FNC.bib

@book{abramowitzHandbookMathematical2013,
  title = {Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables},
  shorttitle = {Handbook of Mathematical Functions},
  editor = {Abramowitz, Milton and Stegun, Irene A.},
  year = {2013},
  publisher = {{Dover Publ}},
  address = {{New York, NY}},
  isbn = {978-0-486-61272-0},
  language = {eng},
  series = {Dover Books on Mathematics}
}

@book{ascherComputerMethods1998,
  title = {Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations},
  author = {Ascher, U. M. and Petzold, Linda Ruth},
  year = {1998},
  publisher = {{Society for Industrial and Applied Mathematics}},
  address = {{Philadelphia}},
  isbn = {978-0-89871-412-8},
  keywords = {Data processing,Differential equations,Differential-algebraic equations},
  lccn = {QA372 .A78 1998}
}

@book{ascherNumericalSolution1995,
  title = {Numerical Solution of Boundary Value Problems for Ordinary Differential Equations},
  author = {Ascher, U. M. and Mattheij, Robert M. M. and Russell, R. D.},
  year = {1995},
  publisher = {{Society for Industrial and Applied Mathematics}},
  address = {{Philadelphia}},
  isbn = {978-0-89871-354-1},
  keywords = {Boundary value problems,Numerical solutions},
  lccn = {QA379 .A83 1995},
  number = {13},
  series = {Classics in Applied Mathematics}
}

@book{atkinsonElementaryNumerical2004,
  title = {Elementary Numerical Analysis},
  author = {Atkinson, Kendall E. and Han, Weimin},
  year = {2004},
  edition = {3rd ed},
  publisher = {{J. Wiley \& Sons}},
  address = {{Hoboken, NJ}},
  isbn = {978-0-471-43337-8},
  keywords = {Numerical analysis},
  lccn = {QA297 .A83 2004}
}

@book{atkinsonIntroductionNumerical1989,
  title = {An Introduction to Numerical Analysis},
  author = {Atkinson, Kendall E.},
  year = {1989},
  edition = {2nd ed},
  publisher = {{Wiley}},
  address = {{New York}},
  isbn = {978-0-471-62489-9},
  keywords = {Numerical analysis},
  lccn = {QA297 .A84 1989}
}

@article{aurentzFastBackward2015,
  title = {Fast and {{Backward Stable Computation}} of {{Roots}} of {{Polynomials}}},
  author = {Aurentz, Jared L. and Mach, Thomas and Vandebril, Raf and Watkins, David S.},
  year = {2015},
  month = jan,
  volume = {36},
  pages = {942--973},
  issn = {0895-4798, 1095-7162},
  doi = {10.1137/140983434},
  file = {/Users/driscoll/Dropbox/library/Journal Article/Aurentz et al-2015-Fast and Backward Stable Computation of Roots of Polynomials.pdf},
  journal = {SIAM Journal on Matrix Analysis and Applications},
  language = {en},
  number = {3}
}

@article{baerSingularHopf1986,
  title = {Singular {{Hopf Bifurcation}} to {{Relaxation Oscillations}}},
  author = {Baer, S. M. and Erneux, T.},
  year = {1986},
  month = oct,
  volume = {46},
  pages = {721--739},
  issn = {0036-1399, 1095-712X},
  doi = {10.1137/0146047},
  journal = {SIAM Journal on Applied Mathematics},
  language = {en},
  number = {5}
}

@article{baileyComparisonThree2005,
  title = {A {{Comparison}} of {{Three High}}-{{Precision Quadrature Schemes}}},
  author = {Bailey, David H. and Jeyabalan, Karthik and Li, Xiaoye S.},
  year = {2005},
  month = jan,
  volume = {14},
  pages = {317--329},
  issn = {1058-6458, 1944-950X},
  doi = {10.1080/10586458.2005.10128931},
  file = {/Users/driscoll/Dropbox/library/Journal Article/Bailey_Jeyabalan_Li-2005-A Comparison of Three High-Precision Quadrature Schemes.pdf},
  journal = {Experimental Mathematics},
  language = {en},
  number = {3}
}

@incollection{berkeKineticsLid1998,
  title = {The {{Kinetics}} of {{Lid Motion}} and Its {{Effects}} on the {{Tear Film}}},
  booktitle = {Lacrimal {{Gland}}, {{Tear Film}}, and {{Dry Eye Syndromes}} 2},
  author = {Berke, A. and Mueller, S.},
  editor = {Sullivan, David A. and Dartt, Darlene A. and Meneray, Michele A.},
  year = {1998},
  volume = {438},
  pages = {417--424},
  publisher = {{Springer US}},
  address = {{Boston, MA}},
  doi = {10.1007/978-1-4615-5359-5_58},
  isbn = {978-1-4613-7445-9 978-1-4615-5359-5},
  language = {en}
}

@book{bjorckNumericalMethods1996,
  title = {Numerical Methods for Least Squares Problems},
  author = {Bj{\"o}rck, {\AA}ke},
  year = {1996},
  publisher = {{SIAM}},
  address = {{Philadelphia}},
  isbn = {978-0-89871-360-2},
  keywords = {Equations; Simultaneous,Least squares,Numerical solutions},
  lccn = {QA214 .B56 1996}
}

@book{brenanNumericalSolution1996,
  title = {Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations},
  author = {Brenan, Kathryn E. and Campbell, S. L. and Petzold, Linda R.},
  year = {1996},
  publisher = {{Society for Industrial and Applied Mathematics}},
  address = {{Philadelphia}},
  isbn = {978-0-89871-353-4},
  keywords = {Initial value problems,Numerical solutions},
  lccn = {QA378 .B73 1996},
  number = {14},
  series = {Classics in Applied Mathematics}
}

@book{brittonEssentialMathematical2003,
  title = {Essential Mathematical Biology},
  author = {Britton, N. F.},
  year = {2003},
  publisher = {{Springer}},
  address = {{London ; New York}},
  isbn = {978-1-85233-536-6},
  keywords = {Biomathematics},
  lccn = {QH323.5 .B745 2003},
  series = {Springer Undergraduate Mathematics Series}
}

@article{broschBlinkCharacterization2017,
  title = {Blink Characterization Using Curve Fitting and Clustering Algorithms},
  author = {Brosch, Joseph K and Wu, Ziwei and Begley, Carolyn G and Driscoll, Tobin A and Braun, Richard J},
  year = {2017},
  volume = {1},
  pages = {60--81},
  copyright = {All rights reserved},
  journal = {Journal for Modeling in Ophthalmology},
  doi = {10.35119/maio.v1i3.38},
  keywords = {⛔ No DOI found},
  number = {3}
}

@book{burdenNumericalAnalysis2001,
  title = {Numerical Analysis},
  author = {Burden, Richard L. and Faires, J. Douglas},
  year = {2001},
  edition = {7th ed},
  publisher = {{Brooks/Cole}},
  address = {{Australia ; Pacific Grove, CA}},
  isbn = {978-0-534-38216-2},
  keywords = {Numerical analysis},
  lccn = {QA297 .B84 2001}
}

@book{canutoSpectralMethods1988,
  title = {Spectral {{Methods}} in {{Fluid Dynamics}}},
  author = {Canuto, Claudio and Hussaini, M. Yousuff and Quarteroni, Alfio and Zang, Thomas A},
  year = {1988},
  publisher = {{Springer Berlin Heidelberg}},
  address = {{Berlin, Heidelberg}},
  abstract = {This textbook presents the modern unified theory of spectral methods and their implementation in the numerical analysis of partial differential equations occuring in fluid dynamical problems of transition, turbulence, and aerodynamics. It provides the engineer with the tools and guidance necessary to apply the methods successfully, and it furnishes the mathematician with a comprehensive, rigorous theory of the subject. All of the essential components of spectral algorithms currently employed for large-scale computations in fluid mechanics are described in detail. Some specific applications are linear stability, boundary layer calculations, direct simulations of transition and turbulence, and compressible Euler equations. The authors also present complete algorithms for Poisson's equation, linear hyperbolic systems, the advection diffusion equation, isotropic turbulence, and boundary layer transition. Some recent developments stressed in the book are iterative techniques (including the spectral multigrid method), spectral shock-fitting algorithms, and spectral multidomain methods. The book addresses graduate students and researchers in fluid dynamics and applied mathematics as well as engineers working on problems of practical importance.},
  isbn = {978-3-540-17371-7},
  language = {English}
}

