
Accuracy and Stability of Numerical Algorithms
Nicholas J. Higham(Author)
Society for Industrial & Applied Mathematics,U.S. (Publisher)
2nd Edition
Will be published approx. on 31. August 2002
Book
Hardback
710 pages
978-0-89871-521-7 (ISBN)
Description
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 / Votes
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. Koeckler, Zentrallblatt fuer 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
More details
Edition
Second Edition
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Edition type
New edition
Dimensions
Height: 260 mm
Width: 181 mm
Thickness: 37 mm
Weight
1390 gr
ISBN-13
978-0-89871-521-7 (9780898715217)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
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.
Content
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
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