equations: the {Chebyshev} polynomial proxy and other numerical rootfinders, perturbation series, and oracles", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xviii + 460", year = "2014", ISBN = "1-61197-351-1 (paperback)", ISBN-13 = "978-1-61197-351-8 (paperback)", LCCN = "QA353.T7 B69 2014", bibdate = "Wed Sep 23 17:10:53 MDT 2015", bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/enhancements/fy1503/2014017078-b.html; http://www.loc.gov/catdir/enhancements/fy1503/2014017078-d.html; http://www.loc.gov/catdir/enhancements/fy1503/2014017078-t.html", acknowledgement = ack-nhfb, author-dates = "1951--", subject = "Transcendental functions; Chebyshev polynomials; Transcendental numbers", tableofcontents = "I: Introduction and overview \\ Introduction: Key themes in rootfinding \\ II: the Chebyshev-Proxy rootfinder and its generalizations \\ The Chebyshev-Proxy/Companion matrix rootfinder \\ Adaptive Chebyshev interpolation \\ Adaptive Fourier interpolation and rootfinding \\ Complex zeros: Interpolation on a disk, the Delves--Lyness algorithm, and contour integrals \\ III: Fundamentals: Iterations, bifurcation, and continuation \\ Newton iteration and its kin \\ Bifurcation theory \\ Continuation in a parameter \\ IV: Polynomials \\ Polynomial equations and the irony of Galois Theory \\ The Quadratic Equation \\ Roots of a cubic polynomial \\ Roots of a quartic polynomial \\ V: Analytical methods \\ Methods for explicit solutions \\ Regular perturbation methods for roots \\ Singular perturbation methods: fractional powers, logarithms, and exponential asymptotics \\ VI: Classics, special functions, inverses, and oracles \\ Classical methods for solving one equation in one unknown \\ Special algorithms for special functions \\ Inverse functions of one unknown \\ Oracles: Theorems and algorithms for determining the existence, nonexistence, and number of zeros \\ VII: Bivariate systems \\ Two equations in two unknowns \\ VIII: Challenges \\ Past and future \\ A: Companion matrices \\ B: Chebyshev interpolation and quadrature \\ Marching triangles \\ D: Imbricate-Fourier series and the Poisson Summation Theorem", } @Book{Brandt:2014:DAS, author = "Siegmund Brandt", title = "Data analysis: statistical and computational methods for scientists and engineers", publisher = pub-SV, address = pub-SV:adr, edition = "Fourth", pages = "????", year = "2014", DOI = "https://doi.org/10.1007/978-3-319-03762-2", ISBN = "3-319-03762-5 (e-book)", ISBN-13 = "978-3-319-03762-2 (e-book), 978-3-319-03761-5, 978-3-319-03761-5", LCCN = "QA273; QA273", bibdate = "Sun May 4 11:27:21 MDT 2014", bibsource = "catalog.princeton.edu:7090/voyager; http://www.math.utah.edu/pub/tex/bib/java2010.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/probstat2010.bib; libraries.colorado.edu:210/INNOPAC", abstract = "The fourth edition of this successful textbook presents a comprehensive introduction to statistical and numerical methods for the evaluation of empirical and experimental data. Equal weight is given to statistical theory and practical problems. The concise mathematical treatment of the subject matter is illustrated by many examples, and for the present edition a library of Java programs has been developed. It comprises methods of numerical data analysis and graphical representation as well as many example programs and solutions to programming problems. The programs (source code, Java classes, and documentation) and extensive appendices to the main text are available for free download from the books page at www.springer.com. Contents Probabilities. Random variables. Random numbers and the Monte Carlo Method. Statistical distributions (binomial, Gauss, Poisson). Samples. Statistical tests. Maximum Likelihood. Least Squares. Regression. Minimization. Analysis of Variance. Time series analysis. Audience The book is conceived both as an introduction and as a work of reference. In particular it addresses itself to students, scientists and practitioners in science and engineering as a help in the analysis of their data in laboratory courses, working for bachelor or master degrees, in thesis work, and in research and professional work. The book is concise, but gives a sufficiently rigorous mathematical treatment of practical statistical methods for data analysis; it can be of great use to all who are involved with data analysis. Physicalia. This lively and erudite treatise covers the theory of the main statistical tools and their practical applications. A first rate university textbook, and good background material for the practicing physicist. Physics Bulletin.", acknowledgement = ack-nhfb, subject = "Probabilities; Mathematical statistics", tableofcontents = "Introduction \\ Probabilities \\ Random Variables: Distributions \\ Computer-Generated Random Numbers: The Monte Carlo Method \\ Some Important Distributions and Theorems \\ Samples \\ The Method of Maximum Likelihood \\ Testing Statistical Hypotheses \\ The Method of Least Squares \\ Function Minimization \\ Analysis of Variance \\ Linear and Polynomial Regression \\ Time-Series Analysis \\ (A) Matrix Calculations \\ (B) Combinatorics \\ (C) Formulas and Methods for the Computation of Statistical Functions \\ (D) The Gamma Function and Related Functions: Methods and Programs for their Computation \\ (E) Utility Programs \\ (F) The Graphics Class DatanGraphics \\ (G) Problems, Hints and Solutions and Programming Problems \\ (H) Collection of Formulas \\ (I) Statistical Formulas \\ List of Computer Programs", } @Book{Bronson:2014:LAA, author = "Richard Bronson and Gabriel B. Costa and John T. Saccoman", title = "Linear Algebra: Algorithms, Applications, and Techniques", publisher = pub-ELSEVIER-ACADEMIC, address = pub-ELSEVIER-ACADEMIC:adr, edition = "Third", pages = "xi + 519", year = "2014", ISBN = "0-12-391420-5 (paperback), 0-12-397811-4 (e-book)", ISBN-13 = "978-0-12-391420-0 (paperback), 978-0-12-397811-0 (e-book)", LCCN = "QA184.2 .B76 2014", bibdate = "Mon Sep 15 18:03:00 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.sciencedirect.com/science/book/9780123914200", acknowledgement = ack-nhfb, subject = "Algebras, Linear; Lineare Algebra.", tableofcontents = "1: Matrices / 1--91 \\ 2: Vector Spaces / 93--173 \\ 3: Linear Transformations / 175--235 \\ 4: Eigenvalues, Eigenvectors, and Differential Equations / 237--288 \\ 5: Applications of Eigenvalues / 289--321 \\ 6: Euclidean Inner Product / 323--378 \\ Appendix A: Jordan Canonical Forms / 379--411 \\ Appendix B: Markov Chains / 413--424 \\ Appendix C: More on Spanning Trees of Graphs / 425--431 \\ Appendix D: Technology / 433--434 \\ Appendix E: Mathematical Induction / 435 \\ Answers and Hints to Selected Problems / 437--514", } @Book{Colonius:2014:DSL, author = "Fritz Colonius and Wolfgang Kliemann", title = "Dynamical Systems and Linear Algebra", volume = "ume 158", publisher = pub-AMS, address = pub-AMS:adr, pages = "????", year = "2014", ISBN = "0-8218-8319-4", ISBN-13 = "978-0-8218-8319-8", LCCN = "QA184.2 .C65 2014", MRclass = "15-01 34-01 37-01 39-01 60-01 93-01", bibdate = "Mon Sep 15 18:24:05 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Graduate studies in mathematics", acknowledgement = ack-nhfb, subject = "Algebras, Linear; Topological dynamics; Linear and multilinear algebra; matrix theory -- Instructional exposition (textbooks, tutorial papers, etc.).; Ordinary differential equations -- Instructional exposition (textbooks, tutorial papers, etc.).; Dynamical systems and ergodic theory -- Instructional exposition (textbooks, tutorial papers, etc.).; Difference and functional equations -- Instructional exposition (textbooks, tutorial papers, etc.).; Probability theory and stochastic processes -- Instructional exposition (textbooks, tutorial papers, etc.).; Systems theory; control -- Instructional exposition (textbooks, tutorial papers, etc.).", } @Book{Gruber:2014:MAL, author = "Marvin H. J. Gruber", title = "Matrix Algebra for Linear Models", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xv + 375", year = "2014", ISBN = "1-118-59255-7 (hardcover), 1-118-60881-X (e-book), 1-118-60874-7 (e-book), 1-118-80041-9 (e-book)", ISBN-13 = "978-1-118-59255-7 (hardcover), 978-1-118-60881-4 (e-book), 978-1-118-60874-6 (e-book), 978-1-118-80041-6 (e-book)", LCCN = "QA279 .G78 2014", bibdate = "Mon Sep 15 18:17:46 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "Linear models (Statistics); Matrices", } @Book{Hanson:2014:NCM, author = "Richard J. Hanson and Tim Hopkins", title = "Numerical computing with modern {Fortran}", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xv + 244", year = "2014", ISBN = "1-61197-311-2 (paperback), 1-61197-312-0 (e-book)", ISBN-13 = "978-1-61197-311-2 (paperback), 978-1-61197-312-9 (e-book)", LCCN = "QA76.73.F25 H367 2013", bibdate = "Wed Mar 12 11:09:16 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/fortran3.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/pvm.bib; z3950.loc.gov:7090/Voyager", series = "Applied mathematics", abstract = "The Fortran language standard has undergone significant upgrades in recent years (1990, 1995, 2003, and 2008). \booktitle{Numerical Computing with Modern Fortran} illustrates many of these improvements through practical solutions to a number of scientific and engineering problems. Readers will discover: techniques for modernizing algorithms written in Fortran; examples of Fortran interoperating with C or C++ programs, plus using the IEEE floating-point standard for efficiency; illustrations of parallel Fortran programming using coarrays, MPI, and OpenMP; and a supplementary website with downloadable source codes discussed in the book.", acknowledgement = ack-nhfb, subject = "FORTRAN (Computer program language); Numerical analysis; Computer programs; Science; Mathematics", tableofcontents = "Introduction \\ The modern Fortran source \\ Modules for subprogram libraries \\ Generic subprograms \\ Sparse matrices, defined operations, overloaded assignment \\ Object-oriented programming for numerical applications \\ Recursion in Fortran \\ Case study: toward a modern QUADPACK routine \\ Case study: quadrature routine qag2003 \\ IEEE arithmetic features and exception handling \\ Interoperability with C \\ Defined operations for sparse matrix solutions \\ Case study: two sparse least-squares system examples \\ Message passing with MPI in standard Fortran \\ Coarrays in standard Fortran \\ OpenMP in Fortran \\ Modifying source to remove obsolescent or deleted features \\ Software testing \\ Compilers \\ Software tools \\ Fortran book code on SIAM web site \\ Bibliography \\ Index", } @Book{Hogben:2014:HLA, editor = "Leslie Hogben", title = "Handbook of Linear Algebra", publisher = "CRC Press/Taylor and Francis Group", address = "Boca Raton, FL, USA", edition = "Second", pages = "????", year = "2014", ISBN = "1-4665-0728-4 (hardcover)", ISBN-13 = "978-1-4665-0728-9 (hardcover)", LCCN = "QA184.2 .H36 2014", bibdate = "Mon Sep 15 18:11:33 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Discrete mathematics and its applications", URL = "http://marc.crcnetbase.com/isbn/9781466507296", abstract = "Preface to the Second Edition: Both the format and guiding vision of \booktitle{Handbook of Linear Algebra remain} unchanged, but a substantial amount of new material has been included in the second edition. The length has increased from 1400 pages to 1900 pages. There are 20 new chapters. Subjects such as Schur complements, special types of matrices, generalized inverses, matrices over nite elds, and invariant subspaces are now treated in separate chapters. There are additional chapters on applications of linear algebra, for example, to epidemiology. There is a new chapter on using the free open source computer mathematics system Sage for linear algebra, which also provides a general introduction to Sage. Additional surveys of currently active research topics such as tournaments are also included. Many of the existing articles have been revised and updated, in some cases adding a substantial amount of new material. For example, the chapters on sign pattern matrices and on applications to geometry have additional sections. As was true in the rst edition, the topics range from the most basic linear algebra to advanced topics including background for active research areas. In this edition, many of the chapters on advanced topics now include Conjectures and Open Problems, either as a part of some sections or as a new section at the end of the chapter. The conjectures and questions listed in such sections have been in the literature for more than ve years at the time of writing, and often a number of partial results have been obtained. In most cases, the current (at the time of writing) state of research related to the question is summarized as facts. Of course, there is no guarantee that (years after the writing date) such problems have not been solved (in fact, we hope they \ldots{})''", acknowledgement = ack-nhfb, subject = "Algebras, Linear; MATHEMATICS / General.; MATHEMATICS / Algebra / General.; MATHEMATICS / Applied.", tableofcontents = "Front Cover \\ Dedication \\ Acknowledgments \\ The Editor \\ Contributors \\ Contents \\ Preface \\ Preliminaries \\ I. Linear Algebra \\ Linear Algebra \\ 1. Vectors, Matrices, and Systems of Linear Equations \\ 2. Linear Independence, Span, and Bases \\ 3. Linear Transformations \\ 4. Determinants and Eigenvalues \\ 5. Inner Product Spaces, Orthogonal Projection, Least Squares, and Singular Value Decomposition \\ 6. Canonical Forms for Similarity \\ 7. Other Canonical Forms \\ 8. Unitary Similarity, Normal Matrices, and Spectral Theory \\ 9. Hermitian and Positive Definite Matrices \\ 10. Nonnegative Matrices and Stochastic Matrices \\ 11. Partitioned Matrices \\ Topics in Linear Algebra \\ 12. Schur Complements \\ 13. Quadratic, Bilinear, and Sesquilinear Forms \\ 14. Multilinear Algebra \\ 15. Tensors and Hypermatrices \\ 16. Matrix Equalities and Inequalities \\ 17. Functions of Matrices \\ 18. Matrix Polynomials \\ 19. Matrix Equations \\ 20. Invariant Subspaces \\ 21. Matrix Perturbation Theory \\ 22. Special Types of Matrices \\ 23. Pseudospectra \\ 24. Singular Values and Singular Value Inequalities \\ 25. Numerical Range \\ 26. Matrix Stability and Inertia \\ 27. Generalized Inverses of Matrices \\ 28. Inverse Eigenvalue Problems \\ 29. Totally Positive and Totally Nonnegative Matrices \\ 30. Linear Preserver Problems \\ 31. Matrices over Finite Fields \\ 32. Matrices over Integral Domains \\ 33. Similarity of Families of Matrices \\ 34. Representations of Quivers and Mixed Graphs \\ 35. Max-Plus Algebra \\ 36. Matrices Leaving a Cone Invariant \\ 37. Spectral Sets \\ II. Combinatorial Matrix Theory and Graphs \\ Combinatorial Matrix Theory \\ 38. Combinatorial Matrix Theory \\ 39. Matrices and Graphs \\ 40. Digraphs and Matrices \\ 41. Bipartite Graphs and Matrices \\ 42. Sign Pattern Matrices: Topics in Combinatorial Matrix Theory \\ 43. Permanents \\ 44. D-Optimal Matrices \\ 45. Tournaments \\ 46. Minimum Rank, Maximum Nullity, and Zero Forcing Number of Graphs \\ 47. Spectral Graph Theory \\ 48. Algebraic Connectivity \\ 49. Matrix Completion Problems \\ III. Numerical Methods \\ Numerical Methods for Linear Systems \\ 50. Vector and Matrix Norms, Error Analysis, Efficiency, and Stability \\ 51. Matrix Factorizations and Direct Solution of Linear Systems \\ 52. Least Squares Solution of Linear Systems \\ 53. Sparse Matrix Methods \\ 54. Iterative Solution Methods for Linear Systems: Numerical Methods for Eigenvalues \\ 55. Symmetric Matrix Eigenvalue Techniques \\ 56. Unsymmetric Matrix Eigenvalue Techniques \\ 57. The Implicitly Restarted Arnoldi Method \\ 58. Computation of the Singular Value Decomposition \\ 59. Computing Eigenvalues and Singular Values to High Relative Accuracy \\ 60. Nonlinear Eigenvalue Problems \\ Topics in Numerical Linear Algebra \\ 61. Fast Matrix Multiplication \\ 62. Fast Algorithms for Structured Matrix Computations \\ 63. Structured Eigenvalue Problems: Structure-Preserving Algorithms, Structured Error Analysis \\ 64. Large-Scale Matrix Computations", } @Book{Hunt:2014:GMB, author = "Brian R. Hunt and Ronald L. Lipsman and Jonathan M. (Jonathan Micah) Rosenberg", title = "A guide to {MATLAB}: for beginners and experienced users: updated for {MATLAB 8} and {Simulink 8}", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, edition = "Third", pages = "????", year = "2014", ISBN = "1-107-66222-2 (paperback)", ISBN-13 = "978-1-107-66222-3 (paperback)", LCCN = "QA297 .H86 2014", bibdate = "Thu Aug 28 08:17:57 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", abstract = "MATLAB is a high-level language and interactive environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages.", acknowledgement = ack-nhfb, subject = "MATLAB; Numerical analysis; Data processing; MATHEMATICS / General.", tableofcontents = "Preface \\ 1. Getting started \\ 2. MATLAB basics \\ 3. Interacting with MATLAB \\ Practice Set A. Algebra and arithmetic \\ 4. Beyond the basics \\ 5. MATLAB graphics \\ 6. MATLAB programming \\ 7. Publishing and M-books \\ Practice Set B. Math, graphics, and programming \\ 8. MuPAD \\ 9. Simulink \\ 10. GUIs \\ 11. Applications \\ Practice Set C. Developing your MATLAB skills \\ 12. Troubleshooting \\ Solutions to the practice sets \\ Glossary \\ Index", } @Book{Jones:2014:ISP, author = "Owen (Owen Dafydd) Jones and Robert Maillardet and Andrew (Andrew P.) Robinson", title = "Introduction to scientific programming and simulation using {R}", publisher = pub-CRC, address = pub-CRC:adr, edition = "Second", pages = "xxiv + 582", year = "2014", ISBN = "1-4665-6999-9, 1-4665-7001-6", ISBN-13 = "978-1-4665-6999-7, 978-1-4665-7001-6", LCCN = "Q183.9 .J65 2014", bibdate = "Thu Jul 21 05:52:46 MDT 2016", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/s-plus.bib; z3950.loc.gov:7090/Voyager", series = "The R series", acknowledgement = ack-nhfb, subject = "Science; Data processing; Computer simulation; Stochastic processes; Mathematical models; Numerical analysis; Computer programming; R (Computer program language); Computer simulation; Data processing", } @Book{Kushner:2014:NMS, author = "Harold J. Kushner and Paul Dupuis", title = "Numerical Methods for Stochastic Control Problems in Continuous Time", volume = "24", publisher = pub-SV, address = pub-SV:adr, edition = "Second", pages = "xii + 476", year = "2014", DOI = "https://doi.org/10.1007/978-1-4613-0007-6", ISBN = "1-4612-6531-2", ISBN-13 = "978-1-4612-6531-3", ISSN = "0172-4568", ISSN-L = "0172-4568", LCCN = "QA273.A1-274.9; QA274-274.9", bibdate = "Tue Apr 29 18:44:55 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/probstat2010.bib; prodorbis.library.yale.edu:7090/voyager", series = "Stochastic Modelling and Applied Probability", abstract = "This book presents a comprehensive development of effective numerical methods for stochastic control problems in continuous time. The process models are diffusions, jump-diffusions, or reflected diffusions of the type that occur in the majority of current applications. All the usual problem formulations are included, as well as those of more recent interest such as ergodic control, singular control and the types of reflected diffusions used as models of queuing networks. Applications to complex deterministic problems are illustrated via application to a large class of problems from the calculus of variations. The general approach is known as the Markov Chain Approximation Method. The required background to stochastic processes is surveyed, there is an extensive development of methods of approximation, and a chapter is devoted to computational techniques. The book is written on two levels, that of practice (algorithms and applications) and that of the mathematical development. Thus the methods and use should be broadly accessible. This update to the first edition will include added material on the control of the 'jump term' and the 'diffusion term.' There will be additional material on the deterministic problems, solving the Hamilton-Jacobi equations, for which the authors' methods are still among the most useful for many classes of problems. All of these topics are of great and growing current interest.", acknowledgement = ack-nhfb, subject = "Mathematics; System theory; Mathematical optimization; Distribution (Probability theory)", tableofcontents = "Review of Continuous Time Models \\ Controlled Markov Chains \\ Dynamic Programming Equations \\ Markov Chain Approximation Method \\ The Approximating Markov Chains \\ Computational Methods \\ The Ergodic Cost Problem \\ Heavy Traffic and Singular Control \\ Weak Convergence and the Characterization of Processes \\ Convergence Proofs \\ Convergence Proofs Continued \\ Finite Time and Filtering Problems \\ Controlled Variance and Jumps \\ Problems from the Calculus of Variations: Finite Time Horizon \\ Problems from the Calculus of Variations: Infinite Time Horizon \\ The Viscosity Solution Approach", } @Book{Lay:2014:LAAb, author = "David C. Lay", title = "Linear Algebra and its Applications", publisher = "Pearson Education Limited", address = "Harlow, Essex", edition = "Fourth", pages = "ii + 784", year = "2014", ISBN = "1-292-02055-5", ISBN-13 = "978-1-292-02055-6", LCCN = "????", bibdate = "Mon Sep 15 18:22:44 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", acknowledgement = ack-nhfb, remark = "Oorspr. uitg.: 1994.", subject = "Lineaire algebra.; Toepassingen.", tableofcontents = "Linear Equations in Linear Algebra \\ Matrix Algebra \\ Determinants \\ Vector Spaces \\ Eigenvalues and Eigenvectors \\ Orthogonality and Least Squares \\ Symmetric Matrices and Quadratic Forms \\ The Geometry of Vector Spaces \\ Appendix: Uniqueness of the Reduced Echelon Form \\ Complex Numbers \\ Study guide for each chapter", } @Book{Miller:2014:NAE, author = "G. Miller", title = "Numerical Analysis for Engineers and Scientists", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "x + 572", year = "2014", DOI = "https://doi.org/10.1017/CBO9781139108188", ISBN = "1-107-02108-1 (hardcover), 1-139-10818-2 (ebook)", ISBN-13 = "978-1-107-02108-2 (hardcover), 978-1-139-10818-8 (ebook)", LCCN = "QA297 .M55 2014", bibdate = "Tue Aug 12 15:47:25 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", acknowledgement = ack-nhfb, } @Book{Nassif:2014:INA, author = "Nabil Nassif and Dolly Khuwayri Fayyad", title = "Introduction to Numerical Analysis and Scientific Computing", publisher = pub-CRC, address = pub-CRC:adr, pages = "xix + 311", year = "2014", ISBN = "1-4665-8948-5 (hardcover)", ISBN-13 = "978-1-4665-8948-3 (hardcover)", LCCN = "QA297 .N37 2014", MRclass = "65-01", MRnumber = "3112293", bibdate = "Tue May 27 11:27:40 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", abstract = "Designed for a one-semester course on the subject, this classroom-tested text presents fundamental concepts of numerical mathematics and explains how to implement and program numerical methods. Drawing on their years of teaching students in mathematics, engineering, and the sciences, the authors cover floating-point number representations, nonlinear equations, linear algebra concepts, the Lagrange interpolation theorem, numerical differentiation and integration, and ODEs. They also focus on the implementation of the algorithms using MATLAB.