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Accuracy and Stability of Numerical Algorithms

Second Edition

Nicholas J. Higham (author)

ISBN: 9780898715217

Publication Date: Aug 2002

Format: Hardback

A thorough, up-to-date treatment of the behaviour of numerical algorithms in finite precision arithmetic. The book combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations.
£84.50

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  • Full Description
  • More Information
  • Table of Contents
  • Author Biography
  • Customer Reviews
This book gives a thorough, up-to-date treatment of the behaviour 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. The coverage of the first edition has been expanded and updated, involving numerous improvements. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton'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. This new edition is a suitable reference for an advanced course and can also be used at all levels as a supplementary text from which to draw examples, historical perspective, statements of results, and exercises. In addition the thorough indexes and extensive, up-to-date bibliography are in a readily accessible form.

Reviews

"This book is a monumental work on the analysis of rounding error and will serve as a new standard textbook on this subject, especially for linear computation."- S. Hitotumatu, Mathematical Reviews;

"...This definitive source on the accuracy and stability of numerical algorithms is quite a bargain and a worthwhile addition to the library of any statistician heavily involved in computing."- Robert L. Strawderman, Journal of the American Statistical Association;

"...A monumental book that should be on the bookshelf of anyone engaged in numerics, be it as a specialist or as a user."- A. van der Sluis, ITW Nieuws;

"This text may become the new 'Bible' about accuracy and stability for the solution of systems of linear equations. It covers 688 pages carefully collected, investigated, and written ... One will find that this book is a very suitable and comprehensive reference for research in numerical linear algebra, software usage and development, and for numerical linear algebra courses."- N. Köckler, Zentrallblatt für Mathematik;

"... Nick Higham has assembled an enormous amount of important and useful material in a coherent, readable form. His book belongs on the shelf of anyone who has more than a casual interest in rounding error and matrix computations. I hope the author will give us the 600-odd page sequel. But if not, he has more than earned his respite - and our gratitude."- G. W. Stewart, SIAM Review
Pages 710
Dimensions 229 x 152
Date Published 31 Aug 2002
Publisher SIAM - Society for Industrial and Applied Mathematics
Subject/s Applied mathematics   Information Science & Technology  
  • List of Figures
  • List of Tables
  • Preface to Second Edition
  • Preface to First Edition
  • About the Dedication
  • Chapter 1: Principles of Finite Precision Computation
  • Chapter 2: Floating Point Arithmetic
  • Chapter 3: Basics
  • Chapter 4: Summation
  • Chapter 5: Polynomials
  • Chapter 6: Norms
  • Chapter 7: Perturbation Theory for Linear Systems
  • Chapter 8: Triangular Systems
  • Chapter 9: LU Factorization and Linear Equations
  • Chapter 10: Cholesky Factorization
  • Chapter 11: Symmetric Indefinite and Skew-Symmetric Systems
  • Chapter 12: Iterative Refinement
  • Chapter 13: Block LU Factorization
  • Chapter 14: Matrix Inversion
  • Chapter 15: Condition Number Estimation
  • Chapter 16: The Sylvester Equation
  • Chapter 17: Stationary Iterative Methods
  • Chapter 18: Matrix Powers
  • Chapter 19: QR Factorization
  • Chapter 20: The Least Squares Problem
  • Chapter 21: Underdetermined Systems
  • Chapter 22: Vandermonde Systems
  • Chapter 23: Fast Matrix Multiplication
  • Chapter 24: The Fast Fourier Transform and Applications
  • Chapter 25: Nonlinear Systems and Newton's Method
  • Chapter 26: Automatic Error Analysis
  • Chapter 27: Software Issues in Floating Point Arithmetic
  • Chapter 28: A Gallery of Test Matrices
  • Appendix A: Solutions to Problems
  • Appendix B: Acquiring Software
  • Appendix C: Program Libraries
  • Appendix D: The Matrix Computation Toolbox
  • Bibliography
  • Name Index
  • Subject Index
Nicholas J. Higham is Richardson Professor of Applied Mathematics at the University of Manchester, England. He is the author of more than 80 publications and is a member of the editorial boards of Foundations of Computational Mathematics, the IMA Journal of Numerical Analysis, Linear Algebra and Its Applications, and the SIAM Journal on Matrix Analysis and Applications. His book Handbook of Writing for the Mathematical Sciences (second edition) was published by SIAM in 1998, and his book MATLAB Guide, co-authored with Desmond J. Higham, was published by SIAM in 2000.

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