@article{carrierSingularPerturbation1970,
  title = {Singular {{Perturbation Theory}} and {{Geophysics}}},
  author = {Carrier, G. F.},
  year = {1970},
  month = apr,
  volume = {12},
  pages = {175--193},
  issn = {0036-1445, 1095-7200},
  doi = {10.1137/1012041},
  journal = {SIAM Review},
  language = {en},
  number = {2}
}

@book{cheneyNumericalMathematics2012,
  title = {Numerical {{Mathematics}} and {{Computing}}},
  author = {Cheney, E. Ward and Kincaid, David R.},
  year = {2012},
  month = may,
  publisher = {{Cengage Learning}},
  abstract = {Authors Ward Cheney and David Kincaid show students of science and engineering the potential computers have for solving numerical problems and give them ample opportunities to hone their skills in programming and problem solving. NUMERICAL MATHEMATICS AND COMPUTING, 7th Edition also helps students learn about errors that inevitably accompany scientific computations and arms them with methods for detecting, predicting, and controlling these errors.Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.},
  googlebooks = {tDyYdqyZjSEC},
  isbn = {978-1-133-10371-4},
  keywords = {Mathematics / General},
  language = {en}
}

@article{cohenPolynomialPerfidious1994,
  title = {Is the Polynomial so Perfidious?},
  author = {Cohen, A.M.},
  year = {1994},
  month = jul,
  volume = {68},
  pages = {225--238},
  issn = {0945-3245},
  doi = {10.1007/s002110050058},
  abstract = {Wilkinson, in [1], has given a comprehensive account of the numericaldifficulties of working with polynomials on a floating point computer. Theobject of this note is to attempt to rehabilitate the polynomial to a certainextent. In particular it is shown here that polynomial deflation can beperformed satisfactorily by a method akin to `backward recursion'. Erroranalyses and examples are given to illustrate the stability of theprocess.},
  file = {/Users/driscoll/Dropbox/library/Journal Article/Cohen-1994-Is the polynomial so perfidious.pdf},
  journal = {Numerische Mathematik},
  language = {en},
  number = {2}
}

@book{connIntroductionDerivativeFree2009,
  title = {Introduction to {{Derivative}}-{{Free Optimization}}},
  author = {Conn, Andrew R. and Scheinberg, Katya and Vicente, Luis N.},
  year = {2009},
  month = apr,
  publisher = {{SIAM}},
  abstract = {The absence of derivatives, often combined with the presence of noise or lack of smoothness, is a major challenge for optimization. This book explains how sampling and model techniques are used in derivative-free methods and how these methods are designed to efficiently and rigorously solve optimization problems. Although readily accessible to readers with a modest background in computational mathematics, it is also intended to be of interest to researchers in the field. Introduction to Derivative-Free Optimization is the first contemporary comprehensive treatment of optimization without derivatives. This book covers most of the relevant classes of algorithms from direct search to model-based approaches. It contains a comprehensive description of the sampling and modeling tools needed for derivative-free optimization; these tools allow the reader to better analyze the convergent properties of the algorithms and identify their differences and similarities.},
  googlebooks = {tGbUshriSyYC},
  isbn = {978-0-89871-668-9},
  keywords = {Business \& Economics / Finance / General,Mathematics / Applied,Mathematics / Linear \& Nonlinear Programming},
  language = {en}
}

@article{cooleyAlgorithmMachine1965,
  title = {An Algorithm for the Machine Calculation of Complex {{Fourier}} Series},
  author = {Cooley, James W. and Tukey, John W.},
  year = {1965},
  volume = {19},
  pages = {297--301},
  issn = {0025-5718, 1088-6842},
  doi = {10.1090/S0025-5718-1965-0178586-1},
  abstract = {Advancing research. Creating connections.},
  file = {/Users/driscoll/Dropbox/library/Journal Article/Cooley_Tukey-1965-An algorithm for the machine calculation of complex Fourier.pdf;/Users/driscoll/Zotero/storage/FVXX2TD9/home.html},
  journal = {Mathematics of Computation},
  language = {en},
  number = {90}
}

@book{corlessGraduateIntroduction2013,
  title = {A {{Graduate Introduction}} to {{Numerical Methods}}: {{From}} the {{Viewpoint}} of {{Backward Error Analysis}}},
  shorttitle = {A {{Graduate Introduction}} to {{Numerical Methods}}},
  author = {Corless, Robert M. and Fillion, Nicolas},
  year = {2013},
  month = dec,
  publisher = {{Springer Science \& Business Media}},
  abstract = {This book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations.The book contains detailed illustrations, chapter summaries and a variety of exercises as well some Matlab codes provided online as supplementary material.``I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. ShampineA Graduate Introduction to Numerical Methods and Backward Error Analysis'' has been selected by Computing Reviews as a notable book in computing in 2013. Computing Reviews Best of 2013 list consists of book and article nominations from reviewers, CR category editors, the editors-in-chief of journals, and others in the computing community.},
  googlebooks = {hte4BAAAQBAJ},
  isbn = {978-1-4614-8453-0},
  keywords = {Computers / Computer Science,Mathematics / Applied,Mathematics / Counting \& Numeration,Mathematics / Number Systems,Mathematics / Numerical Analysis,Mathematics / Probability \& Statistics / Stochastic Processes},
  language = {en}
}

@book{davisInterpolationApproximation1963,
  title = {Interpolation and {{Approximation}}},
  author = {Davis, Philip J.},
  year = {1963},
  publisher = {{Blaisdell Publishing Company}},
  isbn = {978-0486624952},
  language = {en}
}

@book{davisMethodsNumerical2014,
  title = {Methods of {{Numerical Integration}}},
  author = {Davis, Philip J. and Rabinowitz, Philip},
  year = {2014},
  month = may,
  publisher = {{Academic Press}},
  abstract = {Methods of Numerical Integration, Second Edition describes the theoretical and practical aspects of major methods of numerical integration. Numerical integration is the study of how the numerical value of an integral can be found. This book contains six chapters and begins with a discussion of the basic principles and limitations of numerical integration. The succeeding chapters present the approximate integration rules and formulas over finite and infinite intervals. These topics are followed by a review of error analysis and estimation, as well as the application of functional analysis to numerical integration. A chapter describes the approximate integration in two or more dimensions. The final chapter looks into the goals and processes of automatic integration, with particular attention to the application of Tschebyscheff polynomials.This book will be of great value to theoreticians and computer programmers.},
  googlebooks = {mbLiBQAAQBAJ},
  isbn = {978-1-4832-6428-8},
  keywords = {Mathematics / Calculus,Mathematics / Mathematical Analysis},
  language = {en}
}

@book{deboorPracticalGuide1978,
  title = {A {{Practical Guide}} to {{Splines}}},
  author = {{de Boor}, Carl},
  year = {1978},
  publisher = {{Springer-Verlag}},
  googlebooks = {7YjBQgAACAAJ},
  isbn = {978-3-540-90356-7},
  language = {en}
}

@book{fornbergPracticalGuide1998,
  title = {A {{Practical Guide}} to {{Pseudospectral Methods}}},
  author = {Fornberg, Bengt},
  year = {1998},
  month = oct,
  publisher = {{Cambridge University Press}},
  abstract = {During the past two decades, pseudospectral methods have emerged as successful, and often superior, alternatives to better known computational procedures, such as finite difference and finite element methods of numerical solution, in several key application areas. These areas include computational fluid dynamics, wave motion, and weather forecasting. This book explains how, when and why this pseudospectral approach works. In order to make the subject accessible to students as well as researchers and engineers, the author presents the subject using illustrations, examples, heuristic explanations, and algorithms rather than rigorous theoretical arguments. This book will be of interest to graduate students, scientists, and engineers interested in applying pseudospectral methods to real problems.},
  googlebooks = {IqJoihDba3gC},
  isbn = {978-0-521-64564-5},
  keywords = {Mathematics / Applied,Mathematics / Mathematical Analysis,Mathematics / Numerical Analysis,Science / Mechanics / Fluids},
  language = {en}
}