\par This work is the result of several years of teaching a one-semester course on Numerical Analysis and Scienti c Computing, addressed primarily to stu- dents in Mathematics, Engineering, and Sciences. Our purpose is to provide those students with fundamental concepts of Numerical Mathematics and at the same time stir their interest in the art of implementing and programming Numerical Methods.", acknowledgement = ack-nhfb, subject = "Numerical analysis; Textbooks; Computer science; Mathematics; MATHEMATICS / Advanced.; MATHEMATICS / Applied.; MATHEMATICS / Number Systems.", } @Book{Quarteroni:2014:SCM, author = "Alfio Quarteroni and Fausto Saleri and Paola Gervasio", title = "Scientific computing with {Matlab} and {Octave}", volume = "2", publisher = pub-SV, address = pub-SV:adr, pages = "xviii + 450 (est.)", year = "2014", DOI = "https://doi.org/10.1007/978-3-642-45367-0", ISBN = "3-642-45366-X (hard cover)", ISBN-13 = "978-3-642-45366-3 (hard cover)", LCCN = "????", bibdate = "Sun Apr 13 16:57:12 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Texts in Computational Science and Engineering", URL = "http://link.springer.com/book/10.1007/978-3-642-45367-0", acknowledgement = ack-nhfb, tableofcontents = "Front Matter / i--xviii \\ What can't be ignored / 1--40 \\ Nonlinear equations / 41--76 \\ Approximation of functions and data / 77--111 \\ Numerical differentiation and integration / 113--136 \\ Linear systems / 137--191 \\ Eigenvalues and eigenvectors / 193--211 \\ Numerical optimization / 213--269 \\ Ordinary differential equations / 271--328 \\ Numerical approximation of boundary-value problems / 329--376 \\ Solutions of the exercises / 377--428 \\ Back Matter / 429--450", } @Book{Rossant:2014:IIC, author = "Cyrille Rossant", title = "{IPython} interactive computing and visualization cookbook: over 100 hands-on recipes to sharpen your skills in high-performance numerical computing and data science with {Python}", publisher = "Packt Publishing Ltd.", address = "Birmingham, UK", pages = "v + 494", year = "2014", ISBN = "1-78328-481-1, 1-78328-482-X (e-book), 1-322-16622-6 (e-book)", ISBN-13 = "978-1-78328-481-8, 978-1-78328-482-5 (e-book), 978-1-322-16622-3 (e-book)", LCCN = "QA76.73.P98 R677 2014", bibdate = "Sat Mar 21 07:16:36 MDT 2015", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/python.bib", abstract = "IPython Interactive Computing and Visualization Cookbook contains many ready-to-use focused recipes for high-performance scientific computing and data analysis. The first part covers programming techniques, including code quality and reproducibility, code optimization, high-performance computing through dynamic compilation, parallel computing, and graphics card programming. The second part tackles data science, statistics, machine learning, signal and image processing, dynamical systems, and pure and applied mathematics.", acknowledgement = ack-nhfb, subject = "Python (Computer program language); Command languages (Computer science); Information visualization; Interactive computer systems; Command languages (Computer science); Information visualization; Interactive computer systems; Python (Computer program language)", } @Book{Stewart:2014:PS, author = "John Stewart", title = "Python for scientists", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "????", year = "2014", ISBN = "1-107-06139-3 (hardcover), 1-107-68642-3", ISBN-13 = "978-1-107-06139-2 (hardcover), 978-1-107-68642-7", LCCN = "Q183.9 .S865 2014", bibdate = "Thu Jun 26 09:42:41 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/python.bib", URL = "http://assets.cambridge.org/97811070/61392/cover/9781107061392.jpg", abstract = "Python is a free, open source, easy-to-use software tool that offers a significant alternative to proprietary packages such as MATLAB and Mathematica. This book covers everything the working scientist needs to know to start using Python effectively. The author explains scientific Python from scratch, showing how easy it is to implement and test non-trivial mathematical algorithms and guiding the reader through the many freely available add-on modules. A range of examples, relevant to many different fields, illustrate the program's capabilities. In particular, readers are shown how to use pre-existing legacy code (usually in Fortran77) within the Python environment, thus avoiding the need to master the original code. Instead of exercises the book contains useful snippets of tested code which the reader can adapt to handle problems in their own field, allowing students and researchers with little computer expertise to get up and running as soon as possible.", acknowledgement = ack-nhfb, author-dates = "1943 July 1", subject = "Science; Data processing; Python (Computer program language); COMPUTERS / General.", tableofcontents = "Preface \\ 1. Introduction \\ 2. Getting started with IPython \\ 3. A short Python tutorial \\ 4. Numpy \\ 5. Two-dimensional graphics \\ 6. Three-dimensional graphics \\ 7. Ordinary differential equations \\ 8. Partial differential equations: a pseudospectral approach \\ 9. Case study: multigrid \\ Appendix A. Installing a Python environment \\ Appendix B. Fortran77 subroutines for pseudospectral methods \\ References \\ Index", } @Book{Stys:2014:LNN, author = "Tadeusz Sty{\'s} and Krystyna Sty{\'s}", title = "Lecture Notes in Numerical Analysis with {Mathematica}", publisher = "Bentham Science Publishers, Inc.", address = "Sharjah, United Arab Emirates", pages = "243", year = "2014", DOI = "https://doi.org/10.2174/97816080594231140101", ISBN = "1-60805-942-1 (e-book), 1-60805-943-X", ISBN-13 = "978-1-60805-942-3 (e-book), 978-1-60805-943-0", LCCN = "QA298 .S797 2014", bibdate = "Tue Apr 28 16:22:45 MDT 2015", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/mathematica.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", URL = "http://ebooks.benthamsciencepublisher.org/book/9781608059423/", acknowledgement = ack-nhfb, subject = "Numerical analysis; Simulation methods; Mathematical physics; Data processing; MATHEMATICS / Numerical Analysis", tableofcontents = "Foreword / O. A. Daman / i \\ Preface / iii--iv (2) \\ The List of Mathematica Functions and Modulae / v \\ Floating Point Computer Arithmetic / 1--26 (26) \\ Natural and Generalized Interpolating Polynomials / 27--62 (36) \\ Polynomial Splines / 63--102 (40) \\ Uniform Approximation / 103--132 (30) \\ Introduction to the Least Squares Analysis / 133--156 (24) \\ Selected Methods for Numerical Integration / 157--198 (42) \\ Solving Nonlinear Equations by Iterative Methods / 199--229 (31) \\ References / 230--231 (2) \\ Index / 233--235 (3)", } @Book{Hill:2015:LSP, author = "Christian Hill", title = "Learning scientific programming with {Python}", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "vii + 452", year = "2015", ISBN = "1-107-07541-6 (hardcover), 1-107-42822-X (paperback)", ISBN-13 = "978-1-107-07541-2 (hardcover), 978-1-107-42822-5 (paperback)", LCCN = "Q183.9 .H58 2015", bibdate = "Mon Aug 21 08:44:22 MDT 2017", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/python.bib; z3950.loc.gov:7090/Voyager", abstract = "Learn to master basic programming tasks from scratch with real-life scientifically relevant examples and solutions drawn from both science and engineering. Students and researchers at all levels are increasingly turning to the powerful Python programming language as an alternative to commercial packages and this fast-paced introduction moves from the basics to advanced concepts in one complete volume, enabling readers to quickly gain proficiency. Beginning with general programming concepts such as loops and functions within the core Python 3 language, and moving onto the NumPy, SciPy and Matplotlib libraries for numerical programming and data visualisation, this textbook also discusses the use of IPython notebooks to build rich-media, shareable documents for scientific analysis. Including a final chapter introducing challenging topics such as floating-point precision and algorithm stability, and with extensive online resources to support advanced study, this textbook represents a targeted package for students requiring a solid foundation in Python programming.", acknowledgement = ack-nhfb, author-dates = "1974--", subject = "Science; Data processing; Mathematics; Python (Computer program language); SCIENCE / Mathematical Physics.", tableofcontents = "1. Introduction \\ 2. The core Python language I \\ 3. Interlude: simple plotting with Pylab \\ 4. The core Python language II \\ 5. IPython and IPython notebook \\ 6. NumPy \\ 7. Matplotlib \\ 8. SciPy \\ 9. General scientific programming \\ Appendix A \\ Solutions \\ Index", } @Book{Mehta:2015:MPS, author = "Hemant Kumar Mehta", title = "Mastering {Python} scientific computing: a complete guide for {Python} programmers to master scientific computing using {Python APIs} and tools", publisher = pub-PACKT, address = pub-PACKT:adr, pages = "????", year = "2015", ISBN = "1-78328-883-3, 1-78328-882-5", ISBN-13 = "978-1-78328-883-0, 978-1-78328-882-3", LCCN = "QA76.73.P98", bibdate = "Fri Oct 23 15:54:07 MDT 2015", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/python.bib", series = "Community experience distilled", URL = "http://proquest.safaribooksonline.com/?fpi=9781783288823", acknowledgement = ack-nhfb, subject = "Python (Computer program language); Computer science", tableofcontents = "Mastering Python Scientific Computing \\ Table of Contents \\ Mastering Python Scientific Computing \\ Credits \\ About the Author \\ About the Reviewers \\ www.PacktPub.com \\ Support files, eBooks, discount offers, and more \\ Why subscribe? \\ Free access for Packt account holders \\ Preface \\ What this book covers \\ What you need for this book \\ Who this book is for \\ Conventions \\ Reader feedback \\ Customer support \\ Downloading the example code \\ Downloading the color images of this book \\ Errata \\ Piracy \\ Questions \\ 1. The Landscape of Scientific Computing --- and Why Python? \\ Definition of scientific computing \\ A simple flow of the scientific computation process \\ Examples from scientific/engineering domains \\ A strategy for solving complex problems \\ Approximation, errors, and associated concepts and terms \\ Error analysis \\ Conditioning, stability, and accuracy \\ Backward and forward error analysis \\ Is it okay to ignore these errors? \\ Computer arithmetic and floating-point numbers \\ The background of the Python programming language \\ The guiding principles of the Python language \\ Why Python for scientific computing? \\ Compact and readable code \\ Holistic language design \\ Free and open source \\ Language interoperability \\ Portable and extensible \\ Hierarchical module system \\ Graphical user interface packages \\ Data structures \\ Python's testing framework \\ Available libraries \\ The downsides of Python \\ Summary \\ 2. A Deeper Dive into Scientific Workflows and the Ingredients of Scientific Computing Recipes \\ Mathematical components of scientific computations \\ A system of linear equations \\ A system of nonlinear equations \\ Optimization \\ Interpolation \\ Extrapolation \\ Numerical integration \\ Numerical differentiation \\ Differential equations \\ The initial value problem \\ The boundary value problem \\ Random number generator \\ Python scientific computing \\ Introduction to NumPy \\ The SciPy library \\ The SciPy Subpackage \\ Data analysis using pandas \\ A brief idea of interactive programming using IPython \\ IPython parallel computing \\ IPython Notebook \\ Symbolic computing using SymPy \\ The features of SymPy \\ Why SymPy? \\ The plotting library \\ Summary \\ 3. Efficiently Fabricating and Managing Scientific Data \\ The basic concepts of data \\ Data storage software and toolkits \\ Files \\ Structured files \\ Unstructured files \\ Database \\ Possible operations on data \\ Scientific data format \\ Ready-to-use standard datasets \\ Data generation \\ Synthetic data generation (fabrication) \\ Using Python's built-in functions for random number generation \\ Bookkeeping functions \\ Functions for integer random number generation \\ Functions for sequences \\ Statistical-distribution-based functions \\ Nondeterministic random number generator \\ Designing and implementing random number generators based on statistical distributions \\ A program with simple logic to generate five-digit random numbers \\ A brief note about large-scale datasets \\ Summary \\ 4. Scientific Computing APIs for Python \\ Numerical scientific computing in Python \\ The NumPy package \\ The ndarrays data structure \\ File handling \\ Some sample NumPy programs \\ The SciPy package \\ The optimization package \\ The interpolation package \\ Integration and differential equations in SciPy \\ The stats module \\ Clustering package and spatial algorithms in SciPy \\ Image processing in SciPy \\ Sample SciPy programs \\ Statistics using SciPy \\ Optimization in SciPy \\ Image processing using SciPy \\ Symbolic computations using SymPy \\ Computer Algebra System \\ Features of a general-purpose CAS \\ A brief idea of SymPy \\ Core capability \\ Polynomials \\ Calculus \\ Solving equations \\ Discrete math \\ Matrices \\ Geometry \\ Plotting \\ Physics \\ Statistics \\ Printing \\ SymPy modules \\ Simple exemplary programs \\ Basic symbol manipulation \\ Expression expansion in SymPy \\ Simplification of an expression or formula \\ Simple integrations \\ APIs and toolkits for data analysis and visualization \\ Data analysis and manipulation using pandas \\ Important data structures of pandas \\ Special features of pandas \\ Data visualization using matplotlib \\ Interactive computing in Python using IPython \\ Sample data analysis and visualization programs \\ Summary \\ 5. Performing Numerical Computing \\ The NumPy fundamental objects \\ The ndarray object \\ The attributes of an array \\ Basic operations on arrays \\ Special operations on arrays (shape change and conversion) \\ Classes associated with arrays \\ The matrix sub class \\ Masked array \\ The structured/recor array \\ The universal function object \\ Attributes \\ Methods \\ Various available ufunc \\ The NumPy mathematical modules \\ Introduction to SciPy \\ Mathematical functions in SciPy \\ Advanced modules/packages \\ Integration \\ Signal processing (scipy.signal) \\ Fourier transforms (scipy.fftpack) \\ Spatial data structures and algorithms (scipy.spatial) \\ Optimization (scipy.optimize) \\ Interpolation (scipy.interpolate) \\ Linear algebra (scipy.linalg) \\ Sparse eigenvalue problems with ARPACK \\ Statistics (scipy.stats) \\ Multidimensional image processing (scipy.ndimage) \\ Clustering \\ Curve fitting \\ File I/O (scipy.io) \\ Summary \\ 6. Applying Python for Symbolic Computing \\ Symbols, expressions, and basic arithmetic \\ Equation solving \\ Functions for rational numbers, exponentials, and logarithms \\ Polynomials \\ Trigonometry and complex numbers \\ Linear algebra \\ Calculus \\ Vectors \\ The physics module \\ Hydrogen wave functions \\ Matrices and Pauli algebra \\ The quantum harmonic oscillator in 1-D and 3-D \\ Second quantization \\ High-energy Physics \\ Mechanics \\ Pretty printing \\ LaTeX Printing \\ The cryptography module \\ Parsing input \\ The logic module \\ The geometry module \\ Symbolic integrals \\ Polynomial manipulation \\ Sets \\ The simplify and collect operations \\ Summary \\ 7. Data Analysis and Visualization \\ Matplotlib \\ The architecture of matplotlib \\ The scripting layer (pyplot) \\ The artist layer \\ The backend layer \\ Graphics with matplotlib \\ Output generation \\ The pandas library \\ Series \\ DataFrame \\ Panel \\ The common functionality among the data structures \\ Time series and date functions \\ Handling missing data \\ I/O operations \\ Working on CSV files \\ Ready-to-eat datasets \\ The pandas plotting \\ IPython \\ The IPython console and system shell \\ The operating system interface \\ Nonblocking plotting \\ Debugging \\ IPython Notebook \\ Summary \\ 8. Parallel and Large-scale Scientific Computing \\ Parallel computing using IPython \\ The architecture of IPython parallel computing \\ The components of parallel computing \\ The IPython engine \\ The IPython controller \\ IPython view and interfaces \\ The IPython client \\ Example of performing parallel computing \\ A parallel decorator \\ IPython's magic functions \\ Activating specific views \\ Engines and QtConsole \\ Advanced features of IPython \\ Fault-tolerant execution \\ Dynamic load balancing \\ Pushing and pulling objects between clients and engines \\ Database support for storing the requests and results \\ Using MPI in IPython \\ Managing dependencies among tasks \\ Functional dependency \\ Decorators for functional dependency \\ Graph dependency \\ Impossible dependencies \\ The DAG dependency and the NetworkX library \\ Using IPython on an Amazon EC2 cluster with StarCluster \\ A note on security of IPython \\ Well-known parallel programming styles \\ Issues in parallel programming \\ Parallel programming \\ Concurrent programming \\ Distributed programming \\ Multiprocessing in Python \\ Multithreading in Python \\ Hadoop-based MapReduce in Python \\ Spark in Python \\ Summary \\ 9. Revisiting Real-life Case Studies \\ Scientific computing applications developed in Python \\ The one Laptop per Child project used Python for their user interface \\ ExpEYES --- eyes for science \\ A weather prediction application in Python \\ An aircraft conceptual designing tool and API in Python \\ OpenQuake Engine \\ SMS Siemag AG application for energy efficiency \\ Automated code generator for analysis of High-energy Physics data \\ Python for computational chemistry applications \\ Python for developing a Blind Audio Tactile Mapping System \\ TAPTools for air traffic control \\ Energy-efficient lights with an embedded system \\ Scientific computing libraries developed in Python \\ A maritime designing API by Tribon \\ Molecular Modeling Toolkit \\ Standard Python packages \\ Summary \\ 10. Best Practices for Scientific Computing \\ The best practices for designing \\ The implementation of best practices \\ The best practices for data management and application deployment \\ The best practices to achieving high performance \\ The best practices for data privacy and security \\ Testing and maintenance best practices \\ General Python best practices \\ Summary \\ Index", } @Book{Scherzer:2015:HMM, editor = "Otmar Scherzer", booktitle = "Handbook of Mathematical Methods in Imaging", title = "Handbook of Mathematical Methods in Imaging", publisher = "SpringerReference", address = "New York, NY, USA", edition = "Second", pages = "xviii + 2178 (3 volumes)", year = "2015", DOI = "https://doi.org/10.1007/978-1-4939-0790-8", ISBN = "1-4939-0789-1 (set), 1-4939-0790-5 (e-book)", ISBN-13 = "978-1-4939-0789-2 (set), 978-1-4939-0790-8 (e-book)", LCCN = "RC78.7.D53 H358 2015", bibdate = "Sat Aug 13 16:08:19 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", abstract = "The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. This expanded and revised second edition contains updates to existing chapters and 16 additional entries on important mathematical methods such as graph cuts, morphology, discrete geometry, PDEs, conformal methods, to name a few. