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A Graduate Introduction to Numerical Methods

From the Viewpoint of Backward Error Analysis

Robert M. Corless, Nicolas Fillion (Autoren)

Buch | Hardcover

869 Seiten

2013
Springer-Verlag New York Inc.
978-1-4614-8452-3 (ISBN)

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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.

“A Graduate Introduction to Numerical Methods and Backward Error Analysis” has been selected 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.

Computer Arithmetic & Fundamental Concepts of Computation.- Polynomials and Series.- Rootfinding and Function Evaluation.- Solving Ax = b .- Solving Ax =l 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.

Zusatzinfo	10 Illustrations, color; 184 Illustrations, black and white; XXXIX, 869 p. 194 illus., 10 illus. in color.
Verlagsort	New York, NY
Sprache	englisch
Maße	178 x 254 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	algorithms • Backward Error Analysis • Barycentric interpolation formulae • boundary value problems • Condition number • Numerical Stability
ISBN-10	1-4614-8452-9 / 1461484529
ISBN-13	978-1-4614-8452-3 / 9781461484523
Zustand	Neuware