@article{golubHistoryConjugate1989,
  title = {Some {{History}} of the {{Conjugate Gradient}} and {{Lanczos Algorithms}}: 1948\textendash 1976},
  shorttitle = {Some {{History}} of the {{Conjugate Gradient}} and {{Lanczos Algorithms}}},
  author = {Golub, Gene H. and O'Leary, Dianne P.},
  year = {1989},
  month = mar,
  volume = {31},
  pages = {50--102},
  publisher = {{Society for Industrial and Applied Mathematics}},
  issn = {0036-1445},
  doi = {10.1137/1031003},
  abstract = {This paper gives some of the history of the conjugate gradient and Lanczos algorithms and an annotated bibliography for the period 1948-1976},
  file = {/Users/driscoll/Dropbox/library/Journal Article/Golub_O’Leary-1989-Some History of the Conjugate Gradient and Lanczos.pdf;/Users/driscoll/Zotero/storage/2W2ID99U/1031003.html},
  journal = {SIAM Review},
  number = {1}
}

@book{golubMatrixComputations1996,
  title = {Matrix {{Computations}}},
  author = {Golub, Gene H. and Van Loan, Charles F.},
  year = {1996},
  month = oct,
  edition = {3rd},
  publisher = {{JHU Press}},
  abstract = {Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.},
  googlebooks = {mlOa7wPX6OYC},
  isbn = {978-0-8018-5414-9},
  keywords = {Mathematics / Algebra / Linear,Mathematics / Applied},
  language = {en}
}

@book{habermanElementaryApplied1998,
  title = {Elementary {{Applied Partial Differential Equations}}: {{With Fourier Series}} and {{Boundary Value Problems}}},
  shorttitle = {Elementary {{Applied Partial Differential Equations}}},
  author = {Haberman, Richard},
  year = {1998},
  publisher = {{Prentice Hall}},
  abstract = {KEY BENEFIT Emphasizing physical interpretations of mathematical solutions, this book introduces applied mathematics and presents partial differential equations. KEY TOPICS Leading readers from simple exercises through increasingly powerful mathematical techniques, this book discusses hear flow and vibrating strings and membranes, for a better understand of the relationship between mathematics and physical problems. It also emphasizes problem solving and provides a thorough approach to solutions. The third edition of , Elementary Applied Partial Differential Equations; With Fourier Series and Boundary Value Problems has been revised to include a new chapter covering dispersive waves. It also includes new sections covering fluid flow past a circular cylinder; reflection and refraction of light and sound waves; the finite element method; partial differential equations with spherical geometry; eigenvalue problems with a continuous and discrete spectrum; and first-order nonlinear partial differential equations. An essential reference for any technical or mathematics professional.},
  googlebooks = {FKRwQgAACAAJ},
  isbn = {978-0-13-263807-4},
  keywords = {Mathematics / Differential Equations / General},
  language = {en}
}

@article{hahnConversationDonald1995,
  title = {A {{Conversation}} with {{Donald Marquardt}}},
  author = {Hahn, Gerald J.},
  year = {1995},
  month = nov,
  volume = {10},
  pages = {377--393},
  publisher = {{Institute of Mathematical Statistics}},
  issn = {0883-4237, 2168-8745},
  doi = {10.1214/ss/1177009871},
  abstract = {Project Euclid - mathematics and statistics online},
  file = {/Users/driscoll/Dropbox/library/Journal Article/Hahn-1995-A Conversation with Donald Marquardt.pdf;/Users/driscoll/Zotero/storage/R8V3EFL5/1177009871.html},
  journal = {Statistical Science},
  language = {EN},
  number = {4}
}

@book{hairerSolvingOrdinary2008,
  title = {Solving {{Ordinary Differential Equations I}}: {{Nonstiff Problems}}},
  shorttitle = {Solving {{Ordinary Differential Equations I}}},
  author = {Hairer, Ernst and N{\o}rsett, Syvert P. and Wanner, Gerhard},
  year = {2008},
  month = apr,
  publisher = {{Springer Science \& Business Media}},
  abstract = {This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory, and the second chapter includes a modern treatment of Runge-Kutta and extrapolation methods. Chapter three begins with the classical theory of multistep methods, and concludes with the theory of general linear methods. The reader will benefit from many illustrations, a historical and didactic approach, and computer programs which help him/her learn to solve all kinds of ordinary differential equations. This new edition has been rewritten and new material has been included.},
  googlebooks = {F93u7VcSRyYC},
  isbn = {978-3-540-56670-0},
  keywords = {Mathematics / Calculus,Mathematics / Mathematical Analysis,Mathematics / Number Systems,Mathematics / Numerical Analysis},
  language = {en}
}

@book{hansenLeastSquares2013,
  title = {Least {{Squares Data Fitting}} with {{Applications}}},
  author = {Hansen, Per Christian and Pereyra, V. and Scherer, Godela},
  year = {2013},
  month = jan,
  publisher = {{JHU Press}},
  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\'ictor 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.Included are\textbullet{} an overview of computational methods together with their properties and advantages\textbullet{} topics from statistical regression analysis that help readers to understand and evaluate the computed solutions\textbullet{} many examples that illustrate the techniques and algorithmsLeast Squares Data Fitting with Applications can be used as a textbook for advanced undergraduate or graduate courses and professionals in the sciences and in engineering.},
  googlebooks = {8IrZe3QX0LQC},
  isbn = {978-1-4214-0786-9},
  keywords = {Mathematics / Applied,Mathematics / General},
  language = {en}
}

@article{hestenesMethodsConjugate1952,
  title = {Methods of Conjugate Gradients for Solving Linear Systems},
  author = {Hestenes, M.R. and Stiefel, E.},
  year = {1952},
  month = dec,
  volume = {49},
  pages = {409},
  issn = {0091-0635},
  doi = {10.6028/jres.049.044},
  file = {/Users/driscoll/Dropbox/library/Journal Article/Hestenes_Stiefel-1952-Methods of conjugate gradients for solving linear systems.pdf;/Users/driscoll/Dropbox/library/Journal Article/Hestenes_Stiefel-1952-Methods of conjugate gradients for solving linear systems2.pdf},
  journal = {Journal of Research of the National Bureau of Standards},
  language = {en},
  number = {6}
}

@book{highamAccuracyStability2002,
  title = {Accuracy and {{Stability}} of {{Numerical Algorithms}}: {{Second Edition}}},
  shorttitle = {Accuracy and {{Stability}} of {{Numerical Algorithms}}},
  author = {Higham, Nicholas J.},
  year = {2002},
  month = jan,
  publisher = {{SIAM}},
  abstract = {Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton\&\#39;s method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.},
  googlebooks = {7J52J4GrsJkC},
  isbn = {978-0-89871-802-7},
  keywords = {Mathematics / Applied,Mathematics / Mathematical Analysis,Mathematics / Number Systems,Mathematics / Numerical Analysis},
  language = {en}
}

@book{iserlesFirstCourse1996,
  title = {A {{First Course}} in the {{Numerical Analysis}} of {{Differential Equations}}},
  author = {Iserles, Arieh},
  year = {1996},
  month = jan,
  publisher = {{Cambridge University Press}},
  abstract = {This book presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives to maintain a balance among theoretical, algorithmic and applied aspects of the subject. In detail, topics covered include numerical solution of ordinary differential equations by multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; a variety of algorithms to solve large, sparse algebraic systems; and methods for parabolic and hyperbolic differential equations and techniques of their analysis. The book is accompanied by an appendix that presents brief back-up in a number of mathematical topics.},
  googlebooks = {7Zofw3SFTWIC},
  isbn = {978-0-521-55655-2},
  keywords = {Mathematics / Differential Equations / General,Mathematics / Mathematical Analysis,Mathematics / Numerical Analysis},
  language = {en}
}