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 200 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.", acknowledgement = ack-nhfb, subject = "Diagnostic imaging; Mathematical models; Image processing; Digital techniques; Imaging systems in medicine", subject = "Mathematics; Medical radiology; Computer vision; Numerical analysis; Computer vision; Mathematics; Medical radiology; Numerical analysis", tableofcontents = "Front Matter / i-xviii \\ Inverse Problems --- Methods \\ Front Matter / 1--1 \\ Linear Inverse Problems / Charles Groetsch / 3--46 \\ Large-Scale Inverse Problems in Imaging / Julianne Chung, Sarah Knepper, James G. Nagy / 47--90 \\ Regularization Methods for Ill-Posed Problems / Jin Cheng, Bernd Hofmann / 91--123 \\ Distance Measures and Applications to Multimodal Variational Imaging / Christiane P{\"o}schl, Otmar Scherzer / 125--155 \\ Energy Minimization Methods / Mila Nikolova / 157--204 \\ Compressive Sensing / Massimo Fornasier, Holger Rauhut / 205--256 \\ Duality and Convex Programming / Jonathan M. Borwein, D. Russell Luke / 257--304 \\ EM Algorithms / Charles Byrne, Paul P. B. Eggermont / 305--388 \\ EM Algorithms from a Non-stochastic Perspective / Charles Byrne / 389--429 \\ Iterative Solution Methods / Martin Burger, Barbara Kaltenbacher, Andreas Neubauer / 431--470 \\ Level Set Methods for Structural Inversion and Image Reconstruction / Oliver Dorn, Dominique Lesselier / 471--532 \\ Inverse Problems --- Case Examples \\ Front Matter / 533--533 \\ Expansion Methods / Habib Ammari, Hyeonbae Kang / 535--590 \\ Sampling Methods / Martin Hanke-Bourgeois, Andreas Kirsch / 591--647 \\ Inverse Scattering / David Colton, Rainer Kress / 649--700 \\ Electrical Impedance Tomography / Andy Adler, Romina Gaburro, William Lionheart / 701--762 \\ Synthetic Aperture Radar Imaging / Margaret Cheney, Brett Borden / 763--799 \\ Tomography / Gabor T. Herman / 801--845 \\ Microlocal Analysis in Tomography / Venkateswaran P. Krishnan, Eric Todd Quinto / 847--902 \\ Mathematical Methods in PET and SPECT Imaging / Athanasios S. Fokas, George A. Kastis / 903--936 \\ Mathematics of Electron Tomography / Ozan {\"O}ktem / 937--1031 \\ Inverse Problems --- Case Examples Front Matter / 533--533 \\ Optical Imaging / Simon R. Arridge, Jari P. Kaipio, Ville Kolehmainen, Tanja Tarvainen / 1033--1079 \\ Photoacoustic and Thermoacoustic Tomography: Image Formation Principles / Kun Wang, Mark A. Anastasio / 1081--1116 \\ Mathematics of Photoacoustic and Thermoacoustic Tomography / Peter Kuchment, Leonid Kunyansky / 1117--1167 \\ Mathematical Methods of Optical Coherence Tomography / Peter Elbau, Leonidas Mindrinos, Otmar Scherzer / 1169--1204 \\ Wave Phenomena / Matti Lassas, Mikko Salo, Gunther Uhlmann / 1205--1252 \\ Sonic Imaging / Frank Natterer / 1253--1278 \\ Imaging in Random Media / Liliana Borcea / 1279--1340 \\ Image Restoration and Analysis \\ Front Matter / 1341--1341 \\ Statistical Methods in Imaging / Daniela Calvetti, Erkki Somersalo / 1343--1392 \\ Supervised Learning by Support Vector Machines / Gabriele Steidl / 1393--1453 \\ Total Variation in Imaging / V. Caselles, A. Chambolle, M. Novaga / 1455--1499 \\ Numerical Methods and Applications in Total Variation Image Restoration / Raymond Chan, Tony F. Chan, Andy Yip / 1501--1537 \\ Mumford and Shah Model and Its Applications to Image Segmentation and Image Restoration / Leah Bar, Tony F. Chan, Ginmo Chung, Miyoun Jung, Luminita A. Vese, Nahum Kiryati, Nir Sochen / 1539--1597 \\ Local Smoothing Neighborhood Filters / Jean-Michel Morel, Antoni Buades, Tomeu Coll / 1599--1643 \\ Neighborhood Filters and the Recovery of 3D Information / Julie Digne, Mariella Dimiccoli, Neus Sabater, Philippe Salembier / 1645--1673 \\ Splines and Multiresolution Analysis / Brigitte Forster / 1675--1716 \\ Gabor Analysis for Imaging / Ole Christensen, Hans G. Feichtinger, Stephan Paukner / 1717--1757 \\ Shape Spaces / Alain Trouv{\'e}, Laurent Younes / 1759--1817 \\ Variational Methods in Shape Analysis / Martin Rumpf, Benedikt Wirth / 1819--1858 \\ Manifold Intrinsic Similarity / Alexander M. Bronstein, Michael M. Bronstein / 1859--1908 \\ Image Segmentation with Shape Priors: Explicit Versus Implicit Representations / Daniel Cremers / 1909--1944 \\ Image Restoration and Analysis \\ Front Matter / 1341--1341 \\ Optical Flow / Florian Becker, Stefania Petra, Christoph Schn{\"o}rr / 1945--2004 \\ Non-linear Image Registration / Lars Ruthotto, Jan Modersitzki / 2005--2051 \\ Starlet Transform in Astronomical Data Processing / Jean-Luc Starck, Fionn Murtagh, Mario Bertero / 2053--2098 \\ Differential Methods for Multi-dimensional Visual Data Analysis / Werner Benger, Ren{\'e} Heinzl, Dietmar Hildenbrand, Tino Weinkauf, Holger Theisel, David Tschumperl{\'e} / 2099--2162 \\ Back Matter / 2163--2178", } @Book{Snieder:2015:GTM, author = "Roel Snieder and Kasper {Van Wijk}", title = "A Guided Tour of Mathematical Methods for the Physical Sciences", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, edition = "Third", pages = "xxii + 560", year = "2015", DOI = "https://doi.org/10.1017/CBO9781139013543", ISBN = "1-107-08496-2 (hardcover), 1-107-64160-8 (paperback), 1-139-01354-8 (e-book)", ISBN-13 = "978-1-107-08496-4 (hardcover), 978-1-107-64160-0 (paperback), 978-1-139-01354-3 (e-book)", LCCN = "QA300 .S794 2015", bibdate = "Fri Jun 15 08:11:31 MDT 2018", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", abstract = "Mathematical methods are essential tools for all physical scientists. This book provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students across the physical sciences. In contrast to more traditional textbooks, all the material is presented in the form of exercises. Within these exercises, basic mathematical theory and its applications in the physical sciences are well integrated. In this way, the mathematical insights that readers acquire are driven by their physical-science insight. This third edition has been completely revised: new material has been added to most chapters, and two completely new chapters on probability and statistics and on inverse problems have been added. This guided tour of mathematical techniques is instructive, applied, and fun. This book is targeted for all students of the physical sciences. It can serve as a stand-alone text, or as a source of exercises and examples to complement other textbooks.", acknowledgement = ack-nhfb, author-dates = "1958--", subject = "Mathematical analysis; Physical sciences; Mathematics; Mathematical physics; Analyse math{\'e}matique; Sciences physiques; Math{\'e}matiques; Physique math{\'e}matique; Mathematical analysis; Mathematical physics; Mathematics", tableofcontents = "Introduction \\ Dimensional analysis \\ Power series \\ Spherical and cylindrical coordinates \\ Gradient \\ Divergence of a vector field \\ Curl of a vector field \\ Theorem of Gauss \\ Theorem of Stokes \\ The Laplacian \\ Scale analysis \\ Linear algebra \\ Dirac delta function \\ Fourier analysis \\ Analytic functions \\ Complex integration \\ Green's functions: principles \\ Green's functions: examples \\ Normal modes \\ Potential field theory \\ Probability and statistics \\ Inverse problems \\ Perturbation theory \\ Asymptotic evaluation of integrals \\ Conservation laws \\ Cartesian tensors \\ Variational calculus \\ Epilogue, on power and knowledge", } @Book{SouzadeCursi:2015:UQS, author = "Eduardo {Souza de Cursi} and Rubens Sampaio", title = "Uncertainty Quantification and Stochastic Modeling with {Matlab}", publisher = "ISTE Press Ltd", address = "London, UK", year = "2015", ISBN = "0-08-100471-0 (e-book), 1-78548-005-7", ISBN-13 = "978-0-08-100471-5 (e-book), 978-1-78548-005-8", LCCN = "QA274.2", bibdate = "Tue Jan 12 16:21:50 MST 2016", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/s-plus.bib", URL = "http://alltitles.ebrary.com/Doc?id=11040161; http://lib.myilibrary.com?id=762946; http://public.eblib.com/choice/PublicFullRecord.aspx?p=2007484; http://www.sciencedirect.com/science/book/9781785480058", abstract = "Uncertainty Quantification (UQ) is a relatively new research area which describes the methods and approaches used to supply quantitative descriptions of the effects of uncertainty, variability and errors in simulation problems and models. It is rapidly becoming a field of increasing importance, with many real-world applications within statistics, mathematics, probability and engineering, but also within the natural sciences. Literature on the topic has up until now been largely based on polynomial chaos, which raises difficulties when considering different types of approximation and does not lead to a unified presentation of the methods. Moreover, this description does not consider either deterministic problems or infinite dimensional ones. This book gives a unified, practical and comprehensive presentation of the main techniques used for the characterization of the effect of uncertainty on numerical models and on their exploitation in numerical problems. In particular, applications to linear and nonlinear systems of equations, differential equations, optimization and reliability are presented. Applications of stochastic methods to deal with deterministic numerical problems are also discussed. Matlab? illustrates the implementation of these methods and makes the book suitable as a textbook and for self-study.", acknowledgement = ack-nhfb, subject = "Stochastic models; Uncertainty (Information theory); MATHEMATICS / Applied; MATHEMATICS / Probability and Statistics / General; Stochastic models.; Uncertainty (Information theory); Stochastic partial differential equations", tableofcontents = "Introduction \\ 1: Elements of Probability Theory and Stochastic Processes \\ 1.1. Notation \\ 1.2. Numerical Characteristics of Finite Populations \\ 1.3. Matlab Implementation \\ 1.4. Couples of Numerical Characteristics \\ 1.5. Matlab Implementation \\ 1.6. Hilbertian Properties of the Numerical Characteristics \\ 1.7. Measure and Probability \\ 1.8. Construction of Measures \\ 1.9. Measures, Probability and Integrals in Infinite Dimensional Spaces \\ 1.10. Random Variables \\ 1.11. Hilbertian Properties of Random Variables \\ 1.12. Sequences of Random Variables \\ 1.13. Some Usual Distributions \\ 1.14. Samples of Random Variables \\ 1.15. Gaussian Samples \\ 1.16. Stochastic Processes \\ 1.17. Hilbertian Structure \\ 1.18. Wiener Process \\ 1.19. Ito Integrals \\ 1.20. Ito Calculus \\ 2: Maximum Entropy and Information \\ 2.1. Construction of a Stochastic Model \\ 2.2. The Principle of Maximum Entropy \\ 2.3. Generating Samples of Random Variables, Random Vectors and Stochastic Processes \\ 2.4. Karhunen-Lo{\`e}ve Expansions and Numerical Generation of Variates from Stochastic Processes 3: Representation of Random Variables \\ 3.1. Approximations Based on Hilbertian Properties \\ 3.2. Approximations Based on Statistical Properties (Moment Matching Method) \\ 3.3. Interpolation-Based Approximations (Collocation) \\ 4: Linear Algebraic Equations Under Uncertainty \\ 4.1. Representation of the Solution of Uncertain Linear Systems \\ 4.2. Representation of Eigenvalues and Eigenvectors of Uncertain Matrices \\ 4.3. Stochastic Methods for Deterministic Linear Systems \\ 5: Nonlinear Algebraic Equations Involving Random Parameters 5.1. Nonlinear Systems of Algebraic Equations \\ 5.2. Numerical Solution of Noisy Deterministic Systems of Nonlinear Equations \\ 6: Differential Equations Under Uncertainty \\ 6.1. The Case of Linear Differential Equations \\ 6.2. The Case of Nonlinear Differential Equations \\ 6.3. The Case of Partial Differential Equations \\ 6.4. Reduction of Hamiltonian Systems \\ 6.5. Local Solution of Deterministic Differential Equations by Stochastic Simulation \\ 6.6. Statistics of Dynamical Systems \\ 7: Optimization Under Uncertainty 7.1. Representation of the Solutions in Unconstrained Optimization \\ 7.2. Stochastic Methods in Deterministic Continuous Optimization \\ 7.3. Population-Based Methods \\ 7.4. Determination of Starting Points \\ 8: Reliability-Based Optimization \\ 8.1. The Model Situation \\ 8.2. Reliability Index \\ 8.3. FORM \\ 8.4. The Bi-Level or Double-Loop Method \\ 8.5. One-Level or Single-Loop Approach \\ 8.6. Safety Factors \\ Bibliography \\ Index", } @Book{Temme:2015:AMI, author = "Nico M. Temme", title = "Asymptotic Methods for Integrals", volume = "6", publisher = pub-WORLD-SCI, address = pub-WORLD-SCI:adr, pages = "xxii + 605", year = "2015", ISBN = "981-4612-15-4 (hardcover), 981-4612-16-2 (e-book)", ISBN-13 = "978-981-4612-15-9 (hardcover), 978-981-4612-16-6 (e-book)", MRclass = "41-02 (33Cxx 33E20 65D30)", MRnumber = "3328507", MRreviewer = "Jos{\'e} Luis L{\'o}pez", bibdate = "Tue Feb 06 11:44:21 2018", bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Series in Analysis", abstract = "This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals. The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on.", acknowledgement = ack-nhfb, shorttableofcontents = "Basic methods for integrals \\ Basic methods: examples for special functions \\ Other methods for integrals \\ Uniform methods for integrals \\ Uniform methods for Laplace-type integrals \\ Uniform examples for special functions \\ A class of cumulative distribution factors", tableofcontents = "Preface / vii \\ Acknowledgments / ix \\ Part 1: Basic Methods for Integrals / 1 \\ 1. Introduction / 3 \\ 1.1 Symbols used in asymptotic estimates / 3 \\ 1.2 Asymptotic expansions / 4 \\ 1.3 A first example: Exponential integral / 5 \\ 1.4 Generalized asymptotic expansions / 7 \\ 1.5 Properties of asymptotic power series / 8 \\ 1.6 Optimal truncation of asymptotic expansions / 10 \\ 2. Expansions of Laplace-type integrals: Watson's lemma / 13 \\ 2.1 Watson's lemma / 13 \\ 2.1.1 Watson's lemma for extended sectors / 14 \\ 2.1.2 More general forms of Watson's lemma / 16 \\ 2.2 Watson's lemma for loop integrals / 16 \\ 2.3 More general forms of Laplace-type integrals / 19 \\ 2.3.1 Transformation to the standard form / 19 \\ 2.4 How to compute the coefficients / 20 \\ 2.4.1 Inversion method for computing the coefficients / 20 \\ 2.4.2 Integrating by parts / 22 \\ 2.4.3 Manipulating power series / 23 \\ 2.4.4 Explicit forms of the coefficients in the expansion / 25 \\ 2.5 Other kernels / 26 \\ 2.6 Exponentially improved asymptotic expansions / 27 \\ 2.7 Singularities of the integrand / 29 \\ 2.7.1 A pole near the endpoint / 29 \\ 2.7.2 More general cases / 32 \\ 3. The method of Laplace / 33 \\ 3.1 A theorem for the general case / 33 \\ 3.2 Constructing the expansion / 35 \\ 3.2.1 Inversion method for computing the coefficients / 36 \\ 3.3 Explicit forms of the coefficients in the expansion / 37 \\ 3.4 The complementary error function / 38 \\ 4. The saddle point method and paths of steepest descent / 41 \\ 4.1 The axis of the valley at the saddle point / 43 \\ 4.2 Examples with simple exponentials / 43 \\ 4.2.1 A first example / 43 \\ 4.2.2 A cosine transform / 44 \\ 4.3 Steepest descent paths not through a saddle point / 44 \\ 4.3.1 A gamma function example / 45 \\ 4.3.2 An integral related to the error function / 46 \\ 4.4 An example with strong oscillations: A 100-digit challenge / 48 \\ 4.5 A Laplace inversion formula for $ \erfc z $ / 49 \\ 4.6 A non-oscillatory integral for $ \erfc z $ , $ z \in \mathbb{C} $ / 50 \\ 4.7 The complex Airy function / 50 \\ 4.8 A parabolic cylinder function / 53 \\ 5. The Stokes phenomenon / 57 \\ 5.1 The Airy function / 57 \\ 5.2 The recent interest in the Stokes phenomenon / 58 \\ 5.3 Exponentially small terms in the Airy expansions / 59 \\ 5.4 Expansions in connection with the Stokes phenomenon / 60 \\ 5.4.1 Applications to a Kummer function / 61 \\ Part 2: Basic Methods: Examples for Special Functions / 63 \\ 6. The gamma function / 65 \\ 6.1 $ \Gamma(z) $ by Laplace's method / 66 \\ 6.1.1 Calculating the coefficients / 67 \\ 6.1.2 Details on the transformation / 68 \\ 6.2 $ 1 / \Gamma(z) $ by the saddle point method / 71 \\ 6.2.1 Another integral representation of $ 1 / \Gamma(z) $ / 72 \\ 6.3 The logarithm of the gamma function / 72 \\ 6.3.1 Estimations of the remainder / 73 \\ 6.4 Expansions of $ \Gamma(z + a) $ and $ 1 / \Gamma(z + a) $ / 75 \\ 6.5 The ratio of two gamma functions / 76 \\ 6.5.1 A simple expansion / 77 \\ 6.5.2 A more efficient expansion / 78 \\ 6.6 A binomial coefficient / 80 \\ 6.6.1 A uniform expansion of the binomial coefficient / 83 \\ 6.7 Asymptotic expansion of a product of gamma functions / 85 \\ 6.8 Expansions of ratios of three gamma functions / 88 \\ 7. Incomplete gamma functions / 91 \\ 7.1 Integral representations / 91 \\ 7.2 $ \Gamma(a, x) $ : Asymptotic expansion for $ x \gg a $ / 92 \\ 7.3 $ \gamma(a, x) $ : Asymptotic expansion for $ a > x $ / 93 \\ 7.3.1 Singularity of the integrand / 94 \\ 7.3.2 More details on the transformation $ u = \phi(t) $ / 96 \\ 7.4 $ \Gamma(a, x) $ : Asymptotic expansion for $ x > a $ / 97 \\ 8. The Airy functions / 101 \\ 8.1 Expansions of $ \Ai(z) $, $ \Bi(z) $ / 102 \\ 8.1.1 Transforming the saddle point contour / 102 \\ 8.2 Expansions of $ \Ai(-z) $, $ \Bi(-z) $ / 105 \\ 8.3 Two simple ways to obtain the coefficients / 106 \\ 8.4 A generalized form of the Airy function / 107 \\ 9. Bessel functions: Large argument / 109 \\ 9.1 The modified Bessel function $ K_\nu(z) $ / 109 \\ 9.2 The ordinary Bessel functions / 110 \\ 9.3 The modified Bessel function $ I_\nu(z) $ / 111 9.3.1 A compound expansion of $ I_\nu(z) $ / 111 9.4 Saddle point method for $ K_\nu(z) $ , $ z \in \mathbb{C} $ / 113 \\ 9.4.1 Integral representations from saddle point analysis / 115 \\ 9.4.2 Saddle point method for $ J_\nu(x) $ , $ x < \nu $ / 116 \\ 9.5 Debye-type expansions of the modified Bessel functions / 117 \\ 9.6 Modified Bessel functions of purely imaginary order / 119 \\ 9.6.1 The monotonic case: $ x > \nu > 0 $ / 120 \\ 9.6.2 The oscillatory case: $ \nu > x > 0 $ / 123 \\ 9.7 A $ J $ -Bessel integral / 126 \\ 10. Kummer functions / 129 \\ 10.1 General properties / 129 \\ 10.2 Asymptotic expansions for large $ z $ / 131 \\ 10.3 Expansions for large $ a $ / 132 \\ 10.3.1 Tricomi's function $ E_\nu(z) $ / 132 \\ 10.3.2 Expansion of $ U(a, c, z) $ , $ a \to +\infty $ / 133 \\ 10.3.3 Expansion of $ _1F_1(a; c; z) $ , $ a \to +\infty $ / 135 \\ 10.3.4 Expansion of $ _1F_1(a; c; z) $ , $ a \to -\infty $ / 137 \\ 10.3.5 Expansion of $ U(a, c, z) $ , $ a \to -\infty $ / 138 \\ 10.3.6 Slater's results for large $ a $ / 140 \\ 10.4 Expansions for large $ c $ / 142 \\ 10.4.1 Expansion of $ _1F_1(a; c; z) $ , $ c \to +\infty $ / 142 \\ 10.4.2 Expansion of $ U(a, c, z) $ , $ c \to +\infty $ , $ z < c $ / 143 \\ 10.4.3 Expansion of $ U(a, c, z) $ , $ c \to +\infty $ , $ z > e $ / 144 \\ 10.4.4 Expansion of $ U(a, c, z) $ , $ c \to -\infty $ / 145 \\ 10.4.5 Expansion of $ _1F_1(a; c; z) $ , $ c \to -\infty $ / 147 \\ 10.5 Uniform expansions of the Kummer functions / 147 \\ 11. Parabolic cylinder functions: Large argument / 149 \\ 11.1 A few properties of the parabolic cylinder functions / 149 \\ 11.2 The function $ U(a, z) $ / 150 \\ 11.3 The function $ U(a, -z) $ / 152 \\ 11.4 The function $ V(a, z) $ / 153 \\ 11.5 Expansions of the derivatives / 154 \\ 12. The Gauss hypergeometric function / 155 \\ 12.1 Large values of $ c $ / 156 \\ 12.1.1 Large positive $ c $ ; $ |z| < z_0 $ / 156 \\ 12.1.2 Large negative $ c $ ; $ |z| < z_0 $ / 157 \\ 12.1.3 Large positive $ c $ ; $ |z| > z_0 $ / 158 \\ 12.1.4 Large negative $ c $ ; $ |z| > z_0 $ / 158 \\ 12.2 Large values of $ b $ / 158 \\ 12.2.1 Large negative $ b $ ; $ |z| > z_0 $ / 159 \\ 12.2.2 Large $ b $ , $ |z| < z_0 $ / 159 \\ 12.3 Other large parameter cases / 160 \\ 12.3.1 Jacobi polynomials of large degree / 161 \\ 12.3.2 An example of the case $ _2F_1(a, b - \lambda; c + \lambda; z) $ / 163 \\ 13. Examples of $ _3F_2 $ -polynomials / 167 \\ 13.1 A $ _3F_2 $ associated with the Catalan--Larcombe--French sequence / 167 \\ 13.1.1 Transformations / 169 \\ 13.1.2 Asymptotic analysis / 170 \\ 13.1.3 Asymptotic expansion / 172 \\ 13.1.4 An alternative method / 173 \\ 13.2 An integral of Laguerre polynomials / 175 \\ 13.2.1 A first approach / 176 \\ 13.2.2 A generating function approach / 178 \\ Part 3: Other Methods for Integrals / 181 \\ 14. The method of stationary phase / 183 \\ 14.1 Critical points / 183 \\ 14.2 Integrating by parts: No stationary points / 184 \\ 14.3 Three critical points: A formal approach / 185 \\ 14.4 On the use of neutralizes / 186 \\ 14.5 How to avoid neutralizes? / 188 \\ 14.5.1 A few details about the Fresnel integral / 190 \\ 14.6 Algebraic singularities at both endpoints: Erdelyi's example / 191 \\ 14.6.1 Application: A conical function / 192 \\ 14.6.2 Avoiding neutralizes in Erdelyi's example / 193 \\ 14.7 Transformation to standard form / 194 \\ 14.8 General order stationary points / 196 \\ 14.8.1 Integrating by parts / 196 \\ 14.9 The method fails: Examples / 197 \\ 14.9.1 The Airy function / 198 \\ 14.9.2 A more complicated example / 198 \\ 15. Coefficients of a power series. Darboux's