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A treatment of the behaviour of numerical algorithms in finite precision arithmetic that combines algorithmic derivations, perturbation theory, and rounding error analysis. Software practicalities are emphasized throughout, with particular reference to LAPACK and MATLAB.
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Accuracy and Stability of Numerical Algorithms
Nicholas J. Higham University of Manchester Manchester, England
Accuracy and Stability of Numerical Algorithms
Society for Industrial and Applied Mathematics Philadelphia
Copyright © 1996 by the Society for Industrial and Applied Mathematics. 1098765432 All rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information. write to the Society for Industrial and Applied Mathematics, 3600 University City Science Center, Philadelphia, PA 19104-2688.
Library of Congress Cataloging-in-Publication Data Higham, Nicholas J., 1961Accuracy and stability of numerical algorithms / Nicholas J. Higham. p. cm. Includes bibliographical references (p. - ) and index. ISBN O-8987 l-355-2 (pbk.) 1. Numerical analysis--Data processing. 2. Computer algorithms. I. Title. QA297.H53 1996 5 19.4’0285’5 1 --dc20 95-39903
o is a registered trademark.
Dedicated to Alan M. Turing and James H. Wilkinson
Contents
List of Figures
xvii
List of Tables
xix
Preface
xxi xxvii
About the Dedication
1 Principles of Finite Precision Computation 1.1 Notation and Background . . . . . . . . . . . . . . . . . . . . 1.2 Relative Error and Significant Digits . . . . . . . . . . . . . . 1.3 Sources of Errors . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Precision Versus Accuracy . . . . . . . .