@book{jolliffePrincipalComponent2002,
  title = {Principal {{Component Analysis}}},
  author = {Jolliffe, I. T.},
  year = {2002},
  month = oct,
  edition = {Second},
  publisher = {{Springer Science \& Business Media}},
  abstract = {Principal component analysis is central to the study of multivariate data. Although one of the earliest multivariate techniques it continues to be the subject of much research, ranging from new model- based approaches to algorithmic ideas from neural networks. It is extremely versatile with applications in many disciplines. The first edition of this book was the first comprehensive text written solely on principal component analysis. The second edition updates and substantially expands the original version, and is once again the definitive text on the subject. It includes core material, current research and a wide range of applications. Its length is nearly double that of the first edition. Researchers in statistics, or in other fields that use principal component analysis, will find that the book gives an authoritative yet accessible account of the subject. It is also a valuable resource for graduate courses in multivariate analysis. The book requires some knowledge of matrix algebra. Ian Jolliffe is Professor of Statistics at the University of Aberdeen. He is author or co-author of over 60 research papers and three other books. His research interests are broad, but aspects of principal component analysis have fascinated him and kept him busy for over 30 years.},
  isbn = {978-0-387-95442-4},
  keywords = {Mathematics / Probability \& Statistics / General,Mathematics / Probability \& Statistics / Multivariate Analysis,Mathematics / Probability \& Statistics / Stochastic Processes},
  language = {en}
}

@book{kelleyIterativeMethods1995,
  title = {Iterative {{Methods}} for {{Linear}} and {{Nonlinear Equations}}},
  author = {Kelley, C. T.},
  year = {1995},
  month = jan,
  publisher = {{SIAM}},
  abstract = {Linear and nonlinear systems of equations are the basis for many, if not most, of the models of phenomena in science and engineering, and their efficient numerical solution is critical to progress in these areas. This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, such as Newton-Krylov methods, considerable material on linear equations has been incorporated. This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden\&\#39;s method, and globalization of inexact Newton methods.},
  isbn = {978-0-89871-352-7},
  keywords = {Mathematics / Applied,Mathematics / Differential Equations / General,Mathematics / Linear \& Nonlinear Programming,Mathematics / Numerical Analysis,Mathematics / Optimization},
  language = {en}
}

@article{kermackContributionMathematical1927,
  title = {A Contribution to the Mathematical Theory of Epidemics},
  author = {Kermack, William Ogilvy and McKendrick, A. G. and Walker, Gilbert Thomas},
  year = {1927},
  month = aug,
  volume = {115},
  pages = {700--721},
  publisher = {{Royal Society}},
  doi = {10.1098/rspa.1927.0118},
  abstract = {(1) One of the most striking features in the study of epidemics is the difficulty of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population. It was with a view to obtaining more insight regarding the effects of the various factors which govern the spread of contagious epidemics that the present investigation was undertaken. Reference may here be made to the work of Ross and Hudson (1915-17) in which the same problem is attacked. The problem is here carried to a further stage, and it is considered from a point of view which is in one sense more general. The problem may be summarised as follows: One (or more) infected person is introduced into a community of individuals, more or less susceptible to the disease in question. The disease spreads from the affected to the unaffected by contact infection. Each infected person runs through the course of his sickness, and finally is removed from the number of those who are sick, by recovery or by death. The chances of recovery or death vary from day to day during the course of his illness. The chances that the affected may convey infection to the unaffected are likewise dependent upon the stage of the sickness. As the epidemic spreads, the number of unaffected members of the community becomes reduced. Since the course of an epidemic is short compared with the life of an individual, the population may be considered as remaining constant, except in as far as it is modified by deaths due to the epidemic disease itself. In the course of time the epidemic may come to an end. One of the most important probems in epidemiology is to ascertain whether this termination occurs only when no susceptible individuals are left, or whether the interplay of the various factors of infectivity, recovery and mortality, may result in termination, whilst many susceptible individuals are still present in the unaffected population. It is difficult to treat this problem in its most general aspect. In the present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.},
  file = {/Users/driscoll/Dropbox/library/Journal Article/Kermack_McKendrick_Walker-1927-A contribution to the mathematical theory of epidemics.pdf;/Users/driscoll/Zotero/storage/S9NEPI6U/rspa.1927.html},
  journal = {Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character},
  number = {772}
}

@book{layLinearAlgebra2012,
  title = {Linear Algebra and Its Applications},
  author = {Lay, David C.},
  year = {2012},
  edition = {4th ed},
  publisher = {{Addison-Wesley}},
  address = {{Boston}},
  isbn = {978-0-321-38517-8},
  keywords = {Algebras; Linear,Textbooks},
  lccn = {QA184.2 .L39 2012}
}

@book{leonLinearAlgebra2006,
  title = {Linear {{Algebra}} with {{Applications}}},
  author = {Leon, Steven J.},
  year = {2006},
  publisher = {{Pearson Prentice Hall}},
  abstract = {This thorough and accessible book from one of the leading figures in the field of linear algebra provides readers with both a challenging and broad understanding of linear algebra. The author infuses key concepts with their modern practical applications to offer readers examples of how mathematics is used in the real world. Topics such as linear systems theory, matrix theory, and vector space theory are integrated with real world applications to give a clear understanding of the material and the application of the concepts to solve real world problems. Each chapter contains integrated worked examples and chapter tests. The book stresses the important role geometry and visualization play in understanding linear algebra.For anyone interested in the application of linear algebra theories to solve real world problems.},
  isbn = {978-0-13-185785-8},
  keywords = {Mathematics / Algebra / Linear},
  language = {en}
}

@article{levenbergMethodSolution1944,
  title = {A Method for the Solution of Certain Non-Linear Problems in Least Squares},
  author = {Levenberg, Kenneth},
  year = {1944},
  volume = {2},
  pages = {164--168},
  issn = {0033-569X, 1552-4485},
  doi = {10.1090/qam/10666},
  abstract = {Advancing research. Creating connections.},
  file = {/Users/driscoll/Dropbox/library/Journal Article/Levenberg-1944-A method for the solution of certain non-linear problems in.pdf;/Users/driscoll/Zotero/storage/6LE7DNEQ/S0033-569X-1944-10666-0.html},
  journal = {Quarterly of Applied Mathematics},
  language = {en},
  number = {2}
}

@book{levequeFiniteDifference2007,
  title = {Finite {{Difference Methods}} for {{Ordinary}} and {{Partial Differential Equations}}: {{Steady}}-{{State}} and {{Time}}-{{Dependent Problems}}},
  shorttitle = {Finite {{Difference Methods}} for {{Ordinary}} and {{Partial Differential Equations}}},
  author = {LeVeque, Randall J.},
  year = {2007},
  month = sep,
  publisher = {{SIAM}},
  abstract = {This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples. Exercises and student projects are available on the book\&\#39;s webpage, along with Matlab mfiles for implementing methods. Readers will gain an understanding of the essential ideas that underlie the development, analysis, and practical use of finite difference methods as well as the key concepts of stability theory, their relation to one another, and their practical implications. The author provides a foundation from which students can approach more advanced topics.},
  googlebooks = {qsvmsXe8Ug4C},
  isbn = {978-0-89871-629-0},
  keywords = {Mathematics / Differential Equations / General,Mathematics / Finite Mathematics,Mathematics / Mathematical Analysis},
  language = {en}
}

@book{levequeFiniteVolume2002,
  title = {Finite {{Volume Methods}} for {{Hyperbolic Problems}}},
  author = {LeVeque, Randall J.},
  year = {2002},
  month = aug,
  publisher = {{Cambridge University Press}},
  abstract = {This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, (including both linear problems and nonlinear conservation laws). These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are applied to eliminate numerical oscillations. The methods were orginally designed to capture shock waves accurately, but are also useful tools for studying linear wave-progagation problems, particulary in heterogenous material. The methods studied are in the CLAWPACK software package. Source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.},
  googlebooks = {QazcnD7GUoUC},
  isbn = {978-0-521-00924-9},
  keywords = {Mathematics / Applied,Mathematics / Differential Equations / General,Mathematics / Mathematical Analysis,Mathematics / Numerical Analysis},
  language = {en}
}