method / 203 \\ 15.1 A first example: A binomial coefficient / 204 \\ 15.2 Legendre polynomials of large degree / 205 \\ 15.2.1 A paradox in asymptotics / 207 \\ 15.3 Gegenbauer polynomials of large degree / 208 \\ 15.4 Jacobi polynomials of large degree / 209 \\ 15.5 Laguerre polynomials of large degree / 209 \\ 15.6 Generalized Bernoulli polynomials $ B_n^{(\mu)}(z) $ / 210 \\ 15.6.1 Asymptotic expansions for large degree / 211 \\ 15.6.2 An alternative expansion / 213 \\ 15.7 Generalized Euler polynomials $ E_n^{(\mu)}(z) $ / 215 \\ 15.7.1 Asymptotic expansions for large degree / 215 \\ 15.7.2 An alternative expansion / 216 \\ 15.8 Coefficients of expansions of the $ _1F_1 $ -function / 218 \\ 15.8.1 Coefficients of Tricomi's expansion / 218 \\ 15.8.2 Coefficients of Buchholz's expansion / 221 \\ 16. Mellin--Barnes integrals and Mellin convolution integrals / 225 \\ 16.1 Mellin--Barnes integrals / 226 \\ 16.2 Mellin convolution integrals / 228 \\ 16.3 Error bounds / 230 \\ 17. Alternative expansions of Laplace-type integrals / 231 \\ 17.1 Hadamard-type expansions / 231 \\ 17.2 An expansion in terms of Kummer functions / 233 \\ 17.3 An expansion in terms of factorial series / 234 \\ 17.4 The Franklin--Friedman expansion / 237 \\ 18. Two-point Taylor expansions / 241 \\ 18.1 The expansions / 242 \\ 18.2 An alternative form of the expansion / 243 \\ 18.3 Explicit forms of the coefficients / 244 \\ 18.4 Manipulations with two-point Taylor expansions / 245 \\ 19. Hermite polynomials as limits of other classical orthogonal polynomials / 249 \\ 19.1 Limits between orthogonal polynomials / 249 \\ 19.2 The Askey scheme of orthogonal polynomials / 251 \\ 19.3 Asymptotic representations / 251 \\ 19.4 Gegenbauer polynomials / 253 \\ 19.5 Laguerre polynomials / 254 \\ 19.6 Generalized Bessel polynomials / 255 \\ 19.7 Meixner--Pollaczek polynomials into Laguerre polynomials / 257 \\ Part 4: Uniform Methods for Integrals / 259 \\ 20. An overview of standard forms / 261 \\ 20.1 Comments on the table / 263 \\ 21. A saddle point near a pole / 267 \\ 21.1 A saddle point near a pole: Van der Waerden's method / 267 \\ 21.2 An alternative expansion / 269 \\ 21.3 An example from De Bruijn / 270 \\ 21.4 A pole near a double saddle point / 271 \\ 21.5 A singular perturbation problem and $ K $ -Bessel integrals / 272 \\ 21.5.1 A Bessel $ K_0 $ integral / 272 \\ 21.5.2 A similar Bessel $ K_1 $ integral / 274 \\ 21.5.3 A singular perturbation problem / 275 \\ 21.6 A double integral with poles near saddle points / 277 \\ 21.6.1 Application to a singular perturbation problem / 278 \\ 21.7 The Fermi--Dirac integral / 281 \\ 22. Saddle point near algebraic singularity / 285 \\ 22.1 A saddle point near an endpoint of the interval / 285 \\ 22.2 The Bleistein expansion / 286 \\ 22.3 Extending the role of the parameter /3 / 289 \\ 22.4 Contour integrals / 291 \\ 22.5 Kummer functions in terms of parabolic cylinder functions / 292 \\ 22.5.1 Uniform expansion of $ U(a, c, z) $ , $ c \to +\infty $ / 293 \\ 22.5.2 Uniform expansion of $ _1F_1(a; c; z) $ , $ c \to +\infty $ / 296 \\ 23. Two coalescing saddle points: Airy-type expansions / 299 \\ 23.1 The standard form / 299 \\ 23.2 An integration by parts method / 300 \\ 23.3 How to compute the coefficients / 302 \\ 23.4 An Airy-type expansion of the Hermite polynomial / 305 \\ 23.4.1 The cubic transformation / 306 \\ 23.4.2 Details on the coefficients / 308 \\ 23.5 An Airy-type expansion of the Bessel function $ J_\nu(z) $ / 309 \\ 23.6 A semi-infinite interval: Incomplete Scorer function / 313 \\ 23.6.1 A singular perturbation problem inside a circle / 315 \\ 24. Hermite-type expansions of integrals / 319 \\ 24.1 An expansion in terms of Hermite polynomials / 320 \\ 24.1.1 Cauchy-type integrals for the coefficients / 321 \\ 24.2 Gegenbauer polynomials / 323 \\ 24.2.1 Preliminary steps / 324 \\ 24.2.2 A first approximation / 325 \\ 24.2.3 Transformation to the standard form / 326 \\ 24.2.4 Special cases of the expansion / 331 \\ 24.2.5 Approximating the zeros / 332 \\ 24.2.6 The relativistic Hermite polynomials / 333 \\ 24.3 Tricomi--Carlitz polynomials / 333 \\ 24.3.1 Contour integral and saddle points / 335 \\ 24.3.2 A first approximation / 337 \\ 24.3.3 Transformation to the standard form / 337 \\ 24.3.4 Approximating the zeros / 339 \\ 24.4 More examples / 340 \\ Part 5: Uniform Methods for Laplace-Type Integrals / 341 \\ 25. The vanishing saddle point / 343 \\ 25.1 Expanding at the saddle point / 344 \\ 25.2 An integration by parts method / 346 \\ 25.2.1 Representing coefficients as a Cauchy-type integral / 347 \\ 25.3 Expansions for loop integrals / 348 \\ 25.4 Rummer functions / 350 \\ 25.5 Generalized zeta function / 350 \\ 25.6 Transforming to the standard form / 351 \\ 25.6.1 The ratio of two gamma functions / 352 \\ 25.6.2 Parabolic cylinder functions / 354 \\ 26. A moving endpoint: Incomplete Laplace integrals / 355 \\ 26.1 The standard form / 355 \\ 26.2 Constructing the expansion / 356 \\ 26.2.1 The complementary function / 357 \\ 26.3 Application to the incomplete beta function / 358 \\ 26.3.1 Expansions of the coefficients / 361 \\ 26.4 A corresponding loop integral / 362 \\ 26.4.1 Application to the incomplete beta function / 363 \\ 27. An essential singularity: Bessel-type expansions / 365 \\ 27.1 Expansions in terms of modified Bessel functions / 365 \\ 27.2 A corresponding loop integral / 368 \\ 27.3 Expansion at the internal saddle point / 368 \\ 27.4 Application to Kummer functions / 369 \\ 27.4.1 Expansion of $ U(a, c, z) $ , $ a \to +\infty $ , $ z > 0 $ / 369 \\ 27.4.2 Auxiliary expansions and further details / 372 \\ 27.4.3 Expansion of $ _1F_1(a: c; z) $ , $ a \to +\infty $ , $ z > 0 $ / 374 \\ 27.4.4 Expansion of $ _1F_1(a; c: z) $ , $ a \to -\infty $ , $ 0 < z < -4a $ / 375 \\ 27.4.5 Expansion of $ U(a, c, z) $ , $ a \to -\infty $ , $ 0 < z < -4a $ / 377 \\ 27.5 A second uniformity parameter / 378 \\ 27.5.1 Expansion of $ U(a, c, z) $ , $ a \to \infty $ , $ z > 0 $ , $ c < 1 $ / 380 \\ 27.5.2 Expansion of $ _1F_1(a; c; z), $ a \to \infty $ , $ z > 0 $ , $ c > 1 $ / 381 \\ 28. Expansions in terms of Kummer functions / 383 \\ 28.1 Approximation in terms of the Kummer J7-function / 383 \\ 28.1.1 Constructing the expansions / 384 \\ 28.1.2 Expansion for the loop integral / 387 \\ 28.2 The $ _2F_1 $ function, large $ c $ , in terms of $ U $ / 387 \\ 28.2.1 Legendre polynomials: Uniform expansions / 388 \\ 28.3 The $ _2F_1 $ -function, large $ b $ : in terms of $ _1F_1 $ / 389 \\ 28.3.1 Using a real integral / 390 \\ 28.3.2 Using a loop integral / 394 \\ 28.4 Jacobi polynomials of large degree: Laguerre-type expansion / 394 \\ 28.4.1 Laguerre-type expansion for large values of /3 / 398 \\ 28.5 Expansion of a Dirichlet-type integral / 401 \\ Part 6: Uniform Examples for Special Functions / 403 \\ 29. Legendre functions / 405 \\ 29.1 Expansions of $ P_\nu^\mu(z) $ , $ Q_\nu^\mu(z) $ ; $ \nu \to \infty $ , $ z \geq 1 $ / 406 \\ 29.1.1 Expansions for $ z > z_0 > 1 $ / 400 \\ 29.1.2 Expansion in terms of modified Bessel functions / 407 \\ 29.1.3 Expansions of $ P_\nu^\mu(z) $ and $ Q_\nu^\mu(z) $ in terms of Bessel functions / 411 \\ 29.2 Expansions of $ P_\nu^\mu(z) $ , $ Q_\nu^\mu(z) $ ; $ p \to \infty $ , $ z > 1 $ / 412 \\ 29.2.1 Expansions for bounded $ z $ / 412 \\ 29.2.2 Expansions in terms of modified Bessel functions / 412 \\ 29.2.3 Expansions of $ P_\nu^\mu(z) $ and $ Q_\nu^\mu(z) $ / 413 \\ 29.3 Integrals with nearly coincident branch points / 414 \\ 29.3.1 Ursell's expansions of Legendre functions / 415 \\ 29.3.2 Coefficients of the expansion / 416 \\ 29.3.3 An alternative expansion of $ P_n^m(\cosh z) $ / 417 \\ 29.3.4 A related integral with nearly coincident branch points / 418 \\ 29.4 Toroidal harmonics and conical functions / 418 \\ 30. Parabolic cylinder functions: Large parameter / 419 \\ 30.1 Notation for uniform asymptotic expansions / 419 \\ 30.2 The case $ a < 0 $ / 421 \\ 30.2.1 The case $ z > 2\sqrt{-a} $ : $ -a + z \to \infty $ / 421 \\ 30.2.2 The case $ z < -2\sqrt{-a} $ : $ -a - z \to \infty $ / 422 \\ 30.2.3 The case -2\sqrt{-a} < z < 2\sqrt{-a} / 423 \\ 30.3 The case $ a > 0 $ / 424 \\ 30.3.1 The case $ z > 0 $ , $ a + z \to \infty $ / 425 \\ 30.3.2 The case $ z < 0 $ , $ a - z \to \infty $ / 425 \\ 30.4 Expansions from integral representations / 426 \\ 30.4.1 The case $ a > 0 $ , $ z > 0 $ ; $ a + z \to \infty $ / 426 \\ 30.4.2 The case $ a > 0 $ , $ z < 0 $ ; $ a - z \to \infty $ / 428 \\ 30.4.3 The case $ a < 0 $ , $ |z| > 2\sqrt{-a} $ ; $ -a + |z| \to \infty $ / 429 \\ 30.5 Airy-type expansions / 430 \\ 31. Coulomb wave functions / 433 \\ 31.1 Contour integrals for Coulomb functions / 434 \\ 31.2 Expansions for $ \rho \to \infty $ and bounded $ \eta $ / / 435 \\ 31.3 Expansions for $ \eta \to \infty $ and bounded $ \rho $ / 437 \\ 31.4 Expansions for $ \eta \to -\infty $ and bounded $ \rho $ / 439 \\ 31.5 Expansions for $ \eta \to -\infty and $ \rho \geq \rho_0 > 0 $ / 440 \\ 31.6 Expansions for $ \eta \to -\infty $ and $ \rho \geq 0 $ / 442 \\ 31.7 Expansions for $ \eta $ , $ \rho \to \infty $ ; Airy-type expansions / 444 \\ 32. Laguerre polynomials: Uniform expansions / 449 \\ 32.1 An expansion for bounded $ z $ and $ a $ / 449 \\ 32.2 An expansion for bounded $ z $ ; $ a $ depends on $ n $ / 451 \\ 32.3 Expansions for bounded $ a $ ; $ z $ depends on $ n $ / 454 \\ 32.3.1 An expansion in terms of Airy functions / 455 \\ 32.3.2 An expansion in terms of Bessel functions / 456 \\ 32.4 An expansion in terms of Hermite polynomials; large $ a $ / 458 \\ 32.4.1 A first approximation / 459 \\ 32.4.2 Transformation to the standard form / 460 \\ 32.4.3 Approximating the zeros / 462 \\ 33. Generalized Bessel polynomials / 465 \\ 33.1 Relations to Bessel and Kummer functions / 466 \\ 33.2 An expansion in terms of Laguerre polynomials / 467 \\ 33.3 Expansions in terms of elementary functions / 470 \\ 33.3.1 The case $ |\ph z| < \pi/2 $ / 470 \\ 33.3.2 The case $ |\ph(-z)| < \pi/2 $ / 471 \\ 33.3.3 Integral representations / 472 \\ 33.3.4 Construction of the expansions / 472 \\ 33.4 Expansions in terms of modified Bessel functions / 476 \\ 33.4.1 Construction of the expansion / 476 \\ 34. Stirling numbers / 479 \\ 34.1 Definitions and integral representations / 479 \\ 34.2 Stirling number of the second kind / 481 \\ 34.2.1 Higher-order approximations / 483 \\ 34.2.2 About the positive saddle point / 486 \\ 34.2.3 About the quantity $ A $ / 487 \\ 34.3 Stirling numbers of the first kind / 488 \\ 35. Asymptotics of the integral $ \int_0^1 \cos(b x + a / x) \, dx $ / 491 \\ 35.1 The case $ b < a $ / 491 \\ 35.2 The case $ a = b $ / 493 \\ 35.3 The case $ b > a $ / 494 \\ 35.3.1 The contribution from $ \mathcal{P}_1 $ / 495 \\ 35.3.2 The contribution from $ \mathcal{P}_2 $ / 496 \\ 35.4 A Fresnel-type expansion / 497 \\ Part 7: A Class of Cumulative Distribution Functions / 499 \\ 36. Expansions of a class of cumulative distribution functions / 501 \\ 36.1 Cumulative distribution functions: A standard form / 501 \\ 36.2 An incomplete normal distribution function / 505 \\ 36.3 The Sievert integral / 506 \\ 36.4 The Pearson type IV distribution / 507 \\ 36.5 The Von Mises distribution / 509 \\ 36.5.1 An expansion near the lower endpoint of integration / 511 \\ 37. Incomplete gamma functions: Uniform expansions / 513 \\ 37.1 Using the standard integral representations / 513 \\ 37.2 Representations by contour integrals / 514 \\ 37.2.1 Constructing the expansions / 516 \\ 37.2.2 Details on the coefficients / 518 \\ 37.2.3 Relations to the coefficients of earlier expansions / 520 \\ 37.3 Incomplete gamma functions, negative parameters / 520 \\ 37.3.1 Expansions near the transition point / 522 \\ 37.3.2 A real expansion of 7*(-a, -z) / 524 \\ 38. Incomplete beta function / 525 \\ 38.1 A power series expansion for large p / 526 \\ 38.2 A uniform expansion for large p / 526 \\ 38.3 The nearly symmetric case / 527 \\ 38.4 The general error function case / 529 \\ 39. Non-central chi-square, Marcum functions / 531 \\ 39.1 Properties of the Marcum functions / 532 \\ 39.2 More integral representations / 533 \\ 39.3 Asymptotic expansion; $ \mu $ fixed, $ \xi $ large / 535 \\ 39.4 Asymptotic expansion; $ \xi + \mu $ large / 537 \\ 39.5 An expansion in terms of the incomplete gamma function / 540 \\ 39.6 Comparison of the expansions numerically / 543 \\ 40. A weighted sum of exponentials / 545 \\ 40.1 An integral representation / 546 \\ 40.2 Saddle point analysis / 547 \\ 40.3 Details on the coefficients / 548 \\ 40.4 Auxiliary expansions / 550 \\ 40.5 Numerical verification / 551 \\ 41. A generalized incomplete gamma function / 553 \\ 41.1 An expansion in terms of incomplete gamma functions / 554 \\ 41.2 An expansion in terms of Laguerre polynomials / 554 \\ 41.3 An expansion in terms of Kummer functions / 555 \\ 41.4 An expansion in terms of the error function / 555 \\ 42. Asymptotic inversion of cumulative distribution functions / 559 \\ 42.1 The asymptotic inversion method / 559 \\ 42.2 Asymptotic inversion of the gamma distribution / 561 \\ 42.2.1 Numerical verification / 563 \\ 42.2.2 Other asymptotic inversion methods / 564 \\ 42.2.3 Asymptotics of the zeros of $ \Gamma(a, z) $ / 565 \\ 42.3 Asymptotic inversion of the incomplete beta function / 567 \\ 42.3.1 Inverting by using the error function / 568 \\ 42.3.2 Inverting by using the incomplete gamma function / 569 \\ 42.3.3 Numerical verification / 572 \\ 42.4 The hyperbolic cumulative distribution / 573 \\ 42.4.1 Numerical verification / 574 \\ 42.5 The Marcum functions / 575 \\ 42.5.1 Asymptotic inversion / 576 \\ 42.5.2 Asymptotic inversion with respect to $ x $ / 576 \\ 42.5.3 Asymptotic inversion with respect to $ y $ / 579 \\ Bibliography / 583 \\ Index / 597", } @Book{Green:2016:CMC, author = "Dan Green", title = "Cosmology with {MATLAB}: with companion media pack", publisher = "World Scientific Publishing Co. Pte. Ltd.", address = "Singapore", pages = "xi + 250", year = "2016", ISBN = "981-310-839-8 (hardcover), 981-310-840-1 (paperback)", ISBN-13 = "978-981-310-839-4 (hardcover), 978-981-310-840-0 (paperback)", LCCN = "QB981 .G74 2016", bibdate = "Thu Nov 30 10:51:08 MST 2017", bibsource = "http://www.math.utah.edu/pub/tex/bib/contempphys.bib; http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", abstract = "This volume makes explicit use of the synergy between cosmology and high energy physics, for example, supersymmetry and dark matter, or nucleosynthesis and the baryon-to-photon ratio. In particular the exciting possible connection between the recently discovered Higgs scalar and the scalar field responsible for inflation is explored. The recent great advances in the accuracy of the basic cosmological parameters is exploited in that no free scale parameters such as h appear, rather the basic calculations are done numerically using all sources of energy density simultaneously. Scripts are provided that allow the reader to calculate exact results for the basic parameters. Throughout MATLAB tools such as symbolic math, numerical solutions, plots and ``movies'' of the dynamical evolution of systems are used. The GUI package is also shown as an example of the real time manipulation of parameters which is available to the reader. All the MATLAB scripts are made available to the reader to explore examples of the uses of the suite of tools which are available. Indeed, readers should be able to engage in a command line ``dialogue'' or go on to edit the scripts and write their own versions.", acknowledgement = ack-nhfb, author-dates = "1943--", subject = "Cosmology; Data processing; Data processing", tableofcontents = "1. Introduction \\ 2. From the Big Bang \\ 3. Inflation and Big Bang issues \\ 4. Fluctuations to Perturbations \\ 5. The Cosmic Microwave background \\ 6. Large Scale Structure \\ 7. The Higgs Boson and Inflation \\ Appendix A: Matlab tools \\ Appendix B: Power law, RD or MD Formulae \\ Appendix C: Symbol and Acronym Tables \\ Appendix D: MATLAB Script (with Companion Media Pack)", } @Book{Kneusel:2016:NC, author = "Ronald T. Kneusel", title = "Numbers and Computers", publisher = pub-SV, address = pub-SV:adr, pages = "xi + 231", year = "2016", ISBN = "3-319-35940-1 (softcover), 3-319-17260-3 (e-book)", ISBN-13 = "978-3-319-35940-3 (softcover), 978-3-319-17260-6 (e-book)", LCCN = "QA241 .K54 2016", bibdate = "Tue Aug 22 05:53:26 MDT 2017", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", abstract = "This is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers. Divided into two parts, the first deals with standard representations of integers and floating point numbers, while the second details several other number representations. Each chapter ends with exercises to review the key points. Topics covered include interval arithmetic, fixed-point numbers, floating point numbers, big integers and rational arithmetic. This book is for anyone who develops software including software engineering, scientists, computer science students, engineering students and anyone who programs for fun.", acknowledgement = ack-nhfb, subject = "Number theory; Numerals; Numeration; Computer science; Mathematics", tableofcontents = "Number Systems \\ Integers \\ Floating Point \\ Big Integers and Rational Arithmetic \\ Fixed-Point Numbers \\ Decimal Floating Point \\ Interval Arithmetic", } @Book{Muller:2016:EFA, author = "Jean-Michel Muller", title = "Elementary Functions: Algorithms and Implementation", publisher = pub-BIRKHAUSER-BOSTON, address = pub-BIRKHAUSER-BOSTON:adr, edition = "Third", pages = "xxv + 283", year = "2016", DOI = "https://doi.org/10.1007/978-1-4899-7983-4", ISBN = "1-4899-7981-6 (print), 1-4899-7983-2 (e-book)", ISBN-13 = "978-1-4899-7981-0 (print), 978-1-4899-7983-4 (e-book)", LCCN = "QA331 .M866 2016", bibdate = "Sun Dec 04 15:12:36 2016", bibsource = "http://www.math.utah.edu/pub/tex/bib/mathcw.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", abstract = "This textbook presents the concepts and tools necessary to understand, build, and implement algorithms for computing elementary functions (e.g., logarithms, exponentials, and the trigonometric functions). Both hardware- and software-oriented algorithms are included, along with issues related to accurate floating-point implementation. This third edition has been updated and expanded to incorporate the most recent advances in the field, new elementary function algorithms, and function software. After a preliminary chapter that briefly introduces some fundamental concepts of computer arithmetic, such as floating-point arithmetic and redundant number systems, the text is divided into three main parts. Part I considers the computation of elementary functions using algorithms based on polynomial or rational approximations and using table-based methods; the final chapter in this section deals with basic principles of multiple-precision arithmetic. Part II is devoted to a presentation of shift-and-add algorithms (hardware-oriented algorithms that use additions and shifts only). Issues related to accuracy, including range reduction, preservation of monotonicity, and correct rounding, as well as some examples of implementation are explored in Part III. Numerous examples of command lines and full programs are provided throughout for various software packages, including Maple, Sollya, and Gappa. New to this edition are an in-depth overview of the IEEE-754-2008 standard for floating-point arithmetic; a section on using double- and triple-word numbers; a presentation of new tools for designing accurate function software; and a section on the Toom--Cook family of multiplication algorithms. The techniques presented in this book will be of interest to implementors of elementary function libraries or circuits and programmers of numerical applications. Additionally, graduate and advanced undergraduate students, professionals, and researchers in scientific computing, numerical analysis, software engineering, and computer engineering will find this a useful reference and resource.", acknowledgement = ack-nhfb, subject = "Functions; Data processing; Algorithms", tableofcontents = "Introduction \\ Introduction to Computer Arithmetic \\ Part I: Algorithms Based on Polynomial Approximation and/or Table Lookup, Multiple-Precision Evaluation of Functions \\ The Classical Theory of Polynomial or Rational Approximations \\ Polynomial Approximations with Special Constraints \\ Polynomial Evaluation \\ Table-Based Methods \\ Multiple-Precision Evaluation of Functions \\ Part II: Shift-and-Add Algorithms \\ Introduction to Shift-and-Add Algorithms \\ The CORDIC Algorithm \\ Some Other Shift-and-Add Algorithms \\ Part III: Range Reduction, Final Rounding, and Exceptions \\ Range Reduction \\ Final Rounding \\ Miscellaneous \\ Examples of Implementation \\ References \\ Index", } @Book{Romisch:2016:MAM, author = "Werner R{\"o}misch and Thomas Zeugmann", title = "Mathematical Analysis and the Mathematics of Computation", publisher = "Springer", address = "Cham, Switzerland", pages = "xxiii + 704", year = "2016", DOI = "https://doi.org/10.1007/978-3-319-42755-3", ISBN = "3-319-42753-9 (hardcover), 3-319-42755-5 (e-book)", ISBN-13 = "978-3-319-42753-9 (hardcover), 978-3-319-42755-3 (e-book)", MRclass = "26-01 (34-01 41-01 65Jxx)", MRnumber = "3524911", MRreviewer = "Sorin Gheorghe Gal", bibdate = "Sat Feb 2 16:19:35 2019", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/z/zeugmann-thomas-u.