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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 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.
£86.50

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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'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.

An expanded treatment of Gaussian elimination incorporates rook pivoting, along with a thorough discussion of the choice of pivoting strategy and the effects of scaling. The book's detailed descriptions of floating point arithmetic and of software issues reflect the fact that IEEE arithmetic is now ubiquitous.

Although not designed specifically as a textbook, this new edition is a suitable reference for an advanced course. It can also be used by instructors at all levels as a supplementary text from which to draw examples, historical perspective, statements of results, and exercises. With its thorough indexes and extensive, up-to-date bibliography, the book provides a mine of information in a readily accessible form.
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.

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