@book{levequeNumericalMethods1992,
  title = {Numerical {{Methods}} for {{Conservation Laws}}},
  author = {LeVeque, Randall J.},
  year = {1992},
  publisher = {{Springer Science \& Business Media}},
  abstract = {These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. Without the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are. not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.},
  googlebooks = {3WhqLPcMdPsC},
  isbn = {978-3-7643-2723-1},
  keywords = {Mathematics / Calculus,Mathematics / Counting \& Numeration,Mathematics / Mathematical Analysis,Mathematics / Numerical Analysis,Mathematics / Probability \& Statistics / Stochastic Processes},
  language = {en}
}

@article{marquardtAlgorithmLeastSquares1963,
  title = {An {{Algorithm}} for {{Least}}-{{Squares Estimation}} of {{Nonlinear Parameters}}},
  author = {Marquardt, Donald W.},
  year = {1963},
  month = jun,
  volume = {11},
  pages = {431--441},
  issn = {0368-4245, 2168-3484},
  doi = {10.1137/0111030},
  file = {/Users/driscoll/Dropbox/library/Journal Article/Marquardt-1963-An Algorithm for Least-Squares Estimation of Nonlinear2.pdf},
  journal = {Journal of the Society for Industrial and Applied Mathematics},
  language = {en},
  number = {2}
}

@article{meadeDifferentialEquations1999,
  title = {Differential Equations in the New Millennium: {{The}} Parachute Problem},
  author = {Meade, Douglas B. and Struthers, A. A.},
  year = {1999},
  volume = {15},
  pages = {417--424},
  journal = {International Journal of Engineering Education},
  number = {6}
}

@book{molerNumericalComputing2010,
  title = {Numerical {{Computing}} with {{MATLAB}}: {{Revised Reprint}}},
  shorttitle = {Numerical {{Computing}} with {{MATLAB}}},
  author = {Moler, Cleve B.},
  year = {2010},
  month = aug,
  publisher = {{SIAM}},
  abstract = {This is a lively textbook for an introductory course in numerical methods, MATLAB, and technical computing, which emphasises the informed use of mathematical software.?Numerical Computing with MATLAB?helps readers learn about the mathematical functions in?MATLAB, how to appreciate their limitations, and how to use and modify them appropriately. The book makes extensive use of computer graphics, and provides more than 70 M-files, which can be downloaded from the text Web site www.mathworks.com/moler. Many of the numerous exercises involve modifying and extending these programs. The theory can be adapted to apply to modern problems from cryptography, touch-tone dialing, Google page-ranking, atmospheric science and image processing, as well as classical problems from physics and engineering. This book will appeal to advanced undergraduate and beginning graduate students in science and engineering. This revision includes changes and corrections made since the book was originally published in 2004.},
  googlebooks = {\_Cad7uaYcloC},
  isbn = {978-0-89871-660-3},
  keywords = {Computers / General},
  language = {en}
}

@book{mortonNumericalSolution2005,
  title = {Numerical {{Solution}} of {{Partial Differential Equations}}: {{An Introduction}}},
  shorttitle = {Numerical {{Solution}} of {{Partial Differential Equations}}},
  author = {Morton, K. W. and Mayers, D. F.},
  year = {2005},
  month = apr,
  edition = {Second},
  publisher = {{Cambridge University Press}},
  abstract = {This is the 2005 second edition of a highly successful and well-respected textbook on the numerical techniques used to solve partial differential equations arising from mathematical models in science, engineering and other fields. The authors maintain an emphasis on finite difference methods for simple but representative examples of parabolic, hyperbolic and elliptic equations from the first edition. However this is augmented by new sections on finite volume methods, modified equation analysis, symplectic integration schemes, convection-diffusion problems, multigrid, and conjugate gradient methods; and several sections, including that on the energy method of analysis, have been extensively rewritten to reflect modern developments. Already an excellent choice for students and teachers in mathematics, engineering and computer science departments, the revised text includes more latest theoretical and industrial developments.},
  googlebooks = {GW6\_AwAAQBAJ},
  isbn = {978-1-139-44320-3},
  keywords = {Business \& Economics / Investments \& Securities / General,Mathematics / Applied,Mathematics / Mathematical Analysis,Mathematics / Numerical Analysis},
  language = {en}
}

@book{nashHistoryScientific1990,
  title = {A {{History}} of {{Scientific Computing}}},
  author = {Nash, Stephen},
  year = {1990},
  publisher = {{Addison-Wesley Publishing Company}},
  abstract = {Essays about pioneers in the field of scientific and numeric computing--John von Neumann, James Wilkinson, George Forsythe, and Howard Aiken--show how the drive to solve particular problems influenced the development of algorithms, software, and even computers. Methods that have led to new tools in computer analysis, such as the fast Fourier transform and finite-element and iterative methods, also are discussed, as well as the contributions of scientific organizations like ACM and SIAM and institutions like the Los Alamos Laboratory and the former National Bureau of Standards. The volume concludes with a view of numerical analysis in Europe and the Soviet Union. Annotation copyrighted by Book News, Inc., Portland, OR},
  googlebooks = {XscmAAAAMAAJ},
  isbn = {978-0-201-50814-7},
  keywords = {Computers / General},
  language = {en}
}

@article{newtonPlasmaSalivary1981,
  title = {Plasma and Salivary Pharmacokinetics of Caffeine in Man},
  author = {Newton, R. and Broughton, L. J. and Lind, M. J. and Morrison, P. J. and Rogers, H. J. and Bradbrook, I. D.},
  year = {1981},
  month = jan,
  volume = {21},
  pages = {45--52},
  issn = {1432-1041},
  doi = {10.1007/BF00609587},
  abstract = {Plasma and salivary caffeine concentrations were measured by gas-liquid chromatography in 6 healthy caffeine-free volunteers following oral administration of 50, 300, 500 and 750 mg caffeine. Caffeine was also given to a single subject intravenously in doses of 300, 500 and 750 mg. Caffeine was rapidly absorbed and was completely available at all doses. The apparent first-order elimination rate constant decreased linearly with dose and was 0.163{$\pm$}0.081 h-1 for 50 mg and 0.098{$\pm$}0.027 h-1 for 750 mg. The total body clearance was unaffected by dose and was 0.98{$\pm$}0.38 ml/min/kg. There was a trend towards increasing apparent volume of distribution with increasing dose. A linear relationship existed between the area under the plasma concentration, time curve and dose and dose-normalised plasma concentration, time plots were superimposable. These findings suggest that caffeine obeys linear pharmacokinetics over the dose range investigated. Despite significant inter-individual differences in pharmacokinetic parameters there was good reproducibility within 5 subjects given 300 mg caffeine orally on 3 occasions. Salivary caffeine levels probably reflect the unbound plasma caffeine concentration and can be used to estimate the pharmacokinetic parameters of the drug. Overall the saliva/plasma concentration ratio was 0.74{$\pm$}0.08 but within subjects some time-dependence of the ratio was found with higher ratios initially (even after intravenous administration) and lower ratios at longer time intervals after the dose. Urinary elimination of caffeine was low and independent of dose: 1.83\% of the dose was eliminated unchanged.},
  file = {/Users/driscoll/Dropbox/library/Journal Article/Newton et al-1981-Plasma and salivary pharmacokinetics of caffeine in man.pdf},
  journal = {European Journal of Clinical Pharmacology},
  language = {en},
  number = {1}
}

@book{ockendonAppliedPartial2003,
  title = {Applied {{Partial Differential Equations}}},
  author = {Ockendon, J. R. and Howison, Sam and Lacey, Andrew and Movchan, Alexander},
  year = {2003},
  publisher = {{Oxford University Press}},
  abstract = {Partial differential equations are used in mathematical models of a huge range of real-world phenomena, from electromagnetism to financial markets. This new edition of Applied PDEs contains many new sections and exercises Including, American options, transform methods, free surface flows, linear elasticity and complex characteristics.},
  googlebooks = {CdA6jcJWCToC},
  isbn = {978-0-19-852771-8},
  keywords = {Mathematics / Applied,Science / History},
  language = {en}
}