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", URL = "http://link.springer.com/10.1007/978-3-319-42755-3", abstract = "This book is a comprehensive, unifying introduction to the field of mathematical analysis and the mathematics of computing. It develops the relevant theory at a modern level and it directly relates modern mathematical ideas to their diverse applications. The authors develop the whole theory. Starting with a simple axiom system for the real numbers, they then lay the foundations, developing the theory, exemplifying where it's applicable, in turn motivating further development of the theory. They progress from sets, structures, and numbers to metric spaces, continuous functions in metric spaces, linear normed spaces and linear mappings; and then differential calculus and its applications, the integral calculus, the gamma function, and linear integral operators. They then present important aspects of approximation theory, including numerical integration. The remaining parts of the book are devoted to ordinary differential equations, the discretization of operator equations, and numerical solutions of ordinary differential equations. This textbook contains many exercises of varying degrees of difficulty, suitable for self-study, and at the end of each chapter the authors present more advanced problems that shed light on interesting features, suitable for classroom seminars or study groups. It will be valuable for undergraduate and graduate students in mathematics, computer science, and related fields such as engineering. This is a rich field that has experienced enormous development in recent decades, and the book will also act as a reference for graduate students and practitioners who require a deeper understanding of the methodologies, techniques, and foundations.", acknowledgement = ack-nhfb, subject = "Mathematical analysis; Computer science; Mathematics; Mathematics.; Mathematical analysis.", tableofcontents = "Sets, Structures, Numbers \\ Metric Spaces \\ Continuous Functions in Metric Spaces \\ Linear Normed Spaces, Linear Operators \\ The Differential Calculus \\ Applications of the Differential Calculus \\ The Integral Calculus \\ Linear Integral Operators \\ Inner Product Spaces \\ Approximative Representation of Functions \\ Ordinary Differential Equations \\ Discretization of Operator Equations \\ Numerical Solution of Ordinary Differential Equations", } @Book{Beebe:2017:MFC, author = "Nelson H. F. Beebe", title = "The Mathematical-Function Computation Handbook: Programming Using the {MathCW} Portable Software Library", publisher = pub-SV, address = pub-SV:adr, pages = "xxxvi + 1114", year = "2017", DOI = "https://doi.org/10.1007/978-3-319-64110-2", ISBN = "3-319-64109-3 (hardcover), 3-319-64110-7 (e-book)", ISBN-13 = "978-3-319-64109-6 (hardcover), 978-3-319-64110-2 (e-book)", LCCN = "QA75.5-76.95", bibdate = "Sat Jul 15 19:34:43 MDT 2017", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib; http://www.math.utah.edu/pub/tex/bib/axiom.bib; http://www.math.utah.edu/pub/tex/bib/cryptography2010.bib; http://www.math.utah.edu/pub/tex/bib/elefunt.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/maple-extract.bib; http://www.math.utah.edu/pub/tex/bib/master.bib; http://www.math.utah.edu/pub/tex/bib/mathematica.bib; http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/mupad.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/prng.bib; http://www.math.utah.edu/pub/tex/bib/redbooks.bib", URL = "http://www.springer.com/us/book/9783319641096", acknowledgement = ack-nhfb, tableofcontents = "List of figures / xxv \\ List of tables / xxxi \\ Quick start / xxxv \\ 1: Introduction / 1 \\ 1.1: Programming conventions / 2 \\ 1.2: Naming conventions / 4 \\ 1.3: Library contributions and coverage / 5 \\ 1.4: Summary / 6 \\ 2: Iterative solutions and other tools / 7 \\ 2.1: Polynomials and Taylor series / 7 \\ 2.2: First-order Taylor series approximation / 8 \\ 2.3: Second-order Taylor series approximation / 9 \\ 2.4: Another second-order Taylor series approximation / 9 \\ 2.5: Convergence of second-order methods / 10 \\ 2.6: Taylor series for elementary functions / 10 \\ 2.7: Continued fractions / 12 \\ 2.8: Summation of continued fractions / 17 \\ 2.9: Asymptotic expansions / 19 \\ 2.10: Series inversion / 20 \\ 2.11: Summary / 22 \\ 3: Polynomial approximations / 23 \\ 3.1: Computation of odd series / 23 \\ 3.2: Computation of even series / 25 \\ 3.3: Computation of general series / 25 \\ 3.4: Limitations of Cody\slash Waite polynomials / 28 \\ 3.5: Polynomial fits with Maple / 32 \\ 3.6: Polynomial fits with Mathematica / 33 \\ 3.7: Exact polynomial coefficients / 42 \\ 3.8: Cody\slash Waite rational polynomials / 43 \\ 3.9: Chebyshev polynomial economization / 43 \\ 3.10: Evaluating Chebyshev polynomials / 48 \\ 3.11: Error compensation in Chebyshev fits / 50 \\ 3.12: Improving Chebyshev fits / 51 \\ 3.13: Chebyshev fits in rational form / 52 \\ 3.14: Chebyshev fits with Mathematica / 56 \\ 3.15: Chebyshev fits for function representation / 57 \\ 3.16: Extending the library / 57 \\ 3.17: Summary and further reading / 58 \\ 4: Implementation issues / 61 \\ 4.1: Error magnification / 61 \\ 4.2: Machine representation and machine epsilon / 62 \\ 4.3: IEEE 754 arithmetic / 63 \\ 4.4: Evaluation order in C / 64 \\ 4.5: The {\tt volatile} type qualifier / 65 \\ 4.6: Rounding in floating-point arithmetic / 66 \\ 4.7: Signed zero / 69 \\ 4.8: Floating-point zero divide / 70 \\ 4.9: Floating-point overflow / 71 \\ 4.10: Integer overflow / 72 \\ 4.11: Floating-point underflow / 77 \\ 4.12: Subnormal numbers / 78 \\ 4.13: Floating-point inexact operation / 79 \\ 4.14: Floating-point invalid operation / 79 \\ 4.15: Remarks on NaN tests / 80 \\ 4.16: Ulps --- units in the last place / 81 \\ 4.17: Fused multiply-add / 85 \\ 4.18: Fused multiply-add and polynomials / 88 \\ 4.19: Significance loss / 89 \\ 4.20: Error handling and reporting / 89 \\ 4.21: Interpreting error codes / 93 \\ 4.22: C99 changes to error reporting / 94 \\ 4.23: Error reporting with threads / 95 \\ 4.24: Comments on error reporting / 95 \\ 4.25: Testing function implementations / 96 \\ 4.26: Extended data types on Hewlett--Packard HP-UX IA-64 / 100 \\ 4.27: Extensions for decimal arithmetic / 101 \\ 4.28: Further reading / 103 \\ 4.29: Summary / 104 \\ 5: The floating-point environment / 105 \\ 5.1: IEEE 754 and programming languages / 105 \\ 5.2: IEEE 754 and the mathcw library / 106 \\ 5.3: Exceptions and traps / 106 \\ 5.4: Access to exception flags and rounding control / 107 \\ 5.5: The environment access pragma / 110 \\ 5.6: Implementation of exception-flag and rounding-control access / 110 \\ 5.7: Using exception flags: simple cases / 112 \\ 5.8: Using rounding control / 115 \\ 5.9: Additional exception flag access / 116 \\ 5.10: Using exception flags: complex case / 120 \\ 5.11: Access to precision control / 123 \\ 5.12: Using precision control / 126 \\ 5.13: Summary / 127 \\ 6: Converting floating-point values to integers / 129 \\ 6.1: Integer conversion in programming languages / 129 \\ 6.2: Programming issues for conversions to integers / 130 \\ 6.3: Hardware out-of-range conversions / 131 \\ 6.4: Rounding modes and integer conversions / 132 \\ 6.5: Extracting integral and fractional parts / 132 \\ 6.6: Truncation functions / 135 \\ 6.7: Ceiling and floor functions / 136 \\ 6.8: Floating-point rounding functions with fixed rounding / 137 \\ 6.9: Floating-point rounding functions: current rounding / 138 \\ 6.10: Floating-point rounding functions without {\em inexact\/} exception / 139 \\ 6.11: Integer rounding functions with fixed rounding / 140 \\ 6.12: Integer rounding functions with current rounding / 142 \\ 6.13: Remainder / 143 \\ 6.14: Why the remainder functions are hard / 144 \\ 6.15: Computing {\tt fmod} / 146 \\ 6.16: Computing {\tt remainder} / 148 \\ 6.17: Computing {\tt remquo} / 150 \\ 6.18: Computing one remainder from the other / 152 \\ 6.19: Computing the remainder in nonbinary bases / 155 \\ 6.20: Summary / 156 \\ 7: Random numbers / 157 \\ 7.1: Guidelines for random-number software / 157 \\ 7.2: Creating generator seeds / 158 \\ 7.3: Random floating-point values / 160 \\ 7.4: Random integers from floating-point generator / 165 \\ 7.5: Random integers from an integer generator / 166 \\ 7.6: Random integers in ascending order / 168 \\ 7.7: How random numbers are generated / 169 \\ 7.8: Removing generator bias / 178 \\ 7.9: Improving a poor random number generator / 178 \\ 7.10: Why long periods matter / 179 \\ 7.11: Inversive congruential generators / 180 \\ 7.12: Inversive congruential generators, revisited / 189 \\ 7.13: Distributions of random numbers / 189 \\ 7.14: Other distributions / 195 \\ 7.15: Testing random-number generators / 196 \\ 7.16: Applications of random numbers / 202 \\ 7.17: The \textsf {mathcw} random number routines / 208 \\ 7.18: Summary, advice, and further reading / 214 \\ 8: Roots / 215 \\ 8.1: Square root / 215 \\ 8.2: Hypotenuse and vector norms / 222 \\ 8.3: Hypotenuse by iteration / 227 \\ 8.4: Reciprocal square root / 233 \\ 8.5: Cube root / 237 \\ 8.6: Roots in hardware / 240 \\ 8.7: Summary / 242 \\ 9: Argument reduction / 243 \\ 9.1: Simple argument reduction / 243 \\ 9.2: Exact argument reduction / 250 \\ 9.3: Implementing exact argument reduction / 253 \\ 9.4: Testing argument reduction / 265 \\ 9.5: Retrospective on argument reduction / 265 \\ 10: Exponential and logarithm / 267 \\ 10.1: Exponential functions / 267 \\ 10.2: Exponential near zero / 273 \\ 10.3: Logarithm functions / 282 \\ 10.4: Logarithm near one / 290 \\ 10.5: Exponential and logarithm in hardware / 292 \\ 10.6: Compound interest and annuities / 294 \\ 10.7: Summary / 298 \\ 11: Trigonometric functions / 299 \\ 11.1: Sine and cosine properties / 299 \\ 11.2: Tangent properties / 302 \\ 11.3: Argument conventions and units / 304 \\ 11.4: Computing the cosine and sine / 306 \\ 11.5: Computing the tangent / 310 \\ 11.6: Trigonometric functions in degrees / 313 \\ 11.7: Trigonometric functions in units of $ \pi $ / 315 \\ 11.8: Computing the cosine and sine together / 320 \\ 11.9: Inverse sine and cosine / 323 \\ 11.10: Inverse tangent / 331 \\ 11.11: Inverse tangent, take two / 336 \\ 11.12: Trigonometric functions in hardware / 338 \\ 11.13: Testing trigonometric functions / 339 \\ 11.14: Retrospective on trigonometric functions / 340 \\ 12: Hyperbolic functions / 341 \\ 12.1: Hyperbolic functions / 341 \\ 12.2: Improving the hyperbolic functions / 345 \\ 12.3: Computing the hyperbolic functions together / 348 \\ 12.4: Inverse hyperbolic functions / 348 \\ 12.5: Hyperbolic functions in hardware / 350 \\ 12.6: Summary / 352 \\ 13: Pair-precision arithmetic / 353 \\ 13.1: Limitations of pair-precision arithmetic / 354 \\ 13.2: Design of the pair-precision software interface / 355 \\ 13.3: Pair-precision initialization / 356 \\ 13.4: Pair-precision evaluation / 357 \\ 13.5: Pair-precision high part / 357 \\ 13.6: Pair-precision low part / 357 \\ 13.7: Pair-precision copy / 357 \\ 13.8: Pair-precision negation / 358 \\ 13.9: Pair-precision absolute value / 358 \\ 13.10: Pair-precision sum / 358 \\ 13.11: Splitting numbers into pair sums / 359 \\ 13.12: Premature overflow in splitting / 362 \\ 13.13: Pair-precision addition / 365 \\ 13.14: Pair-precision subtraction / 367 \\ 13.15: Pair-precision comparison / 368 \\ 13.16: Pair-precision multiplication / 368 \\ 13.17: Pair-precision division / 371 \\ 13.18: Pair-precision square root / 373 \\ 13.19: Pair-precision cube root / 377 \\ 13.20: Accuracy of pair-precision arithmetic / 379 \\ 13.21: Pair-precision vector sum / 384 \\ 13.22: Exact vector sums / 385 \\ 13.23: Pair-precision dot product / 385 \\ 13.24: Pair-precision product sum / 386 \\ 13.25: Pair-precision decimal arithmetic / 387 \\ 13.26: Fused multiply-add with pair precision / 388 \\ 13.27: Higher intermediate precision and the FMA / 393 \\ 13.28: Fused multiply-add without pair precision / 395 \\ 13.29: Fused multiply-add with multiple precision / 401 \\ 13.30: Fused multiply-add, Boldo/\penalty \exhyphenpenalty Melquiond style / 403 \\ 13.31: Error correction in fused multiply-add / 406 \\ 13.32: Retrospective on pair-precision arithmetic / 407 \\ 14: Power function / 411 \\ 14.1: Why the power function is hard to compute / 411 \\ 14.2: Special cases for the power function / 412 \\ 14.3: Integer powers / 414 \\ 14.4: Integer powers, revisited / 420 \\ 14.5: Outline of the power-function algorithm / 421 \\ 14.6: Finding $a$ and $p$ / 423 \\ 14.7: Table searching / 424 \\ 14.8: Computing $\log_n(g/a)$ / 426 \\ 14.9: Accuracy required for $\log_n(g/a)$ / 429 \\ 14.10: Exact products / 430 \\ 14.11: Computing $w$, $w_1$ and $w_2$ / 433 \\ 14.12: Computing $n^{w_2}$ / 437 \\ 14.13: The choice of $q$ / 438 \\ 14.14: Testing the power function / 438 \\ 14.15: Retrospective on the power function / 440 \\ 15: Complex arithmetic primitives / 441 \\ 15.1: Support macros and type definitions / 442 \\ 15.2: Complex absolute value / 443 \\ 15.3: Complex addition / 445 \\ 15.4: Complex argument / 445 \\ 15.5: Complex conjugate / 446 \\ 15.6: Complex conjugation symmetry / 446 \\ 15.7: Complex conversion / 448 \\ 15.8: Complex copy / 448 \\ 15.9: Complex division: C99 style / 449 \\ 15.10: Complex division: Smith style / 451 \\ 15.11: Complex division: Stewart style / 452 \\ 15.12: Complex division: Priest style / 453 \\ 15.13: Complex division: avoiding subtraction loss / 455 \\ 15.14: Complex imaginary part / 456 \\ 15.15: Complex multiplication / 456 \\ 15.16: Complex multiplication: error analysis / 458 \\ 15.17: Complex negation / 459 \\ 15.18: Complex projection / 460 \\ 15.19: Complex real part / 460 \\ 15.20: Complex subtraction / 461 \\ 15.21: Complex infinity test / 462 \\ 15.22: Complex NaN test / 462 \\ 15.23: Summary / 463 \\ 16: Quadratic equations / 465 \\ 16.1: Solving quadratic equations / 465 \\ 16.2: Root sensitivity / 471 \\ 16.3: Testing a quadratic-equation solver / 472 \\ 16.4: Summary / 474 \\ 17: Elementary functions in complex arithmetic / 475 \\ 17.1: Research on complex elementary functions / 475 \\ 17.2: Principal values / 476 \\ 17.3: Branch cuts / 476 \\ 17.4: Software problems with negative zeros / 478 \\ 17.5: Complex elementary function tree / 479 \\ 17.6: Series for complex functions / 479 \\ 17.7: Complex square root / 480 \\ 17.8: Complex cube root / 485 \\ 17.9: Complex exponential / 487 \\ 17.10: Complex exponential near zero / 492 \\ 17.11: Complex logarithm / 495 \\ 17.12: Complex logarithm near one / 497 \\ 17.13: Complex power / 500 \\ 17.14: Complex trigonometric functions / 502 \\ 17.15: Complex inverse trigonometric functions / 504 \\ 17.16: Complex hyperbolic functions / 509 \\ 17.17: Complex inverse hyperbolic functions / 514 \\ 17.18: Summary / 520 \\ 18: The Greek functions: gamma, psi, and zeta / 521 \\ 18.1: Gamma and log-gamma functions / 521 \\ 18.2: The {\tt psi} and {\tt psiln} functions / 536 \\ 18.3: Polygamma functions / 547 \\ 18.4: Incomplete gamma functions / 560 \\ 18.5: A Swiss diversion: Bernoulli and Euler / 568 \\ 18.6: An Italian excursion: Fibonacci numbers / 575 \\ 18.7: A German gem: the Riemann zeta function / 579 \\ 18.8: Further reading / 590 \\ 18.9: Summary / 591 \\ 19: Error and probability functions / 593 \\ 19.1: Error functions / 593 \\ 19.2: Scaled complementary error function / 598 \\ 19.3: Inverse error functions / 600 \\ 19.4: Normal distribution functions and inverses / 610 \\ 19.5: Summary / 617 \\ 20: Elliptic integral functions / 619 \\ 20.1: The arithmetic-geometric mean / 619 \\ 20.2: Elliptic integral functions of the first kind / 624 \\ 20.3: Elliptic integral functions of the second kind / 627 \\ 20.4: Elliptic integral functions of the third kind / 630 \\ 20.5: Computing $K(m)$ and $K'(m)$ / 631 \\ 20.6: Computing $E(m)$ and $E'(m)$ / 637 \\ 20.7: Historical algorithms for elliptic integrals / 643 \\ 20.8: Auxiliary functions for elliptic integrals / 645 \\ 20.9: Computing the elliptic auxiliary functions / 648 \\ 20.10: Historical elliptic functions / 650 \\ 20.11: Elliptic functions in software / 652 \\ 20.12: Applications of elliptic auxiliary functions / 653 \\ 20.13: Elementary functions from elliptic auxiliary functions / 654 \\ 20.14: Computing elementary functions via $R_C(x,y)$ / 655 \\ 20.15: Jacobian elliptic functions / 657 \\ 20.16: Inverses of Jacobian elliptic functions / 664 \\ 20.17: The modulus and the nome / 668 \\ 20.18: Jacobian theta functions / 673 \\ 20.19: Logarithmic derivatives of the Jacobian theta functions / 675 \\ 20.20: Neville theta functions / 678 \\ 20.21: Jacobian Eta, Theta, and Zeta functions / 679 \\ 20.22: Weierstrass elliptic functions / 682 \\ 20.23: Weierstrass functions by duplication / 689 \\ 20.24: Complete elliptic functions, revisited / 690 \\ 20.25: Summary / 691 \\ 21: Bessel functions / 693 \\ 21.1: Cylindrical Bessel functions / 694 \\ 21.2: Behavior of $J_n(x)$ and $Y_n(x)$ / 695 \\ 21.3: Properties of $J_n(z)$ and $Y_n(z)$ / 697 \\ 21.4: Experiments with recurrences for $J_0(x)$ / 705 \\ 21.5: Computing $J_0(x)$ and $J_1(x)$ / 707 \\ 21.6: Computing $J_n(x)$ / 710 \\ 21.7: Computing $Y_0(x)$ and $Y_1(x)$ / 713 \\ 21.8: Computing $Y_n(x)$ / 715 \\ 21.9: Improving Bessel code near zeros / 716 \\ 21.10: Properties of $I_n(z)$ and $K_n(z)$ / 718 \\ 21.11: Computing $I_0(x)$ and $I_1(x)$ / 724 \\ 21.12: Computing $K_0(x)$ and $K_1(x)$ / 726 \\ 21.13: Computing $I_n(x)$ and $K_n(x)$ / 728 \\ 21.14: Properties of spherical Bessel functions / 731 \\ 21.15: Computing $j_n(x)$ and $y_n(x)$ / 735 \\ 21.16: Improving $j_1(x)$ and $y_1(x)$ / 740 \\ 21.17: Modified spherical Bessel functions / 743 \\ 21.18: Software for Bessel-function sequences / 755 \\ 21.19: Retrospective on Bessel functions / 761 \\ 22: Testing the library / 763 \\ 22.1: Testing {\tt tgamma} and {\tt lgamma} / 765 \\ 22.2: Testing {\tt psi} and {\tt psiln} / 768 \\ 22.3: Testing {\tt erf} and {\tt erfc} / 768 \\ 22.4: Testing cylindrical Bessel functions / 769 \\ 22.5: Testing exponent/\penalty \exhyphenpenalty significand manipulation / 769 \\ 22.6: Testing inline assembly code / 769 \\ 22.7: Testing with Maple / 770 \\ 22.8: Testing floating-point arithmetic / 773 \\ 22.9: The Berkeley Elementary Functions Test Suite / 774 \\ 22.10: The AT\&T floating-point test package / 775 \\ 22.11: The Antwerp test suite / 776 \\ 22.12: Summary / 776 \\ 23: Pair-precision elementary functions / 777 \\ 23.1: Pair-precision integer power / 777 \\ 23.2: Pair-precision machine epsilon / 779 \\ 23.3: Pair-precision exponential / 780 \\ 23.4: Pair-precision logarithm / 787 \\ 23.5: Pair-precision logarithm near one / 793 \\ 23.6: Pair-precision exponential near zero / 793 \\ 23.7: Pair-precision base-$n$ exponentials / 795 \\ 23.8: Pair-precision trigonometric functions / 796 \\ 23.9: Pair-precision inverse trigonometric functions / 801 \\ 23.10: Pair-precision hyperbolic functions / 804 \\ 23.11: Pair-precision inverse hyperbolic functions / 808 \\ 23.12: Summary / 808 \\ 24: Accuracy of the Cody\slash Waite algorithms / 811 \\ 25: Improving upon the Cody\slash Waite algorithms / 823 \\ 25.1: The Bell Labs libraries / 823 \\ 25.2: The {Cephes} library / 823 \\ 25.3: The {Sun} libraries / 824 \\ 25.4: Mathematical functions on EPIC / 824 \\ 25.5: The GNU libraries / 825 \\ 25.6: The French libraries / 825 \\ 25.7: The NIST effort / 826 \\ 25.8: Commercial mathematical libraries / 826 \\ 25.9: Mathematical libraries for decimal arithmetic / 826 \\ 25.10: Mathematical library research publications / 826 \\ 25.11: Books on computing mathematical functions / 827 \\ 25.12: Summary / 828 \\ 26: Floating-point output / 829 \\ 26.1: Output character string design issues / 830 \\ 26.2: Exact output conversion / 831 \\ 26.3: Hexadecimal floating-point output / 832 \\ 26.4: Octal floating-point output / 850 \\ 26.5: Binary floating-point output / 851 \\ 26.6: Decimal floating-point output / 851 \\ 26.7: Accuracy of output conversion / 865 \\ 26.8: Output conversion to a general base / 865 \\ 26.9: Output conversion of Infinity / 866 \\ 26.10: Output conversion of NaN / 866 \\ 26.11: Number-to-string conversion / 867 \\ 26.12: The {\tt printf} family / 867 \\ 26.13: Summary / 878 \\ 27: Floating-point input / 879 \\ 27.1: Binary floating-point input / 879 \\ 27.2: Octal floating-point input / 894 \\ 27.3: Hexadecimal floating-point input / 895 \\ 27.4: Decimal floating-point input / 895 \\ 27.5: Based-number input / 899 \\ 27.6: General floating-point input / 900 \\ 27.7: The {\tt scanf} family / 901 \\ 27.8: Summary / 910 \\ A: Ada interface / 911 \\ A.1: Building the Ada interface / 911 \\ A.2: Programming the Ada interface / 912 \\ A.3: Using the Ada interface / 915 \\ B: C\# interface / 917 \\ B.1: C\# on the CLI virtual machine / 917 \\ B.2: Building the C\# interface / 918 \\ B.3: Programming the C\# interface / 920 \\ B.4: Using the C\# interface / 922 \\ C: C++ interface / 923 \\ C.1: Building the C++ interface / 923 \\ C.2: Programming the C++ interface / 924 \\ C.3: Using the C++ interface / 925 \\ D: Decimal arithmetic / 927 \\ D.1: Why we need decimal floating-point arithmetic / 927 \\ D.2: Decimal floating-point arithmetic design issues / 928 \\ D.3: How decimal and binary arithmetic differ / 931 \\ D.4: Initialization of decimal floating-point storage / 935 \\ D.5: The {\tt <decfloat.h>} header file / 936 \\ D.6: Rounding in decimal arithmetic / 936 \\ D.7: Exact scaling in decimal arithmetic / 937 \\ E: Errata in the Cody\slash Waite book / 939 \\ F: Fortran interface / 941 \\ F.1: Building the Fortran interface / 943 \\ F.2: Programming the Fortran interface / 944 \\ F.3: Using the Fortran interface / 945 \\ H: Historical floating-point architectures / 947 \\ H.1: CDC family / 949 \\ H.2: Cray family / 952 \\ H.3: DEC PDP-10 / 953 \\ H.4: DEC PDP-11 and VAX / 956 \\ H.5: General Electric 600 series / 958 \\ H.6: IBM family / 959 \\ H.7: Lawrence Livermore S-1 Mark IIA / 965 \\ H.8: Unusual floating-point systems / 966 \\ H.9: Historical retrospective / 967 \\ I: Integer arithmetic / 969 \\ I.1: Memory addressing and integers / 971 \\ I.2: Representations of signed integers / 971 \\ I.3: Parity testing / 975 \\ I.4: Sign testing / 975 \\ I.5: Arithmetic exceptions / 975 \\ I.6: Notations for binary numbers / 977 \\ I.7: Summary / 978 \\ J: Java interface / 979 \\ J.1: Building the Java interface / 979 \\ J.2: Programming the Java MathCW class / 980 \\ J.3: Programming the Java C interface / 982 \\ J.4: Using the Java interface / 985 \\ L: Letter notation / 987 \\ P: Pascal interface / 989 \\ P.1: Building the Pascal interface / 989 \\ P.2: Programming the Pascal MathCW module / 990 \\ P.3: Using the Pascal module interface / 993 \\ P.4: Pascal and numeric programming / 994 \\ Bibliography / 995 \\ Author/editor index / 1039 \\ Function and macro index / 1049 \\ Subject index / 1065 \\ Colophon / 1115", } @Book{Boldo:2017:CAF, author = "Sylvie Boldo and Guillaume Melquiond", title = "Computer arithmetic and formal proofs: verifying floating-point algorithms with the {Coq} system", publisher = "ISTE Press", address = "London, UK", year = "2017", ISBN = "1-78548-112-6, 0-08-101170-9 (e-book)", ISBN-13 = "978-1-78548-112-3, 978-0-08-101170-6 (e-book)", LCCN = "QA76.9.C62", bibdate = "Tue Nov 28 08:55:56 MST 2017", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", URL = "http://iste.co.uk/book.php?id=1238", abstract = "Floating-point arithmetic is ubiquitous in modern computing, as it is the tool of choice to approximate real numbers. Due to its limited range and precision, its use can become quite involved and potentially lead to numerous failures. One way to greatly increase confidence in floating-point software is by computer-assisted verification of its correctness proofs. This book provides a comprehensive view of how to formally specify and verify tricky floating-point algorithms with the Coq proof assistant. It describes the Flocq formalization of floating-point arithmetic and some methods to automate theorem proofs. It then presents the specification and verification of various algorithms, from error-free transformations to a numerical scheme for a partial differential equation. The examples cover not only mathematical algorithms but also C programs as well as issues related to compilation. Describes the notions of specification and weakest precondition computation and their practical use. Shows how to tackle algorithms that extend beyond the realm of simple floating-point arithmetic. Includes real analysis and a case study about numerical analysis.", acknowledgement = ack-nhfb, subject = "Coq (Electronic resource); Computer arithmetic; Floating-point arithmetic; Computer algorithms; COMPUTERS / Computer Literacy; COMPUTERS / Computer Science; COMPUTERS / Data Processing; COMPUTERS / Hardware / General; COMPUTERS / Information Technology; COMPUTERS / Machine Theory; COMPUTERS / Reference; MATHEMATICS / Discrete Mathematics", tableofcontents = "1. Floating-Point Arithmetic \\ 2. The Coq System \\ 3. Formalization of Formats and Basic Operators \\ 4. Automated Methods \\ 5. Error-Free Computations and Applications \\ 6. Example Proofs of Advanced Operators \\ 7. Compilation of FP Programs \\ 8. Deductive Program Verification \\ 9. Real and Numerical Analysis", } @Book{Garcia:2017:SCL, author = "Stephan Ramon Garcia and Roger A. Horn", title = "A Second Course in Linear Algebra", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "442 (est.)", year = "2017", ISBN = "1-107-10381-9 (hardcover)", ISBN-13 = "978-1-107-10381-8 (hardcover)", LCCN = "QA184.2 .G37 2017", bibdate = "Tue Jul 11 16:36:22 MDT 2017", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "Algebras, Linear; Textbooks", URL = "http://www.cambridge.org/us/academic/subjects/mathematics/algebra/second-course-linear-algebra?format=HB", } @Book{Higham:2017:MG, author = "Desmond J. Higham and Nicholas J. Higham", title = "{MATLAB} guide", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xxvi + 476", year = "2017", ISBN = "1-61197-465-8", ISBN-13 = "978-1-61197-465-2", MRclass = "65-00 (00A20)", MRnumber = "3601107", bibdate = "Sat Aug 26 17:40:10 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", abstract = "MATLAB is an interactive system for numerical computation that is widely used for teaching and research in industry and academia. It provides a modern programming language and problem solving environment, with powerful data structures, customizable graphics, and easy-to-use editing and debugging tools. This third edition of MATLAB Guide completely revises and updates the best-selling second edition and is more than 25 percent longer. The book remains a lively, concise introduction to the most popular and important features of MATLAB and the Symbolic Math Toolbox. Key features are a tutorial in Chapter 1 that gives a hands-on overview of MATLAB, a thorough treatment of MATLAB mathematics, including the linear algebra and numerical analysis functions and the differential equation solvers, and a web page that provides a link to example program files, updates, and links to MATLAB resources. The new edition contains color figures throughout, includes pithy discussions of related topics in new `Asides' boxes that augment the text, has new chapters on the Parallel Computing Toolbox, object-oriented programming, graphs, and large data sets, covers important new MATLAB data types such as categorical arrays, string arrays, tall arrays, tables, and timetables, contains more on MATLAB workflow, including the Live Editor and unit tests, and fully reflects major updates to the MATLAB graphics system.", acknowledgement = ack-nhfb, remark = "Third edition of \cite{Higham:2000:MG,Higham:2005:MG}.", subject = "MATLAB (logiciel).; Analyse num{\'e}rique; Logiciels.; Numerical analysis; Data processing; Data processing.", tableofcontents = "1: A Brief Tutorial \\ 2: Basics \\ 3: Distinctive Features of MATLAB \\ 4: Arithmetic \\ 5: Matrices \\ 6: Operators and Flow Control \\ 7: Program Files \\ 8: Graphics \\ 9: Linear Algebra \\ 10: More on Functions \\ 11: Numerical Methods: Part I \\ 12: Numerical Methods: Part II \\ 13: Input and Output \\ 14: Troubleshooting \\ 15: Sparse Matrices \\ 16: More on Coding \\ 17: Advanced Graphics \\ 18: Other Data Types and Multidimensional Arrays \\ 19: Object-Oriented Programming \\ 20: The Symbolic Math Toolbox \\ 21: Graphs \\ 22: Large Data Sets \\ 23: Optimizing Codes \\ 24: Tricks and Tips \\ 25: The Parallel Computing Toolbox \\ 26: Case Studies", } @Book{Howard:2017:CMN, author = "James Patrick {Howard, II}", title = "Computational methods, for numerical analysis with {R}", publisher = "CRC Press/Taylor and Francis Group", address = "Boca Raton, FL, USA", pages = "xx + 257", year = "2017", ISBN = "1-4987-2363-2 (hardcover), 1-4987-2364-0 (e-book), 1-315-12019-4 (e-book)", ISBN-13 = "978-1-4987-2363-3 (hardcover), 978-1-4987-2364-0 (e-book), 978-1-315-12019-5 (e-book)", LCCN = "QA297 .H67 2017", bibdate = "Sat Mar 16 12:09:51 MDT 2019", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/s-plus.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.crcnetbase.com/isbn/9781498723640", acknowledgement = ack-nhfb, subject = "Numerical analysis; Data processing; R (Computer program language)", tableofcontents = "1: Introduction to Numerical Analysis / 28 pages \\ 2: Error Analysis / 30 pages \\ 3: Linear Algebra / 36 pages \\ 4: Interpolation and Extrapolation / 38 pages \\ 5: Differentiation and Integration / 42 pages \\ 6: Root Finding and Optimization / 37 pages \\ 7: Differential Equations / 35 pages", } @Book{Schiesser:2017:SCM, author = "William E. Schiesser", title = "Spline Collocation Methods for Partial Differential Equations: with Applications in {R}", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xv + 549", year = "2017", DOI = "https://doi.org/10.1002/9781119301066", ISBN = "1-119-30103-3 (hardcover), 1-119-30105-X (PDF), 1-119-30104-1 (ePub), 1-119-30106-8 (online)", ISBN-13 = "978-1-119-30103-5 (hardcover), 978-1-119-30105-9 (PDF), 978-1-119-30104-2 (ePub), 978-1-119-30106-6 (online)", LCCN = "QA377 .S355 2017", bibdate = "Tue Mar 13 10:16:43 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/clerk-maxwell-james.bib; http://www.math.utah.edu/pub/bibnet/authors/p/planck-max.bib; http://www.math.utah.edu/pub/tex/bib/einstein.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/s-plus.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, shorttableofcontents = "One-dimensional PDEs \\ Multidimensional PDEs \\ Navier--Stokes, Burgers equations \\ Korteweg--deVries equation \\ Maxwell equations \\ Poisson--Nernst--Planck equations \\ Fokker--Planck equation \\ Fisher--Kolmogorov equation \\ Klein--Gordon equation \\ Boussinesq equation \\ Cahn--Hilliard equation \\ Camassa--Holm equation \\ Burgers--Huxley equation \\ Gierer--Meinhardt equations \\ Keller--Segel equations \\ Fitzhugh--Nagumo equations \\ Euler--Poisson--Darboux equation \\ Kuramoto--Sivashinsky equation \\ Einstein--Maxwell equations", subject = "Differential equations, Partial; Mathematical models; Spline theory", tableofcontents = "Preface / xiii \\ About the Companion Website / xv \\ 1 Introduction / 1 \\ 1.1 Uniform Grids / 2 \\ 1.2 Variable Grids / 18 \\ 1.3 Stagewise Differentiation / 24 \\ Appendix A1 --- Online Documentation for splinefun / 27 \\ Reference / 30 \\ 2 One-Dimensional PDEs / 31 \\ 2.1 Constant Coefficient / 31 \\ 2.1.1 Dirichlet BCs / 32 \\ 2.1.1.1 Main Program / 33 \\ 2.1.1.2 ODE Routine / 40 \\ 2.1.2 Neumann BCs / 43 \\ 2.1.2.1 Main Program / 44 \\ 2.1.2.2 ODE Routine / 46 \\ 2.1.3 Robin BCs / 49 \\ 2.1.3.1 Main Program / 50 \\ 2.1.3.2 ODE Routine / 55 \\ 2.1.4 Nonlinear BCs / 60 \\ 2.1.4.1 Main Program / 61 \\ 2.1.4.2 ODE Routine / 63 \\ 2.2 Variable Coefficient / 64 \\ 2.2.1 Main Program / 67 \\ 2.2.2 ODE Routine / 71 \\ 2.3 Inhomogeneous, Simultaneous, Nonlinear / 76 \\ 2.3.1 Main Program / 78 \\ 2.3.2 ODE routine / 85 \\ 2.3.3 Subordinate Routines / 88 \\ 2.4 First Order in Space and Time / 94 \\ 2.4.1 Main Program / 96 \\ 2.4.2 ODE Routine / 101 \\ 2.4.3 Subordinate Routines / 105 \\ 2.5 Second Order in Time / 107 \\ 2.5.1 Main Program / 109 \\ 2.5.2 ODE Routine / 114 \\ 2.5.3 Subordinate Routine / 117 \\ 2.6 Fourth Order in Space / 120 \\ 2.6.1 First Order in Time / 120 \\ 2.6.1.1 Main Program / 121 \\ 2.6.1.2 ODE Routine / 125 \\ 2.6.2 Second Order in Time / 138 \\ 2.6.2.1 Main Program / 140 \\ 2.6.2.2 ODE Routine / 143 \\ References / 155 \\ 3 Multidimensional PDEs / 157 \\ 3.1 2D in Space / 157 \\ 3.1.1 Main Program / 158 \\ 3.1.2 ODE Routine / 163 \\ 3.2 3D in Space / 170 \\ 3.2.1 Main Program, Case 1 / 170 \\ 3.2.2 ODE Routine / 174 \\ 3.2.3 Main Program, Case 2 / 183 \\ 3.2.4 ODE Routine / 187 \\ 3.3 Summary and Conclusions / 193 \\ 4 Navier--Stokes, Burgers' Equations / 197 \\ 4.1 PDE Model / 197 \\ 4.2 Main Program / 198 \\ 4.3 ODE Routine / 203 \\ 4.4 Subordinate Routine / 205 \\ 4.5 Model Output / 206 \\ 4.6 Summary and Conclusions / 208 \\ Reference / 209 \\ 5 Korteweg--de Vries Equation / 211 \\ 5.1 PDE Model / 211 \\ 5.2 Main Program / 212 \\ 5.3 ODE Routine / 225 \\ 5.4 Subordinate Routines / 228 \\ 5.5 Model Output / 234 \\ 5.6 Summary and Conclusions / 238 \\ References / 239 \\ 6 Maxwell Equations / 241 \\ 6.1 PDE Model / 241 \\ 6.2 Main Program / 243 \\ 6.3 ODE Routine / 248 \\ 6.4 Model Output / 252 \\ 6.5 Summary and Conclusions / 252 \\ Appendix A6.1. Derivation of the Analytical Solution / 257 \\ Reference / 259 \\ 7 Poisson--Nernst--Planck Equations / 261 \\ 7.1 PDE Model / 261 \\ 7.2 Main Program / 265 \\ 7.3 ODE Routine / 271 \\ 7.4 Model Output / 276 \\ 7.5 Summary and Conclusions / 284 \\ References / 286 \\ 8 Fokker--Planck Equation / 287 \\ 8.1 PDE Model / 287 \\ 8.2 Main Program / 288 \\ 8.3 ODE Routine / 293 \\ 8.4 Model Output / 295 \\ 8.5 Summary and Conclusions / 301 \\ References / 303 \\ 9 Fisher--Kolmogorov Equation / 305 \\ 9.1 PDE Model / 305 \\ 9.2 Main Program / 306 \\ 9.3 ODE Routine / 311 \\ 9.4 Subordinate Routine / 313 \\ 9.5 Model Output / 314 \\ 9.6 Summary and Conclusions / 316 \\ Reference / 316 \\ 10 Klein--Gordon Equation / 317 \\ 10.1 PDE Model, Linear Case / 317 \\ 10.2 Main Program / 318 \\ 10.3 ODE Routine / 323 \\ 10.4 Model Output / 326 \\ 10.5 PDE Model, Nonlinear Case / 328 \\ 10.6 Main Program / 330 \\ 10.7 ODE Routine / 335 \\ 10.8 Subordinate Routines / 338 \\ 10.9 Model Output / 339 \\ 10.10 Summary and Conclusions / 342 \\ Reference / 342 \\ 11 Boussinesq Equation / 343 \\ 11.1 PDE Model / 343 \\ 11.2 Main Program / 344 \\ 11.3 ODE Routine / 350 \\ 11.4 Subordinate Routines / 354 \\ 11.5 Model Output / 355 \\ 11.6 Summary and Conclusions / 358 \\ References / 358 \\ 12 Cahn--Hilliard Equation / 359 \\ 12.1 PDE Model / 359 \\ 12.2 Main Program / 360 \\ 12.3 ODE Routine / 366 \\ 12.4 Model Output / 369 \\ 12.5 Summary and Conclusions / 379 \\ References / 379 \\ 13 Camassa--Holm Equation / 381 \\ 13.1 PDE Model / 381 \\ 13.2 Main Program / 382 \\ 13.3 ODE Routine / 388 \\ 13.4 Model Output / 391 \\ 13.5 Summary and Conclusions / 394 \\ 13.6 Appendix A13.1: Second Example of a PDE with a Mixed Partial Derivative / 395 \\ 13.7 Main Program / 395 \\ 13.8 ODE Routine / 398 \\ 13.9 Model Output / 400 \\ Reference / 403 \\ 14 Burgers--Huxley Equation / 405 \\ 14.1 PDE Model / 405 \\ 14.2 Main Program / 406 \\ 14.3 ODE Routine / 411 \\ 14.4 Subordinate Routine / 416 \\ 14.5 Model Output / 417 \\ 14.6 Summary and Conclusions / 422 \\ References / 422 \\ 15 Gierer--Meinhardt Equations / 423 \\ 15.1 PDE Model / 423 \\ 15.2 Main Program / 424 \\ 15.3 ODE Routine / 429 \\ 15.4 Model Output / 432 \\ 15.5 Summary and Conclusions / 437 \\ Reference / 440 \\ 16 Keller--Segel Equations / 441 \\ 16.1 PDE Model / 441 \\ 16.2 Main Program / 443 \\ 16.3 ODE Routine / 449 \\ 16.4 Subordinate Routines / 453 \\ 16.5 Model Output / 453 \\ 16.6 Summary and Conclusions / 458 \\ Appendix A16.1. Diffusion Models / 458 \\ References / 459 \\ 17 Fitzhugh--Nagumo Equations / 461 \\ 17.1 PDE Model / 461 \\ 17.2 Main Program / 462 \\ 17.3 ODE Routine / 467 \\ 17.4 Model Output / 470 \\ 17.5 Summary and Conclusions / 475 \\ Reference / 475 \\ 18 Euler--Poisson--Darboux Equation / 477 \\ 18.1 PDE Model / 477 \\ 18.2 Main Program / 478 \\ 18.3 ODE Routine / 483 \\ 18.4 Model Output / 488 \\ 18.5 Summary and Conclusions / 493 \\ References / 493 \\ 19 Kuramoto--Sivashinsky Equation / 495 \\ 19.1 PDE Model / 495 \\ 19.2 Main Program / 496 \\ 19.3 ODE Routine / 503 \\ 19.4 Subordinate Routines / 506 \\ 19.5 Model Output / 508 \\ 19.6 Summary and Conclusions / 513 \\ References / 514 \\ 20 Einstein--Maxwell Equations / 515 \\ 20.1 PDE Model / 515 \\ 20.2 Main Program / 516 \\ 20.3 ODE Routine / 521 \\ 20.4 Model Output / 526 \\ 20.5 Summary and Conclusions / 533 \\ Reference / 536 \\ A Differential Operators in Three Orthogonal Coordinate Systems / 537 \\ References / 539 \\ Index / 541", } @Book{Boyd:2018:IAL, author = "Stephen P. In. Boyd and Lieven Vandenberghe", title = "Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "xii + 463", year = "2018", ISBN = "1-108-69394-6, 1-316-51896-5 (hardcover)", ISBN-13 = "978-1-108-69394-3, 978-1-316-51896-0 (hardcover)", LCCN = "QA184.2 .B69 2018", bibdate = "Thu Mar 14 10:47:12 MDT 2019", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", abstract = "This groundbreaking textbook combines straightforward explanations with a wealth of practical examples to offer an innovative approach to teaching linear algebra. Requiring no prior knowledge of the subject, it covers the aspects of linear algebra --- vectors, matrices, and least squares --- that are needed for engineering applications, discussing examples across data science, machine learning and artificial intelligence, signal and image processing, tomography, navigation, control, and finance. The numerous practical exercises throughout allow students to test their understanding and translate their knowledge into solving real-world problems, with lecture slides, additional computational exercises in Julia and MATLAB, and data sets accompanying the book online. It is suitable for both one-semester and one-quarter courses, as well as self-study, this self-contained text provides beginning students with the foundation they need to progress to more advanced study.", acknowledgement = ack-nhfb, author-dates = "1958--", subject = "Algebras, Linear; Textbooks; Matrices; Vector algebra; Least squares", tableofcontents = "Part I. Vectors: \\ 1. Vectors \\ 2. Linear functions \\ 3. Norm and distance \\ 4. Clustering \\ 5. Linear independence \\ Part II. Matrices: \\ 6. Matrices \\ 7. Matrix examples \\ 8. Linear equations \\ 9. Linear dynamical systems \\ 10. Matrix multiplication \\ 11. Matrix inverses \\ Part III. Least Squares: \\ 12. Least squares \\ 13. Least squares data fitting \\ 14. Least squares classification \\ 15. Multi-objective least squares \\ 16. Constrained least squares \\ 17. Constrained least squares applications \\ 18. Nonlinear least squares \\ 19. Constrained nonlinear least squares \\ Appendix A \\ Appendix B \\ Appendix C \\ Appendix D \\ Index", } @Book{Li:2018:NSD, author = "Zhilin Li and Zhonghua Qiao and Tao Tang", title = "Numerical solution of differential equations: introduction to finite difference and finite element methods", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "ix + 293", year = "2018", DOI = "https://doi.org/10.1017/9781316678725", ISBN = "1-107-16322-6 (hardcover), 1-316-61510-3 (paperback), 1-316-67872-5", ISBN-13 = "978-1-107-16322-5 (hardcover), 978-1-316-61510-2 (paperback)", LCCN = "QA371 .L59 2018", bibdate = "Tue Jan 9 07:30:12 MST 2018", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", abstract = "This introduction to finite difference and finite element methods is aimed at graduate students who need to solve differential equations. The prerequisites are few (basic calculus, linear algebra, and ODEs) and so the book will be accessible and useful to readers from a range of disciplines across science and engineering. Part I begins with finite difference methods. Finite element methods are then introduced in Part II. In each part, the authors begin with a comprehensive discussion of one-dimensional problems, before proceeding to consider two or higher dimensions. An emphasis is placed on numerical algorithms, related mathematical theory, and essential details in the implementation, while some useful packages are also introduced. The authors also provide well-tested MATLAB codes, all available online.", acknowledgement = ack-nhfb, author-dates = "1956--", subject = "Differential equations; Numerical solutions", } @Book{Meckes:2018:LA, author = "Elizabeth S. Meckes and Mark W. Meckes", title = "Linear Algebra", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "xvi + 427", year = "2018", ISBN = "1-107-17790-1 (hardcover)", ISBN-13 = "978-1-107-17790-1 (hardcover)", LCCN = "QA184.2 .M43 2018", bibdate = "Tue Feb 26 17:13:01 MST 2019", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Cambridge mathematical textbooks", abstract = "\booktitle{Linear Algebra} offers a unified treatment of both matrix-oriented and theoretical approaches to the course, which will be useful for classes with a mix of mathematics, physics, engineering, and computer science students. Major topics include singular value decomposition, the spectral theorem, linear systems of equations, vector spaces, linear maps, matrices, eigenvalues and eigenvectors, linear independence, bases, coordinates, dimension, matrix factorizations, inner products, norms, and determinants.", acknowledgement = ack-nhfb, subject = "Algebras, Linear; Textbooks; Lineare Algebra", } @Book{Salehi:2018:NISa, author = "Younes Salehi and William E. Schiesser", title = "Numerical integration of space fractional partial differential equations. {Volume 1}, {Introduction} to algorithms and computer coding in {R}", volume = "19", publisher = "Morgan and Claypool Publishers", address = "San Rafael, CA, USA", pages = "xii + 189", year = "2018", DOI = "https://doi.org/10.2200/S00806ED1V01Y201709MAS019", ISBN = "1-68173-207-6 (paperback), 1-68173-208-4 (e-book)", ISBN-13 = "978-1-68173-207-7 (paperback), 978-1-68173-208-4 (e-book)", ISSN = "1938-1743 (print), 1938-1751 (electronic)", ISSN-L = "1938-1743", LCCN = "QA372 .S266 2018", bibdate = "Tue Mar 13 17:09:10 MDT 2018", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/s-plus.bib", series = "Synthesis lectures on mathematics and statistics", abstract = "Partial differential equations (PDEs) are one of the most used widely forms of mathematics in science and engineering. PDEs can have partial derivatives with respect to (1) an initial value variable, typically time, and (2) boundary value variables, typically spatial variables. Therefore, two fractional PDEs can be considered, (1) fractional in time (TFPDEs), and (2) fractional in space (SFPDEs). The two volumes are directed to the development and use of SFPDEs, with the discussion divided as: Vol 1: Introduction to Algorithms and Computer Coding in R Vol 2: Applications from Classical Integer PDEs. Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann--Liouville derivative. The Caputo derivative is defined as a convolution integral. Thus, rather than being local (with a value at a particular point in space), the Caputo derivative is non-local (it is based on an integration in space), which is one of the reasons that it has properties not shared by integer derivatives. A principal objective of the two volumes is to provide the reader with a set of documented R routines that are discussed in detail, and can be downloaded and executed without having to first study the details of the relevant numerical analysis and then code a set of routines. In the first volume, the emphasis is on basic concepts of SFPDEs and the associated numerical algorithms. The presentation is not as formal mathematics, e.g., theorems and proofs. Rather, the presentation is by examples of SFPDEs, including a detailed discussion of the algorithms for computing numerical solutions to SFPDEs and a detailed explanation of the associated source code.", acknowledgement = ack-nhfb, subject = "Fractional differential equations; Differential equations, Partial; Spatial analysis (Statistics); R (Computer program language); Differential equations, Partial; Fractional differential equations; R (Computer program language); Spatial analysis (Statistics)", tableofcontents = "1. Introduction to fractional partial differential equations \\ 1.1 Introduction \\ 1.2 Computer routines, example 1 \\ 1.2.1 Main program \\ 1.2.2 Subordinate ODE/MOL routine \\ 1.2.3 Model output \\ 1.3 Computer routines, example 2 \\ 1.3.1 Main program \\ 1.3.2 Subordinate ODE/MOL routine \\ 1.3.3 Model output \\ 1.3.4 Summary and conclusions \\ References \\ 2. Variation in the order of the fractional derivatives \\ 2.1 Introduction \\ 2.2 Computer routines, example 1 \\ 2.2.1 Main program \\ 2.2.2 Subordinate ODE/MOL routine \\ 2.2.3 Model output \\ 2.3 Computer routines, example 2 \\ 2.3.1 Main program \\ 2.3.2 Subordinate ODE/MOL routine \\ 2.3.3 Model output \\ 2.4 Summary and discussion \\ 3. Dirichlet, Neumann, Robin BCs \\ 3.1 Introduction \\ 3.2 Example 1, Dirichlet BCs \\ 3.2.1 Main program \\ 3.2.2 Subordinate ODE/MOL routine \\ 3.2.3 Model output \\ 3.3 Example 2, Dirichlet BCs \\ 3.3.1 Main program \\ 3.3.2 Subordinate ODE/MOL routine \\ 3.3.3 Model output \\ 3.4 Example 2, Neumann BCs \\ 3.4.1 Main program \\ 3.4.2 Subordinate ODE/MOL routine \\ 3.4.3 Model output \\ 3.5 Example 2, Robin BCs \\ 3.5.1 Main program \\ 3.5.2 Subordinate ODE/MOL routine \\ 3.5.3 Model output \\ 3.6 Summary and conclusions \\ 4. Convection SFPDEs \\ 4.1 Introduction \\ 4.2 Integer/fractional convection model \\ 4.2.1 Main program \\ 4.2.2 Subordinate ODE/MOL routine \\ 4.2.3 SFPDE output \\ 4.3 Summary and conclusions 5. Nonlinear SFPDEs \\ 5.1 Introduction \\ 5.1.1 Example 1 \\ 5.1.2 Main program \\ 5.1.3 Subordinate ODE/MOL routine \\ 5.1.4 Model output \\ 5.2 Example 2 \\ 5.2.1 Main program \\ 5.2.2 Subordinate ODE/MOL routine \\ 5.2.3 Model output \\ 5.3 Summary and conclusions \\ A. Analytical Caputo differentiation of selected functions \\ B. Derivation of a SFPDE analytical solution \\ Introduction \\ SFPDE equations \\ Main program \\ ODE/MOL routine \\ Numerical output \\ Summary and conclusions \\ Authors' Biographies \\ Index", } @Book{Salehi:2018:NISb, author = "Younes Salehi and William E. Schiesser", title = "Numerical integration of space fractional partial differential equations. {Volume 2}, {Applications} from classical integer {PDEs}", volume = "20", publisher = "Morgan and Claypool Publishers", address = "San Rafael, CA, USA", pages = "xii + 183--375", year = "2018", DOI = "https://doi.org/10.2200/S00808ED1V02Y201710MAS020", ISBN = "1-68173-209-2 (hardcover), 1-68173-210-6 (e-book)", ISBN-13 = "978-1-68173-209-1 (hardcover), 978-1-68173-210-7 (e-book)", ISSN = "1938-1743 (print), 1938-1751 (electronic)", ISSN-L = "1938-1743", LCCN = "QA372 .S2662 2018", bibdate = "Tue Mar 13 17:13:47 MDT 2018", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/s-plus.bib", series = "Synthesis lectures on mathematics and statistics", abstract = "Partial differential equations (PDEs) are one of the most used widely forms of mathematics in science and engineering. PDEs can have partial derivatives with respect to (1) an initial value variable, typically time, and (2) boundary value variables, typically spatial variables. Therefore, two fractional PDEs can be considered, (1) fractional in time (TFPDEs), and (2) fractional in space (SFPDEs). The two volumes are directed to the development and use of SFPDEs, with the discussion divided as: Vol 1: Introduction to Algorithms and Computer Coding in R Vol 2: Applications from Classical Integer PDEs. Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann--Liouville derivative. In the second volume, the emphasis is on applications of SFPDEs developed mainly through the extension of classical integer PDEs to SFPDEs. The example applications are: Fractional diffusion equation with Dirichlet, Neumann and Robin boundary conditions Fisher--Kolmogorov SFPDE Burgers SFPDE Fokker--Planck SFPDE Burgers--Huxley SFPDE Fitzhugh--Nagumo SFPDE. These SFPDEs were selected because they are integer first order in time and integer second order in space. The variation in the spatial derivative from order two (parabolic) to order one (first order hyperbolic) demonstrates the effect of the spatial fractional order $ \alpha $ with $ 1 \leq \alpha \leq 2 $. All of the example SFPDEs are one dimensional in Cartesian coordinates. Extensions to higher dimensions and other coordinate systems, in principle, follow from the examples in this second volume. The examples start with a statement of the integer PDEs that are then extended to SFPDEs. The format of each chapter is the same as in the first volume. The R routines can be downloaded and executed on a modest computer (R is readily available from the Internet).", acknowledgement = ack-nhfb, subject = "Fractional differential equations; Differential equations, Partial; Spatial analysis (Statistics); Differential equations, Partial; Fractional differential equations; Spatial analysis (Statistics)", tableofcontents = "6. Simultaneous SFPDEs \\ 6.1 Introduction \\ 6.2 Simultaneous SFPDEs \\ 6.2.1 Main program \\ 6.2.2 ODE/MOL routine \\ 6.2.3 SFPDEs output \\ 6.2.4 Variation of the parameters \\ 6.3 Summary and conclusions \\ 7. Two sided SFPDEs \\ 7.1 Introduction \\ 7.2 Two-sided convective SFPDE, Caputo derivatives \\ 7.2.1 Main program \\ 7.2.2 ODE/MOL routine \\ 7.2.3 SFPDE output \\ 7.3 Two-sided convective SFPDE, Riemann--Liouville derivatives \\ 7.3.1 Main program \\ 7.3.2 ODE/MOL routine \\ 7.3.3 SFPDE output \\ 7.4 Summary and conclusions \\ 8. Integer to fractional extensions \\ 8.1 Introduction \\ 8.2 Fractional diffusion equation \\ 8.2.1 Main program, Dirchlet BCs \\ 8.2.2 ODE/MOL routine \\ 8.2.3 Model output \\ 8.2.4 Main program, Neumann BCs \\ 8.2.5 ODE/MOL routine \\ 8.2.6 Model output \\ 8.2.7 Main program, Robin BCs \\ 8.2.8 ODE/MOL routine \\ 8.2.9 Model output \\ 8.3 Fractional Burgers equation \\ 8.3.1 Main program, Dirchlet BCs \\ 8.3.2 ODE/MOL routine \\ 8.3.3 Model output \\ 8.4 Fractional Fokker--Planck equation \\ 8.4.1 Main program \\ 8.4.2 ODE/MOL routine \\ 8.4.3 Model output \\ 8.5 Fractional Burgers--Huxley equation \\ 8.5.1 Main program \\ 8.5.2 ODE/MOL routine \\ 8.5.3 Model output \\ 8.6 Fractional Fitzhugh--Nagumo equation \\ 8.6.1 Main program \\ 8.6.2 ODE/MOL routine \\ 8.6.3 Model output \\ 8.7 Summary and conclusions \\ Authors' biographies \\ Index", }

%%% ==================================================================== %%% Cross-referenced entries must come last; entries are sorted by year, %%% and then by citation label.

@Proceedings{Bultheel:2010:BNA, editor = "Adhemar Bultheel and Ronald Cools", booktitle = "{The birth of numerical analysis}", title = "{The birth of numerical analysis}", publisher = pub-WORLD-SCI, address = pub-WORLD-SCI:adr, pages = "xvii + 221", year = "2010", ISBN = "981-283-625-X", ISBN-13 = "978-981-283-625-0", LCCN = "QA297 .B54 2010", bibdate = "Mon Aug 23 11:06:23 MDT 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", abstract = "The 1947 paper by John von Neumann and Herman Goldstine, ``Numerical Inverting of Matrices of High Order'' (Bulletin of the AMS, Nov. 1947), is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous. This book is a unique collection of contributions by researchers who have lived through this evolution, testifying about their personal experiences and sketching the evolution of their respective subdomains since the early years.", acknowledgement = ack-nhfb, remark = "Proceedings of a symposium held at the Department of Computer Science of the K.U. Leuven, October 29--30, 2007.", subject = "numerical analysis; congresses; history", } @Book{Dick:2010:DNS, author = "J. (Josef) Dick and Friedrich Pillichshammer", booktitle = "Digital nets and sequences: discrepancy and quasi-Monte Carlo integration", title = "Digital nets and sequences: discrepancy and quasi-Monte Carlo integration", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "xvii + 600", year = "2010", ISBN = "0-521-19159-9 (hardback)", ISBN-13 = "978-0-521-19159-3 (hardback)", LCCN = "QA298 .D53 2010", bibdate = "Fri Mar 9 13:05:10 MST 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", URL = "http://assets.cambridge.org/97805211/91593/cover/9780521191593.jpg", abstract = "This book is a comprehensive treatment of contemporary quasi-Monte Carlo methods, digital nets and sequences, and discrepancy theory which starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method, quasi-Monte Carlo rules have increased in popularity, with many fruitful applications in mathematical practice. These rules require nodes with good uniform distribution properties, and digital nets and sequences in the sense of Niederreiter are known to be excellent candidates. Besides the classical theory, the book contains chapters on reproducing kernel Hilbert spaces and weighted integration, duality theory for digital nets, polynomial lattice rules, the newest constructions by Niederreiter and Xing and many more. The authors present an accessible introduction to the subject based mainly on material taught in undergraduate courses with numerous examples, exercises and illustrations.", acknowledgement = ack-nhfb, subject = "Monte Carlo method; nets (mathematics); sequences (mathematics); numerical integration; digital filters (mathematics)", tableofcontents = "Preface \\ Notation \\ 1. Introduction \\ 2. Quasi-Monte Carlo integration, discrepancy and reproducing kernel Hilbert spaces \\ 3. Geometric discrepancy \\ 4. Nets and sequences \\ 5. Discrepancy estimates and average type results \\ 6. Connections to other discrete objects \\ 7. Duality Theory \\ 8. Special constructions of digital nets and sequences \\ 9. Propagation rules for digital nets \\ 10. Polynomial lattice point sets \\ 11. Cyclic digital nets and hyperplane nets \\ 12. Multivariate integration in weighted Sobolev spaces \\ 13. Randomisation of digital nets \\ 14. The decay of the Walsh coefficients of smooth functions \\ 15. Arbitrarily high order of convergence of the worst-case error \\ 16. Explicit constructions of point sets with best possible order of $L^2$-discrepancy \\ Appendix A. Walsh functions \\ Appendix B. Algebraic function fields \\ References \\ Index", } @Book{Forster:2010:FSC, editor = "Brigitte Forster and Peter Robert Massopust", booktitle = "Four short courses on harmonic analysis: wavelets, frames, time-frequency methods, and applications to signal and image analysis", title = "Four short courses on harmonic analysis: wavelets, frames, time-frequency methods, and applications to signal and image analysis", publisher = pub-BIRKHAUSER-BOSTON, address = pub-BIRKHAUSER-BOSTON:adr, pages = "xvii + 247", year = "2010", DOI = "https://doi.org/10.1007/978-0-8176-4891-6", ISBN = "0-8176-4891-7, 0-8176-4890-9", ISBN-13 = "978-0-8176-4891-6, 978-0-8176-4890-9", LCCN = "QA403 .F68 2010", bibdate = "Mon Aug 23 11:30:53 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; library.tufts.edu:210/INNOPAC", note = "With contributions by Ole Christensen, Karlheinz Gr{\"o}chenig, Demetrio Labate, Pierre Vandergheynst, Guido Weiss, and Yves Wiaux.", series = "Applied and numerical harmonic analysis", acknowledgement = ack-nhfb, subject = "mathematics; Fourier analysis; harmonic analysis; abstract harmonic analysis; signal, image and speech processing; theoretical, mathematical and computational physics", } @Proceedings{Fukuda:2010:MSI, editor = "Komei Fukuda and Joris {Van der Hoeven} and Michael Joswig and Nobuki Takayama", booktitle = "{Mathematical Software --- ICMS 2010: Third International Congress on Mathematical Software, Kobe, Japan, September 13--17, 2010, Proceedings}", title = "{Mathematical Software --- ICMS 2010: Third International Congress on Mathematical Software, Kobe, Japan, September 13--17, 2010, Proceedings}", publisher = pub-SV, address = pub-SV:adr, pages = "xvi + 368", year = "2010", ISBN = "3-642-15581-2 (paperback)", ISBN-13 = "978-3-642-15581-9 (paperback)", LCCN = "QA76.95 .I5654 2010", bibdate = "Thu May 22 16:13:39 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/kepler.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Lecture Notes in Computer Science / Theoretical Computer Science and General Issues Ser.", URL = "http://link.springer.com/openurl?genre=book&isbn=978-3-642-15581-9", abstract = "This book constitutes the refereed proceedings of the Third International Congress on Mathematical Software, ICMS 2010, held in Kobe, Japan in September 2010. The 49 revised full papers presented were carefully reviewed and selected for presentation. The papers are organized in topical sections on computational group theory, computation of special functions, computer algebra and reliable computing, computer tools for mathematical editing and scientific visualization, exact numeric computation for algebraic and geometric computation, formal proof, geometry and visualization, Groebner bases and applications, number theoretical software as well as software for optimization and polyhedral computation.", acknowledgement = ack-nhfb, keywords = "Project Flyspeck", meetingname = "International Congress of Mathematical Software (3rd : 2010 : K{\=o}be-shi, Japan)", subject = "Mathematics; Data processing; Congresses; Computer software; Computer software.; Data processing.", } @Book{Kilmer:2010:GWS, editor = "Misha Elena Kilmer and Dianne P. O'Leary", booktitle = "{G. W. Stewart}: selected works with commentaries", title = "{G. W. Stewart}: selected works with commentaries", publisher = pub-BIRKHAUSER, address = pub-BIRKHAUSER:adr, pages = "xii + 729", year = "2010", DOI = "https://doi.org/10.1007/978-0-8176-4968-5", ISBN = "0-8176-4967-0 (hardcover), 0-8176-4968-9 (e-book)", ISBN-13 = "978-0-8176-4967-8 (hardcover), 978-0-8176-4968-5 (e-book)", LCCN = "QA188 .S74 2010", bibdate = "Wed May 28 12:51:20 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Contemporary mathematicians", acknowledgement = ack-nhfb, URL = "http://public.eblib.com/EBLPublic/PublicView.do?ptiID=64586; http://rave.ohiolink.edu/ebooks/ebc/978081764968; http://site.ebrary.com/id/1042123", abstract = "Published in honor of his 70th birthday, this volume explores and celebrates the work of G. W. (Pete) Stewart, a world-renowned expert in computational linear algebra. This volume includes: forty-four of Stewart's most influential research papers in two subject areas: matrix algorithms, and rounding and perturbation theory; a biography of Stewart; a complete list of his publications, students, and honors; selected photographs; and commentaries on his works in collaboration with leading experts in the field. \booktitle{G. W. Stewart: Selected Works with Commentaries} will appeal to graduate students, practitioners.", subject = "Stewart, G. W (Gilbert W.); Perturbation (Mathematics); Matrices", tableofcontents = "Cover \\ G. W. Stewart \\ Contents \\ Foreword \\ List of Contributors \\ Part I: G. W. Stewart \\ 1. Biography of G. W. Stewart \\ 2. Publications, Honors, and Students \\ 2.1 Publications of G. W. Stewart \\ 2.2 Major Honors of G. W. Stewart \\ 2.3 Ph.D. Students of G. W. Stewart \\ Part II: Commentaries \\ 3. Introduction to the Commentaries \\ 4. Matrix Decompositions: Linpack and Beyond \\ 4.1 The Linpack Project \\ 4.2 Some Algorithmic Insights \\ 4.3 The Triangular Matrices of Gaussian Elimination and Related Decompositions \\ 4.4 Solving Sylvester Equations \\ 4.5 Perturbation Bounds for Matrix Factorizations \\ 4.6 Rank Degeneracy \\ 4.7 Pivoted $QR$ as an Alternative to SVD \\ 4.8 Summary \\ 5. Updating and Downdating Matrix Decompositions \\ 5.1 Solving Nonlinear Systems of Equations \\ 5.2 More General Update Formulas for $QR$ \\ 5.3 Effects of Rounding Error on Downdating Cholesky Factorizations \\ 5.4 Stability of a Sequence of Updates and Downdates \\ 5.5 An Updating Algorithm for Subspace Tracking \\ 5.6 From the $URV$ to the $ULV$ \\ 5.7 Impact \\ 6. Least Squares, Projections, and Pseudoinverses \\ 6.1 Continuity of the Pseudoinverse \\ 6.2 Perturbation Theory \\ 6.3 Weighted Pseudoinverses \\ 6.4 Impact \\ 7. The Eigenproblem and Invariant Subspaces: Perturbation Theory \\ 7.1 Perturbation of Eigenvalues of General Matrices \\ 7.2 Further Results for Hermitian Matrices \\ 7.3 Stochastic Matrices \\ 7.4 Graded Matrices \\ 7.5 Rayleigh / Ritz Approximations \\ 7.6 Powers of Matrices \\ 7.7 Impact \\ 8. The SVD, Eigenproblem, and Invariant Subspaces: Algorithms \\ 8.1 Who Invented Subspace Iteration? \\ 8.2 Extracting Invariant Subspaces \\ 8.3 Approximating the SVD \\ 8.4 Impact \\ 9. The Generalized Eigenproblem \\ 9.1 Perturbation Theory \\ 9.2 The $QZ$ Algorithm \\ 9.3 Gershgorin's Theorem \\ 9.4 Definite Pairs \\ 10. Krylov Subspace Methods for the Eigenproblem \\ 10.1 A Krylov / Schur Algorithm \\ 10.2 Backward Error Analysis of Krylov Subspace Methods \\ 10.3 Adjusting the Rayleigh Quotient in Lanczos Methods \\ 10.4 Impact \\ 11. Other Contributions \\ References \\ Index \\ Part III: Reprints \\ 12 Papers on Matrix Decompositions \\ 12.1 [GWS-B / 2] (with J. J. Dongarra, J. R. Bunch, and C. B. Moler) Introduction from Linpack Users Guide \\ 12.2 [GWS-J / 17] (with R. H. Bartels), ''Algorithm 432: Solution of the Matrix Equation $AX + XB = C$'' \\ 12.3 [GWS-J / 32] ''The Economical Storage of Plane Rotations'' \\ 12.4 [GWS-J / 34] ''Perturbation Bounds for the $QR$ Factorization of a Matrix'' \\ 12.5 [GWS-J / 42] (with A. K. Cline, C. B. Moler, and J. H. Wilkinson), ''An Estimate for the Condition Number of a Matrix'' \\ 12.6 [GWS-J / 49] ''Rank Degeneracy'' \\ 12.7 [GWS-J / 78] ''On the Perturbation of $LU$, Cholesky, and $QR$ Factorizations'' \\ 12.8 [GWS-J / 89] ''On Graded $QR$ Decompositions of Products of Matrices'' \\ 12.9 [GWS-J / 92] ''On the Perturbation of $LU$ and Cholesky Factors'' \\ 12.10 [GWS-J / 94] ''The Triangular Matrices of Gaussian Elimination and Related Decompositions'' \\ 12.11 [GWS-J / 103] ''Four Algorithms for the the [sic] Efficient Computation of Truncated Pivoted $QR$ Approximations to a Sparse Matrix'' \\ 12.12 GWS-J / 118 (with M. W. Berry and S. A. Pulatova) ''Algorithm 844: Computing Sparse Reduced-Rank Approximations to Sparse Matrices'' \\ 13 Papers on Updating and Downdating Matrix Decompositions \\ 14 Papers on Least Squares, Projections, and Generalized Inverses \\ 15 Papers on the Eigenproblem and Invariant Subspaces: Perturbation Theory \\ 16 Papers on the SVD, Eigenproblem and Invariant Subspaces: Algorithms \\ 17 Papers on the Generalized Eigenproblem \\ 18 Papers on Krylov Subspace Methods for the Eigenproblem", } @Book{Stakgold:2011:GFB, author = "Ivar Stakgold and Michael J. Holst", title = "{Green}'s Functions and Boundary Value Problems", volume = "99", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Third", pages = "xxi + 855", year = "2011", ISBN = "0-470-60970-2 (hardcover)", ISBN-13 = "978-0-470-60970-5 (hardcover)", LCCN = "QA379 .S72 2011", bibdate = "Fri Jul 27 19:07:28 MDT 2018", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Pure and applied mathematics", abstract = "This Third Edition includes basic modern tools of computational mathematics for boundary value