Overview
Provides consistent development of formulae using barycentric interpolation
Independence of chapters allowing for greater teaching flexibility
Integration with Matlab and Maple, many algorithms presented in pseudocode
Includes supplementary material: sn.pub/extras
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Table of contents (16 chapters)
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Front Matter
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Preliminaries
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Front Matter
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Numerical Linear Algebra
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Front Matter
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Interpolation, Differentiation, and Quadrature
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Front Matter
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Differential Equations
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Front Matter
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Keywords
About this book
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. Shampine
A 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.
Reviews
“Corless and Fillion have clearly dedicated several years of their lives to this book. It has been worth it! The result is a carefully judged all-round numerical analysis textbook that expertly serves students and instructors. The book stands out in a crowded market. It is a textbook that numerical analysis can be very proud of.” (Alex Townsend, SIAM Review, Vol. 58 (4), December, 2016)
“This book is intended to be a graduate introduction to numerical methods from the perspective of backward error analysis. … it is the variety of topics and case studies, both theoretical and numerical, presented in the book that is its strongest point, making it a valuable reference work for students and professionals … .” (Justin Steven C. Prentice, Mathematical Reviews, January, 2015)
“This textbook provides a very readable and comprehensive graduate-level introduction to numerical methods and their analysis. … The textbook contains many references, exercises, MATLAB codes, and numerical illustrations. It is written in a style that is both informal and informative which makes this book unique in fact.” (Robert Plato, zbMATH, Vol. 1295, 2014)Authors and Affiliations
About the authors
Bibliographic Information
Book Title: A Graduate Introduction to Numerical Methods
Book Subtitle: From the Viewpoint of Backward Error Analysis
Authors: Robert M. Corless, Nicolas Fillion
DOI: https://doi.org/10.1007/978-1-4614-8453-0
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Hardcover ISBN: 978-1-4614-8452-3Published: 07 December 2013
Softcover ISBN: 978-1-4939-5310-3Published: 20 September 2016
eBook ISBN: 978-1-4614-8453-0Published: 12 December 2013
Edition Number: 1
Number of Pages: XXXIX, 869
Number of Illustrations: 184 b/w illustrations, 10 illustrations in colour
Topics: Computational Mathematics and Numerical Analysis, Computational Science and Engineering, Numerical Analysis