@book{olverNISTHandbook2010,
  title = {{{NIST Handbook}} of {{Mathematical Functions Hardback}} and {{CD}}-{{ROM}}},
  author = {Olver, Frank W. J. and Lozier, Daniel W. and Boisvert, Ronald F. and Clark, Charles W.},
  year = {2010},
  month = may,
  publisher = {{Cambridge University Press}},
  abstract = {Modern developments in theoretical and applied science depend on knowledge of the properties of mathematical functions, from elementary trigonometric functions to the multitude of special functions. These functions appear whenever natural phenomena are studied, engineering problems are formulated, and numerical simulations are performed. They also crop up in statistics, financial models, and economic analysis. Using them effectively requires practitioners to have ready access to a reliable collection of their properties. This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators. Printed in full color, it is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun. Included with every copy of the book is a CD with a searchable PDF of each chapter. Check out the news release and the video for this new book!},
  googlebooks = {3I15Ph1Qf38C},
  isbn = {978-0-521-19225-5},
  keywords = {Mathematics / Applied,Mathematics / Mathematical Analysis,Mathematics / Reference},
  language = {en}
}

@book{ortegaIterativeSolution2014,
  title = {Iterative {{Solution}} of {{Nonlinear Equations}} in {{Several Variables}}},
  author = {Ortega, J. M. and Rheinboldt, W. C.},
  year = {2014},
  month = may,
  publisher = {{Elsevier}},
  abstract = {Computer Science and Applied Mathematics: Iterative Solution of Nonlinear Equations in Several Variables presents a survey of the basic theoretical results about nonlinear equations in n dimensions and analysis of the major iterative methods for their numerical solution.This book discusses the gradient mappings and minimization, contractions and the continuation property, and degree of a mapping. The general iterative and minimization methods, rates of convergence, and one-step stationary and multistep methods are also elaborated. This text likewise covers the contractions and nonlinear majorants, convergence under partial ordering, and convergence of minimization methods.This publication is a good reference for specialists and readers with an extensive functional analysis background.},
  googlebooks = {UMDSBQAAQBAJ},
  isbn = {978-1-4832-7672-4},
  keywords = {Mathematics / General},
  language = {en}
}

@book{parlettSymmetricEigenvalue1980,
  title = {The {{Symmetric Eigenvalue Problem}}},
  author = {Parlett, Beresford N.},
  year = {1980},
  month = jan,
  publisher = {{SIAM}},
  abstract = {According to Parlett, \&\#39;Vibrations are everywhere, and so too are the eigenvalues associated with them. As mathematical models invade more and more disciplines, we can anticipate a demand for eigenvalue calculations in an ever richer variety of contexts.\&\#39; Anyone who performs these calculations will welcome the reprinting of Parlett\&\#39;s book (originally published in 1980). In this unabridged, amended version, Parlett covers aspects of the problem that are not easily found elsewhere. The chapter titles convey the scope of the material succinctly. The aim of the book is to present mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few. The author explains why the selected information really matters and he is not shy about making judgments. The commentary is lively but the proofs are terse.},
  googlebooks = {YAm9Ny6Z7PkC},
  isbn = {978-0-89871-402-9},
  keywords = {Mathematics / Algebra / Linear,Mathematics / Mathematical Analysis,Mathematics / Numerical Analysis},
  language = {en}
}

@article{peleskoEffectSmallaspectratio2006,
  title = {The Effect of the Small-Aspect-Ratio Approximation on Canonical Electrostatic {{MEMS}} Models},
  author = {Pelesko, John A. and Driscoll, Tobin A.},
  year = {2006},
  month = jan,
  volume = {53},
  pages = {239--252},
  issn = {0022-0833},
  doi = {10.1007/s10665-005-9013-2},
  copyright = {All rights reserved},
  journal = {Journal of Engineering Mathematics},
  keywords = {file-import-09-09-29},
  number = {3-4}
}

@book{quarteroniNumericalMathematics2007,
  title = {Numerical {{Mathematics}}},
  author = {Quarteroni, Alfio and Sacco, Riccardo and Saleri, Fausto},
  year = {2007},
  month = jan,
  publisher = {{Springer}},
  abstract = {Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions.As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis.One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performances on examples and counterexamples which outline their pros and cons. This is done using the MATLAB software environment which is user-friendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified on a MATLAB computer implementation. Every chapter is supplied with examples, exercises and applications of the discussed theory to the solution of real-life problems.This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in Engineering, Mathematics, Physics and Computer Sciences. The attention which is paid to the applications and the related development of software makes it valuable also for researchers and users of scientific computing in a large variety of professional fields.},
  googlebooks = {FA3\_DQAAQBAJ},
  isbn = {978-0-387-22750-4},
  keywords = {Mathematics / Applied,Mathematics / Calculus,Mathematics / General,Mathematics / Mathematical Analysis,Mathematics / Number Systems,Mathematics / Numerical Analysis},
  language = {en}
}

@book{roacheFundamentalsComputational1998,
  title = {Fundamentals of {{Computational Fluid Dynamics}}},
  author = {Roache, Patrick J.},
  year = {1998},
  publisher = {{Hermosa Publishers}},
  abstract = {This work is built on the author's 1972 text, Computational Fluid Dynamics. That work is expanded yet essentially reproduced here as Part I, with chapters on incompressible and compressible flow equations, computational methods for incompressible and compressible flow, other mesh and coordinate systems, and recommendations on programming, testing, and information processing. Part II contains newer material on areas including operation count for direct Gaussian elimination, multigrid solvers, a sixth-order accurate direct solver for Poisson and Helmholtz equations in polar coordinates, nonlinear flux limiters applied to groundwater contaminant transport, and verification of codes and calculations. Annotation copyrighted by Book News, Inc., Portland, OR},
  googlebooks = {rhh2QgAACAAJ},
  isbn = {978-0-913478-09-7},
  keywords = {Science / Mechanics / Fluids},
  language = {en}
}

@book{saadIterativeMethods2003,
  title = {Iterative {{Methods}} for {{Sparse Linear Systems}}: {{Second Edition}}},
  shorttitle = {Iterative {{Methods}} for {{Sparse Linear Systems}}},
  author = {Saad, Yousef},
  year = {2003},
  month = jan,
  publisher = {{SIAM}},
  abstract = {Since the first edition of this book was published in 1996, tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. The size and complexity of the new generation of linear and nonlinear systems arising in typical applications has grown. Solving the three-dimensional models of these problems using direct solvers is no longer effective. At the same time, parallel computing has penetrated these application areas as it became less expensive and standardized. Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical methods. Iterative Methods for Sparse Linear Systems, Second Edition gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. These equations can number in the millions and are sparse in the sense that each involves only a small number of unknowns. The methods described are iterative, i.e., they provide sequences of approximations that will converge to the solution.},
  googlebooks = {h9nwszYPblEC},
  isbn = {978-0-89871-800-3},
  keywords = {Mathematics / General,Mathematics / Geometry / General,Mathematics / Numerical Analysis},
  language = {en}
}

@article{shampineMATLABODE1997,
  title = {The {{MATLAB ODE Suite}}},
  author = {Shampine, Lawrence F. and Reichelt, Mark W.},
  year = {1997},
  month = jan,
  volume = {18},
  pages = {1--22},
  issn = {1064-8275, 1095-7197},
  doi = {10.1137/S1064827594276424},
  file = {/Users/driscoll/Dropbox/library/Journal Article/Shampine_Reichelt-1997-The MATLAB ODE Suite.pdf},
  journal = {SIAM Journal on Scientific Computing},
  language = {en},
  number = {1}
}

@book{smithNumericalSolution1985,
  title = {Numerical {{Solution}} of {{Partial Differential Equations}}: {{Finite Difference Methods}}},
  shorttitle = {Numerical {{Solution}} of {{Partial Differential Equations}}},
  author = {Smith, Gordon D.},
  year = {1985},
  edition = {3rd},
  publisher = {{Clarendon Press}},
  abstract = {Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.},
  googlebooks = {hDpvljaHOrMC},
  isbn = {978-0-19-859650-9},
  keywords = {Mathematics / Differential Equations / General,Mathematics / Differential Equations / Partial,Mathematics / Finite Mathematics},
  language = {en}
}