problems and also provides the foundational mathematical material necessary to understand and use the tools. Central to the text is a down-to-earth approach that shows readers how to use differential and integral equations when tackling significant problems in the physical sciences, engineering, and applied mathematics, and the book maintains a careful balance between sound mathematics and meaningful applications. A new co-author, Michael J. Holst, has been added to this new edition, and together he and Ivar Stakgold incorporate recent developments that have altered the field of applied mathematics, particularly in the areas of approximation methods and theory including best linear approximation in linear spaces; interpolation of functions in Sobolev Spaces; spectral, finite volume, and finite difference methods; techniques of nonlinear approximation; and Petrov-Galerkin and Galerkin methods for linear equations. Additional topics have been added including weak derivatives and Sobolev Spaces, linear functionals, energy methods and A Priori estimates, fixed-point techniques, and critical and super-critical exponent problems. The authors have revised the complete book to ensure that the notation throughout remained consistent and clear as well as adding new and updated references. Discussions on modeling, Fourier analysis, fixed-point theorems, inverse problems, asymptotics, and nonlinear methods have also been updated.", acknowledgement = ack-nhfb, subject = "Boundary value problems; Green's functions; Mathematical physics", tableofcontents = "Green's functions (intuitive ideas) \\ The theory of distributions \\ One-dimensional boundary value problems \\ Hilbert and Banach spaces \\ Operator theory \\ Integral equations \\ Spectral theory of second-order differential operators \\ Partial differential equations \\ Nonlinear problems \\ Approximation theory and methods", } @Book{Gilli:2011:NMO, editor = "Manfred Gilli and Dietmar Maringer and Enrico Schumann", booktitle = "Numerical Methods and Optimization in Finance", title = "Numerical Methods and Optimization in Finance", publisher = pub-ELSEVIER-ACADEMIC, address = pub-ELSEVIER-ACADEMIC:adr, pages = "xv + 584", year = "2011", ISBN = "0-12-375662-6", ISBN-13 = "978-0-12-375662-6", LCCN = "HG106 .G55 2011", bibdate = "Wed Feb 8 07:35:45 MST 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/numana2010.bib; http://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "Finance; Mathematical methods", } @Book{Govil:2017:PAT, editor = "Narendra Kumar Govil and Ram Mohapatra and Mohammed A. Qazi and Gerhard Schmeisser", booktitle = "Progress in Approximation Theory and Applicable Complex Analysis: In Memory of {Q. I. Rahman}", title = "Progress in Approximation Theory and Applicable Complex Analysis: In Memory of {Q. I. Rahman}", volume = "117", publisher = pub-SV, address = pub-SV:adr, pages = "", year = "2017", DOI = "https://doi.org/10.1007/978-3-319-49242-1", ISBN = "3-319-49240-3 (print), 3-319-49242-X (e-book)", ISBN-13 = "978-3-319-49240-7 (print), 978-3-319-49242-1 (e-book)", LCCN = "QA402.5-402.6", bibdate = "Sat Feb 10 18:46:45 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Springer Optimization and Its Applications", URL = "https://link.springer.com/chapter/10.1007/978-3-319-49242-1", abstract = "Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies. Graduate students, postdocs, and researchers in mathematics, specifically those working in the theory of functions, approximation theory, geometric function theory, and optimization will find new insights as well as a guide to advanced topics. The chapters in this book are grouped into four themes; the first, polynomials (Chapters 1--8), includes inequalities for polynomials and rational functions, orthogonal polynomials, and location of zeros. The second, inequalities and extremal problems are discussed in Chapters 9--13. The third, approximation of functions, involves the approximants being polynomials, rational functions, and other types of functions and are covered in Chapters 14--19. The last theme, quadrature, cubature and applications, comprises the final three chapters and includes an article coauthored by Rahman. This volume serves as a memorial volume to commemorate the distinguished career of Qazi Ibadur Rahman (1934--2013) of the Universit{\'e} de Montr{\'e}al. Rahman was considered by his peers as one of the prominent experts in analytic theory of polynomials and entire functions. The novelty of his work lies in his profound abilities and skills in applying techniques from other areas of mathematics, such as optimization theory and variational principles, to obtain final answers to countless open problems.", acknowledgement = ack-nhfb, series-URL = "https://link.springer.com/bookseries/7393", tableofcontents = "On the $L_2$ Markov Inequality with Laguerre Weight \\ Markov-Type Inequalities for Products of Muntz Polynomials Revisited \\ On Bernstein-Type Inequalities for the Polar Derivative of a Polynomial \\ On Two Inequalities for Polynomials in the Unit Disk \\ Inequalities for Integral Norms of Polynomials via Multipliers \\ Some Rational Inequalities Inspired by Rahman's Research \\ On an Asymptotic Equality for Reproducing Kernels and Sums of Squares of Orthonormal Polynomials \\ Two Walsh-Type Theorems for the Solutions of Multi-Affine Symmetric Polynomials \\ Vector Inequalities for a Projection in Hilbert Spaces and Applications \\ A Half-Discrete Hardy--Hilbert-Type Inequality with a Best Possible Constant Factor Related to the Hurwitz Zeta Function \\ Quantum Integral Inequalities for Generalized Convex Functions \\ Quantum integral inequalities for generalized preinvex functions \\ On the Bohr inequality \\ Bernstein-Type Polynomials on Several Intervals \\ Best Approximation by Logarithmically Concave Classes of Functions \\ Local approximation using Hermite functions \\ Approximating the Riemann Zeta and Related Functions \\ Overconvergence of Rational Approximants of Meromorphic Functions \\ Approximation by Bernstein--Faber--Walsh and Sz{\'a}sz--Mirakjan--Faber--Walsh Operators in Multiply Connected Compact Sets of $\mathbb{C}$ \\ Summation Formulas of Euler--Maclaurin and Abel--Plana: Old and New Results and Applications \\ A New Approach to Positivity and Monotonicity for the Trapezoidal Method and Related Quadrature Methods \\ A Unified and General Framework for Enriching Finite Element Approximations", } @Book{Kneusel:2017:NC, author = "Ronald T. Kneusel", title = "Numbers and Computers", publisher = pub-SV, address = pub-SV:adr, edition = "Second", pages = "xiii + 346", year = "2017", DOI = "https://doi.org/10.1007/978-3-319-50508-4", ISBN = "3-319-50507-6, 3-319-50508-4 (e-book)", ISBN-13 = "978-3-319-50507-7, 978-3-319-50508-4 (e-book)", LCCN = "????", bibdate = "Tue Aug 22 05:58:01 MDT 2017", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", URL = "http://link.springer.com/10.1007/978-3-319-50508-4", abstract = "This is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers. Divided into two parts, the first deals with standard representations of integers and floating point numbers, while the second examines several other number representations. Details are explained thoroughly, with clarity and specificity. Each chapter ends with a summary, recommendations, carefully selected references, and exercises to review the key points. Topics covered include interval arithmetic, fixed-point numbers, big integers and rational arithmetic. This new edition has three new chapters: Pitfalls of Floating-Point Numbers (and How to Avoid Them), Arbitrary Precision Floating Point, and Other Number Systems. This book is for anyone who develops software including software engineers, scientists, computer science students, engineering students and anyone who programs for fun.", acknowledgement = ack-nhfb, subject = "Number theory; Numerals; Numeration; Computer science; Mathematics; Mathematics; Number theory; Numerals; Numeration; Arithmetic and Logic Structures; Numeric Computing; Arithmetik; Informatik; Software Engineering.", tableofcontents = "Number Systems \\ Integers \\ Floating Point \\ Pitfalls of Floating-Point Numbers (and How to Avoid Them) \\ Big Integers and Rational Arithmetic \\ Fixed-Point Numbers \\ Decimal Floating Point \\ Interval Arithmetic \\ Arbitrary Precision Floating-Point \\ Other Number Systems", } @Book{Saad:2011:NML, author = "Youcef Saad", booktitle = "Numerical Methods for Large Eigenvalue Problems", title = "Numerical Methods for Large Eigenvalue Problems", volume = "66", publisher = pub-SIAM, address = pub-SIAM:adr, edition = "Second", pages = "xv + 276", year = "2011", ISBN = "1-61197-072-5", ISBN-13 = "978-1-61197-072-2", LCCN = "QA188 .S18 2011", bibdate = "Fri Jun 10 21:37:06 2011", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; http://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Classics in applied mathematics", URL = "http://www.cs.umn.edu/~saad/eig_book_2ndEd.pdf", acknowledgement = ack-nhfb, subject = "Nonsymmetric matrices; Eigenvalues", } @Proceedings{Blowey:2012:FNA, editor = "James Blowey and Max Jensen", booktitle = "{Frontiers in Numerical Analysis --- Durham 2010}", title = "{Frontiers in Numerical Analysis --- Durham 2010}", volume = "85", publisher = pub-SV, address = pub-SV:adr, bookpages = "xi + 282", pages = "xi + 282", year = "2012", CODEN = "LNCSA6", DOI = "https://doi.org/10.1007/978-3-642-23914-4", ISBN = "3-642-23913-7 (print), 3-642-23914-5 (e-book)", ISBN-13 = "978-3-642-23913-7 (print), 978-3-642-23914-4 (e-book)", ISSN = "1439-7358", ISSN-L = "1439-7358", LCCN = "????", bibdate = "Thu Dec 20 14:35:54 MST 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/lncse.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", note = "Proceedings of the Twelfth LMS--EPSRC Summer School in Computational Mathematics and Scientific Computation held at the University of Durham, UK, 25--31 July 2010.", series = ser-LNCSE, URL = "http://link.springer.com/book/10.1007/978-3-642-23914-4; http://www.springerlink.com/content/978-3-642-23914-4", acknowledgement = ack-nhfb, series-URL = "http://link.springer.com/bookseries/3527", } @Proceedings{Graham:2012:NAM, editor = "Ivan G. Graham and Thomas Y. Hou and Omar Lakkis and Robert Scheichl", booktitle = "Numerical Analysis of Multiscale Problems", title = "Numerical Analysis of Multiscale Problems", volume = "83", publisher = pub-SV, address = pub-SV:adr, bookpages = "vii + 363", pages = "vii + 363", year = "2012", CODEN = "LNCSA6", DOI = "https://doi.org/10.1007/978-3-642-22061-6", ISBN = "3-642-22060-6 (print), 3-642-22061-4 (e-book)", ISBN-13 = "978-3-642-22060-9 (print), 978-3-642-22061-6 (e-book)", ISSN = "1439-7358", ISSN-L = "1439-7358", LCCN = "QA297 .N844 2012", bibdate = "Thu Dec 20 14:35:50 MST 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/lncse.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", note = "Ten invited expository articles from the 91st LMS Durham Symposium on {\em Numerical Analysis of Multiscale Problems}, Durham, UK, 5--15 July 2010.", series = ser-LNCSE, URL = "http://link.springer.com/book/10.1007/978-3-642-22061-6; http://www.springerlink.com/content/978-3-642-22061-6", acknowledgement = ack-nhfb, series-URL = "http://link.springer.com/bookseries/3527", } @Proceedings{Achdou:2013:HJE, editor = "Yves Achdou and Guy Barles and Hitoshi Ishii and Grigory L. Litvinov", booktitle = "{Hamilton--Jacobi Equations: Approximations, Numerical Analysis and Applications: Cetraro, Italy 2011}", title = "{Hamilton--Jacobi Equations: Approximations, Numerical Analysis and Applications: Cetraro, Italy 2011}", volume = "2074", publisher = pub-SV, address = pub-SV:adr, pages = "xv + 301", year = "2013", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/978-3-642-36433-4", ISBN = "3-642-36432-2 (print), 3-642-36433-0 (e-book)", ISBN-13 = "978-3-642-36432-7 (print), 978-3-642-36433-4 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", LCCN = "QA3 .L28 no. 2074; QA3 .L28 no. 2074; QA316 .C56 2011", bibdate = "Tue May 6 14:56:48 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/lnm2010.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = ser-LECT-NOTES-MATH, URL = "http://link.springer.com/book/10.1007/978-3-642-36433-4; http://www.springerlink.com/content/978-3-642-36433-4", acknowledgement = ack-nhfb, remark = "Editors: Paola Loreti, Nicoletta Anna Tchou", series-URL = "http://link.springer.com/bookseries/304", } @Book{Trefethen:2013:ATA, author = "Lloyd N. Trefethen", title = "Approximation Theory and Approximation Practice", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "viii + 305", year = "2013", ISBN = "1-61197-239-6 (paperback)", ISBN-13 = "978-161-197-2-39-9 (paperback)", LCCN = "QA221 .T73 2013", MRclass = "41-01 (41-04 65-06)", MRnumber = "3012510", MRreviewer = "Ana Cristina Matos", bibdate = "Fri Jun 21 15:10:57 2013", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", acknowledgement = ack-nhfb, tableofcontents = "1. Introduction \\ 2. Chebyshev Points and Interpolants \\ 3. Chebyshev Polynomials and Series \\ 4. Interpolants, Projections, and Aliasing \\ 5. Barycentric Interpolation Formula \\ 6. Weierstrass Approximation Theorem \\ 7. Convergence for Differentiable Functions \\ 8. Convergence for Analytic Functions \\ 9. Gibbs Phenomenon \\ 10. Best Approximation \\ 11. Hermite Integral Formula \\ 12. Potential Theory and Approximation \\ 13. Equispaced Points, Runge Phenomenon \\ 14. Discussion of High-Order Interpolation \\ 15. Lebesgue Constants \\ 16. Best and Near-Best \\ 17. Orthogonal Polynomials \\ 18. Polynomial Roots and Colleague Matrices \\ 19. Clenshaw--Curtis and Gauss Quadrature \\ 20. Carath{\'e}odory--Fej{\'e}r Approximation \\ 21. Spectral Methods \\ 22. Linear Approximation: Beyond Polynomials \\ 23. Nonlinear Approximation: Why Rational Functions \\ 24. Rational Best Approximation \\ 25. Two Famous Problems \\ 26. Rational Interpolation and Linearized Least-Squares \\ 27. Pad{\'e} Approximation \\ 28. Analytic Continuation and Convergence Acceleration \\ Appendix: Six Myths of Polynomial Interpolation and Quadrature \\ References \\ Index", } @Book{Wartak:2013:CPI, author = "Marek S. Wartak", title = "Computational photonics: an introduction with {MATLAB}", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "xiii + 452", year = "2013", ISBN = "1-107-00552-3 (hardcover)", ISBN-13 = "978-1-107-00552-5 (hardcover)", LCCN = "TK8304 .W37 2013", bibdate = "Mon Feb 29 05:42:22 MST 2016", bibsource = "http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", URL = "http://assets.cambridge.org/97811070/05525/cover/9781107005525.jpg", abstract = "A comprehensive manual on the efficient modeling and analysis of photonic devices through building numerical codes, this book provides graduate students and researchers with the theoretical background and MATLAB programs necessary for them to start their own numerical experiments. Beginning by summarizing topics in optics and electromagnetism, the book discusses optical planar waveguides, linear optical fiber, the propagation of linear pulses, laser diodes, optical amplifiers, optical receivers, finite-difference time-domain method, beam propagation method and some wavelength division devices, solitons, solar cells and metamaterials. Assuming only a basic knowledge of physics and numerical methods, the book is ideal for engineers, physicists and practicing scientists. It concentrates on the operating principles of optical devices, as well as the models and numerical methods used to describe them.", acknowledgement = ack-nhfb, subject = "Optoelectronic devices; Mathematical models; Photonics; Mathematics; MATLAB; SCIENCE / Optics", tableofcontents = "1. Introduction \\ 2. Basic facts from optics \\ 3. Basic facts from electromagnetism \\ 4. Slab waveguides \\ 5. Linear optical fibre and signal degradation \\ 6. Propagation of linear pulses \\ 7. Optical sources \\ 8. Optical amplifiers and EDFA \\ 9. Semiconductor optical amplifiers (SOA) \\ 10. Optical receivers \\ 11. Finite difference time domain (FDTD) formulation \\ 12. Solar cells \\ 13. Metamaterials \\ Appendices \\ Index", } @Book{Arfken:2013:MMP, author = "George B. (George Brown) Arfken and Hans-J{\"u}rgen Weber and Frank E. Harris", booktitle = "Mathematical Methods for Physicists: a Comprehensive Guide", title = "Mathematical Methods for Physicists: a Comprehensive Guide", publisher = pub-ELSEVIER-ACADEMIC, address = pub-ELSEVIER-ACADEMIC:adr, edition = "Seventh", pages = "xiii + 1205", year = "2013", ISBN = "0-12-384654-4 (hardcover)", ISBN-13 = "978-0-12-384654-9 (hardcover)", LCCN = "QA37.3 .A74 2013", bibdate = "Thu May 3 08:02:53 MDT 2012", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib; http://www.math.utah.edu/pub/tex/bib/elefunt.bib; http://www.math.utah.edu/pub/tex/bib/master.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; jenson.stanford.edu:2210/unicorn", acknowledgement = ack-nhfb, subject = "Mathematical analysis; Mathematical physics", tableofcontents = "Preface / xi--xiii \\ 1: Mathematical Preliminaries / 1--82 \\ 2: Determinants and Matrices / 83--121 \\ 3: Vector Analysis / 123--203 \\ 4: Tensors and Differential Forms / 205--249 \\ 5: Vector Spaces / 251--297 \\ 6: Eigenvalue Problems / 299--328 \\ 7: Ordinary Differential Equations / 329--380 \\ 8: Sturm--Liouville Theory / 381--399 \\ 9: Partial Differential Equations / 401--445 \\ 10: Green's Functions / 447--467 \\ 11: Complex Variable Theory / 469--550 \\ 12: Further Topics in Analysis / 551--598 \\ 13: Gamma Function / 599--641 \\ 14: Bessel Functions / 643--713 \\ 15: Legendre Functions / 715--772 \\ 16: Angular Momentum / 773--814 \\ 17: Group Theory / 815--870 \\ 18: More Special Functions / 871--933 \\ 19: Fourier Series / 935--962 \\ 20: Integral Transforms / 963--1046 \\ 21: Integral Equations / 1047--1079 \\ 22: Calculus of Variations / 1081--1124 \\ 23: Probability and Statistics / 1125--1179 \\ Index / 1181--1205", } @Proceedings{Reich:2015:IPO, editor = "Simeon Reich and Alexander J. Zaslavski", booktitle = "{Infinite products of operators and their applications: a research workshop of the Israel Science Foundation: May 21--24, 2012, Haifa, Israel: Israel mathematical conference proceedings}", title = "{Infinite products of operators and their applications: a research workshop of the Israel Science Foundation: May 21--24, 2012, Haifa, Israel: Israel mathematical conference proceedings}", volume = "636", publisher = pub-AMS, address = pub-AMS:adr, pages = "xi + 266", year = "2015", DOI = "https://doi.org/10.1090/conm/636", ISBN = "1-4704-1480-5 (paperback)", ISBN-13 = "978-1-4704-1480-1 (paperback)", LCCN = "QA329 .I54 2015", MRclass = "15-XX; 40-XX; 41-XX; 46-XX; 47-XX; 49-XX; 54-XX; 58-XX; 62-XX; 65-XX; 90-XX", bibdate = "Fri Aug 12 19:13:19 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; z3950.loc.gov:7090/Voyager", series = "Contemporary mathematics", URL = "http://www.ams.org/books/conm/636/", acknowledgement = ack-nhfb, subject = "Operator theory; Congresses; Operator spaces; Ergodic theory; Mathematics; Linear and multilinear algebra; matrix theory; Sequences, series, summability; Approximations and expansions; Functional analysis; Operator theory; Calculus of variations and optimal control; optimization; General topology; Global analysis, analysis on manifolds; Statistics; Numerical analysis; Operations research, mathematical programming.", } @Proceedings{Greuel:2016:MSI, editor = "Gert-Martin Greuel", booktitle = "{Mathematical Software --- ICMS 2016: 5th International Conference, Berlin, Germany, July 11--14, 2016: proceedings}", title = "{Mathematical Software --- ICMS 2016: 5th International Conference, Berlin, Germany, July 11--14, 2016: proceedings}", volume = "9725", publisher = pub-SV, address = pub-SV:adr, pages = "xxiv + 532", year = "2016", DOI = "https://doi.org/10.1007/978-3-319-42432-3", ISBN = "3-319-42431-9 (print), 3-319-42432-7 (electronic)", ISBN-13 = "978-3-319-42431-6 (print), 978-3-319-42432-3 (electronic)", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", LCCN = "QA76.9.M35", bibdate = "Mon Feb 5 08:28:37 MST 2018", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/elefunt.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = ser-LNCS # "\slash " # ser-LNAI, URL = "http://zbmath.org/?q=an:1342.68017", abstract = "This book constitutes the proceedings of the 5th International Conference on Mathematical Software, ICMS 2015, held in Berlin, Germany, in July 2016. The 68 papers included in this volume were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections named: univalent foundations and proof assistants; software for mathematical reasoning and applications; algebraic and toric geometry; algebraic geometry in applications; software of polynomial systems; software for numerically solving polynomial systems; high-precision arithmetic, effective analysis, and special functions; mathematical optimization; interactive operation to scientific artwork and mathematical reasoning; information services for mathematics: software, services, models, and data; semDML: towards a semantic layer of a world digital mathematical library; miscellanea.", acknowledgement = ack-nhfb, }