@book{stewartMatrixAlgorithms2001,
  title = {Matrix {{Algorithms Volume}} 2: {{Eigensystems}}},
  shorttitle = {Matrix {{Algorithms Volume}} 2},
  author = {Stewart, G. W.},
  year = {2001},
  month = aug,
  publisher = {{SIAM}},
  abstract = {This is the second volume in a projected five-volume survey of numerical linear algebra and matrix algorithms. It treats the numerical solution of dense and large-scale eigenvalue problems with an emphasis on algorithms and the theoretical background required to understand them. The notes and reference sections contain pointers to other methods along with historical comments. The book is divided into two parts: dense eigenproblems and large eigenproblems. The first part gives a full treatment of the widely used QR algorithm, which is then applied to the solution of generalized eigenproblems and the computation of the singular value decomposition. The second part treats Krylov sequence methods such as the Lanczos and Arnoldi algorithms and presents a new treatment of the Jacobi-Davidson method. These volumes are not intended to be encyclopedic, but provide the reader with the theoretical and practical background to read the research literature and implement or modify new algorithms.},
  googlebooks = {uSOBoVpqVUYC},
  isbn = {978-0-89871-503-3},
  keywords = {Mathematics / Algebra / General,Mathematics / Applied,Mathematics / Mathematical Analysis,Mathematics / Matrices,Mathematics / Numerical Analysis},
  language = {en}
}

@book{stoerIntroductionNumerical2002,
  title = {Introduction to {{Numerical Analysis}}},
  author = {Stoer, Josef and Bulirsch, R.},
  year = {2002},
  month = aug,
  edition = {3rd},
  publisher = {{Springer Science \& Business Media}},
  abstract = {Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in re search and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numeri cal and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.},
  googlebooks = {1oDXWLb9qEkC},
  isbn = {978-0-387-95452-3},
  keywords = {Mathematics / Algebra / General,Mathematics / Applied,Mathematics / Calculus,Mathematics / Counting \& Numeration,Mathematics / Mathematical Analysis,Mathematics / Number Systems,Mathematics / Numerical Analysis},
  language = {en}
}

@book{strangAnalysisFinite1997,
  title = {An {{Analysis}} of the {{Finite Element Method}}},
  author = {Strang, Gilbert and Fix, George J.},
  year = {1997},
  publisher = {{Wellesley-Cambridge Press}},
  isbn = {978-0-9614088-8-6},
  keywords = {Mathematics / Mathematical Analysis},
  language = {en}
}

@book{strangComputationalScience2007,
  title = {Computational {{Science}} and {{Engineering}}},
  author = {Strang, Gilbert},
  year = {2007},
  month = nov,
  publisher = {{Wellesley-Cambridge Press}},
  abstract = {Encompasses the full range of computational science and engineering from modelling to solution, both analytical and numerical. It develops a framework for the equations and numerical methods of applied mathematics. Gilbert Strang has taught this material to thousands of engineers and scientists (and many more on MIT's OpenCourseWare 18.085-6). His experience is seen in his clear explanations, wide range of examples, and teaching method. The book is solution-based and not formula-based: it integrates analysis and algorithms and MATLAB codes to explain each topic as effectively as possible. The topics include applied linear algebra and fast solvers, differential equations with finite differences and finite elements, Fourier analysis and optimization. This book also serves as a reference for the whole community of computational scientists and engineers. Supporting resources, including MATLAB codes, problem solutions and video lectures from Gilbert Strang's 18.085 courses at MIT, are provided at math.mit.edu/cse.},
  googlebooks = {GQ9pQgAACAAJ},
  isbn = {978-0-9614088-1-7},
  keywords = {Computers / General,Mathematics / Applied},
  language = {en}
}

@book{strangIntroductionLinear2016,
  title = {Introduction to {{Linear Algebra}}},
  author = {Strang, Gilbert},
  year = {2016},
  month = aug,
  publisher = {{Wellesley-Cambridge Press}},
  abstract = {Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains all the qualities of earlier editions, while at the same time seeing numerous minor improvements and major additions. The latter include: \textbullet{} A new chapter on singular values and singular vectors, including ways to analyze a matrix of data \textbullet{} A revised chapter on computing in linear algebra, with professional-level algorithms and code that can be downloaded for a variety of languages \textbullet{} A new section on linear algebra and cryptography \textbullet{} A new chapter on linear algebra in probability and statistics. A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (including practice problems, exams, and development of textbook examples), plus codes in MATLAB\textregistered, Julia, and Python.},
  googlebooks = {efbxjwEACAAJ},
  isbn = {978-0-9802327-7-6},
  keywords = {Mathematics / Algebra / General},
  language = {en}
}

@book{strangLinearAlgebra1997,
  title = {Linear {{Algebra}}, {{Geodesy}}, and {{GPS}}},
  author = {Strang, Gilbert and Borre, Kai},
  year = {1997},
  month = jan,
  publisher = {{SIAM}},
  abstract = {Discusses algorithms generally expressed in MATLAB for geodesy and global positioning. Three parts cover basic linear algebra, the application to the (linear and also nonlinear) science of measurement, and the GPS system and its applications. A popular article from SIAM News (June 1997) The Mathematics of GPS is included as an introduction. Annot},
  googlebooks = {MjNwWUY8jx4C},
  isbn = {978-0-9614088-6-2},
  keywords = {Technology \& Engineering / Engineering (General)},
  language = {en}
}

@article{takahasiDoubleExponential1973,
  title = {Double {{Exponential Formulas}} for {{Numerical Integration}}},
  author = {Takahasi, Hidetosi and Mori, Masatake},
  year = {1973},
  month = dec,
  volume = {9},
  pages = {721--741},
  issn = {0034-5318},
  doi = {10.2977/prims/1195192451},
  file = {/Users/driscoll/Dropbox/library/Journal Article/Takahasi_Mori-1973-Double Exponential Formulas for Numerical Integration.pdf;/Users/driscoll/Zotero/storage/N22LS9FX/show_abstract.html},
  journal = {Publications of the Research Institute for Mathematical Sciences},
  number = {3}
}

@book{teunissenDynamicData2001,
  title = {Dynamic Data Processing: Recursive Least-Squares},
  shorttitle = {Dynamic Data Processing},
  author = {Teunissen, P. J. G.},
  year = {2001},
  publisher = {{VSSD}},
  address = {{Delft, the Netherlands}},
  isbn = {9786610450640},
  keywords = {Geodesy,Least squares,Mathematical models,Parameter estimation,Recursive functions},
  lccn = {QA9.615},
  series = {Series on Mathematical Geodesy and Positioning}
}

@book{trangensteinNumericalSolution2009,
  title = {Numerical Solution of Hyperbolic Partial Differential Equations},
  author = {Trangenstein, J. A.},
  year = {2009},
  publisher = {{Cambridge University Press}},
  address = {{Cambridge ; New York}},
  isbn = {978-0-521-87727-5},
  keywords = {Differential equations; Hyperbolic,Numerical solutions,Textbooks},
  lccn = {QA377 .T62 2009}
}

@book{trefethenApproximationTheory2013,
  title = {Approximation {{Theory}} and {{Approximation Practice}}},
  author = {Trefethen, Lloyd N.},
  year = {2013},
  month = jan,
  publisher = {{SIAM}},
  abstract = {This book presents a twenty-first century approach to classical polynomial and rational approximation theory. The reader will find a strikingly original treatment of the subject, completely unlike any of the existing literature on approximation theory, with a rich set of both computational and theoretical exercises for the classroom. There are many original features that set this book apart: the emphasis is on topics close to numerical algorithms; every idea is illustrated with Chebfun examples; each chapter has an accompanying Matlab file for the reader to download; the text focuses on theorems and methods for analytic functions; original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. This textbook is ideal for advanced undergraduates and graduate students across all of applied mathematics.},
  googlebooks = {En41UGQ6YXsC},
  isbn = {978-1-61197-239-9},
  keywords = {Computers / Programming / Algorithms,Mathematics / Calculus,Mathematics / General,Mathematics / Mathematical Analysis,Mathematics / Numerical Analysis},
  language = {en}
}

@article{trefethenGaussQuadrature2008,
  title = {Is {{Gauss Quadrature Better}} than {{Clenshaw}}\textendash{{Curtis}}?},
  author = {Trefethen, Lloyd N.},
  year = {2008},
  month = jan,
  volume = {50},
  pages = {67--87},
  publisher = {{Society for Industrial and Applied Mathematics}},
  issn = {0036-1445},
  doi = {10.1137/060659831},
  abstract = {We compare the convergence behavior of Gauss quadrature with that of its younger brother, Clenshaw\textendash Curtis. Seven-line MATLAB codes are presented that implement both methods, and experiments show that the supposed factor-of-2 advantage of Gauss quadrature is rarely realized. Theorems are given to explain this effect. First, following O'Hara and Smith in the 1960s, the phenomenon is explained as a consequence of aliasing of coefficients in Chebyshev expansions. Then another explanation is offered based on the interpretation of a quadrature formula as a rational approximation of \$\textbackslash log((z+1)/(z-1))\$ in the complex plane. Gauss quadrature corresponds to Pad\'e approximation at \$z=\textbackslash infty\$. Clenshaw\textendash Curtis quadrature corresponds to an approximation whose order of accuracy at \$z=\textbackslash infty\$ is only half as high, but which is nevertheless equally accurate near \$[-1,1]\$.},
  file = {/Users/driscoll/Dropbox/library/Journal Article/Trefethen-2008-Is Gauss Quadrature Better than Clenshaw–Curtis.pdf;/Users/driscoll/Zotero/storage/DNJGBNUG/060659831.html},
  journal = {SIAM Review},
  number = {1}
}

@book{trefethenNumericalLinear1997,
  title = {Numerical {{Linear Algebra}}},
  author = {Trefethen, Lloyd N. and III, David Bau},
  year = {1997},
  month = jun,
  publisher = {{SIAM}},
  abstract = {This is a concise, insightful introduction to the field of numerical linear algebra. The clarity and eloquence of the presentation make it popular with teachers and students alike. The text aims to expand the reader\&\#39;s view of the field and to present standard material in a novel way. All of the most important topics in the field are covered with a fresh perspective, including iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability. Presentation is in the form of 40 lectures, which each focus on one or two central ideas. The unity between topics is emphasized throughout, with no risk of getting lost in details and technicalities. The book breaks with tradition by beginning with the QR factorization - an important and fresh idea for students, and the thread that connects most of the algorithms of numerical linear algebra.},
  googlebooks = {4Mou5YpRD\_kC},
  isbn = {978-0-89871-361-9},
  keywords = {Mathematics / Algebra / General,Mathematics / Algebra / Linear,Mathematics / Applied,Mathematics / Mathematical Analysis,Technology \& Engineering / Engineering (General)},
  language = {en}
}

@incollection{trefethenSixMyths2011,
  title = {Six Myths of Polynomial Interpolation and Quadrature},
  author = {Trefethen, Lloyd N.},
  booktitle = {Approximation {{Theory}} and {{Approximation Practice}}, {{Extended Edition}}},
  year = {2019},
  publisher = {SIAM},
  address = {Philadelphia}
}

@book{trefethenSpectralMethods2000,
  title = {Spectral {{Methods}} in {{MATLAB}}},
  author = {Trefethen, Lloyd N.},
  year = {2000},
  month = jan,
  publisher = {{SIAM}},
  abstract = {This is the only book on spectral methods built around MATLAB programs. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since spectral methods involve significant linear algebra and graphics they are very suitable for the high level programming of MATLAB. This hands-on introduction is built around forty short and powerful MATLAB programs, which the reader can download from the World Wide Web.},
  googlebooks = {9Zu4YqPQKocC},
  isbn = {978-0-89871-959-8},
  keywords = {Computers / Computer Science,Computers / Mathematical \& Statistical Software,Mathematics / Applied,Mathematics / Differential Equations / General,Mathematics / Mathematical Analysis,Mathematics / Numerical Analysis},
  language = {en}
}

@book{trefethenSpectraPseudospectra2005,
  title = {Spectra and {{Pseudospectra}}: {{The Behavior}} of {{Nonnormal Matrices}} and {{Operators}}},
  shorttitle = {Spectra and {{Pseudospectra}}},
  author = {Trefethen, Lloyd N. and Embree, Mark},
  year = {2005},
  month = aug,
  publisher = {{Princeton University Press}},
  abstract = {Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.},
  isbn = {978-0-691-11946-5},
  keywords = {Mathematics / Algebra / General,Mathematics / Applied,Mathematics / Matrices,Mathematics / Numerical Analysis},
  language = {en}
}

@book{vandervorstIterativeKrylov2003,
  title = {Iterative {{Krylov Methods}} for {{Large Linear Systems}}},
  author = {{van der Vorst}, H. A.},
  year = {2003},
  month = apr,
  publisher = {{Cambridge University Press}},
  abstract = {Computational simulation of scientific phenomena and engineering problems often depend on solving linear systems with a large number of unknowns. This book gives an insight into the construction of iterative methods for the solution of such systems and helps the reader to select the best solver for given classes of problems. The emphasis is on the main ideas and how they have led to efficient solvers such as CG, GMRES, and Bi-CGSTAB. The book also explains the main concepts behind the construction of preconditioners. The reader is encouraged to build their own experience by analysing numerous examples that illustrate how best to exploit the methods. The book also hints at many open problems and as such it will appeal to established researchers. There are many exercises that motivate the material and help students to understand the essential steps in the analysis and construction of algorithms.},
  googlebooks = {wE0NrHkrqRAC},
  isbn = {978-0-521-81828-5},
  keywords = {Mathematics / Mathematical Analysis,Mathematics / Numerical Analysis,Mathematics / Probability \& Statistics / General,Technology \& Engineering / Industrial Technology},
  language = {en}
}

@book{vanloanIntroductionScientific2000,
  title = {Introduction to Scientific Computing: A Matrix-Vector Approach Using {{MATLAB}}},
  shorttitle = {Introduction to Scientific Computing},
  author = {Van Loan, Charles F.},
  year = {2000},
  publisher = {{Prentice Hall}},
  address = {{Upper Saddle River, NJ}},
  isbn = {978-0-13-949157-3},
  keywords = {Data processing,Mathematics,MATLAB},
  lccn = {QA76.95 .V35 1999},
  series = {The {{MATLAB}} Curriculum Series}
}

@book{whithamLinearNonlinear1974,
  title = {Linear and {{Nonlinear Waves}}},
  author = {Whitham, G. B.},
  year = {1974},
  publisher = {{John Wiley \& Sons}},
  abstract = {Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. The mathematical principles are presented along with examples of specific cases in communications and specific physical fields, including flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, and ocean waves from storms.},
  isbn = {978-1-118-03120-9},
  keywords = {Mathematics / General,Science / Waves \& Wave Mechanics},
  language = {en}
}

@incollection{wilkinsonPerfidiousPolynomial1984,
  title = {The Perfidious Polynomial},
  booktitle = {Studies in {{Mathematics}}},
  author = {Wilkinson, J. H.},
  year = {1984},
  volume = {24},
  pages = {1--28},
  publisher = {{Mathematical Association of America}}
}

@article{wuEffectsMild2014,
  title = {The {{Effects}} of {{Mild Ocular Surface Stimulation}} and {{Concentration}} on {{Spontaneous Blink Parameters}}},
  author = {Wu, Ziwei and Begley, Carolyn G. and Situ, Ping and Simpson, Trefford and Liu, Haixia},
  year = {2014},
  month = jan,
  volume = {39},
  pages = {9--20},
  issn = {0271-3683, 1460-2202},
  doi = {10.3109/02713683.2013.822896},
  file = {/Users/driscoll/Dropbox/library/Journal Article/Wu et al-2014-The Effects of Mild Ocular Surface Stimulation and.pdf},
  journal = {Current Eye Research},
  language = {en},
  number = {1}
}