Analysis of numerical methods.pdf

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ANALYSIS OF NUMERICAL METHODS EUGENE ISAACSON Professor Emeritus of Mathematics Courant Institute of Mathematical Sciences New York University HERBERT BISHOP KELLER Profes~or of Applied Mathematics Applied Mathematics California Institute of Technology DOVER PUBLICATIONS, INC., NEW YORK

Copyright Copynght © 1966 by John Wiley & Sons. All nghts Conventions. reserved under Pan American and International Copyright Published in Canada by General Publishing Company, Ltd., 30 Lesmill Road, Don Mills, Toronto, Ontario Published in the United Kingdom by Constable and Company, Ltd., 3 The Lanchesters, 162-164 Fulham Palace Road, London W6 9ER Bibliographical Note This Dover edition, first published in 1994, is an unabridged, corrected repub lication of the work first published by John Wiley & Sons, New York, 1966 For this edition the authors have corrected a number of errors and provided a new Preface. Library of Congress Cataloging-in-Publication Data Isaacson, Eugene. Analysis of numerical methods / Eugene Isaacson, Herbert Bishop Keller. p. em. Originally published: New York: Wiley, 1966. With new pref. Includes bibliographical references and index. ISBN 0-486-68029-0 (pbk.) I. Numerical analysis. I Keller, Herbert Bishop. II Title QA297.18 519.4-dc20 1994 94-7740 CIP Manufactured in the United States of Amenca Dover Publications, Inc., 31 East 2nd Street, Mineola, N. Y. 11501

To our understanding wives, Muriel and Loretta

Preface to the Dover Edition This edition contains minor corrections to the original edition. In the 28 years that have elapsed between these two editions, there have been great changes in computing equipment and in the development of numerical methods. However, the analysis required to understand and to devise new methods has not changed, and, thus, this somewhat mature text is still relevant. To the list of important tOpiCS omitted in the original edition (namely, linear programming, rational approximation and Monte Carlo) we must now add fast transforms, finite elements, wavelets, complexity theory, multigrid methods, adaptive gridding, path following and parallel algorithms. Hopefully, some energetic young numerical analyst will incorporate all these missing topics into an updated version to aid the burgeoning field of scientific computing. We thank the many people who have pointed out errors and misprints in the original edition. In particular, Mr. Carsten Elsner suggested an elegant improvement in our demonstration of the Runge phenomenon, which we have adopted in Problem 8 on page 280. EUGENE ISAACSON AND HERBERT B KELL~.R New York and Pasadena July 1993

Preface to the First Edition Digital computers, though mass produced for no more than fifteen years, have become indispensable for much current scientific research. One basic reason for this is that by implementing numerical methods, computers form a universal tool for "solving" broad classes of problems. While numerical methods have always been useful it is clear that their role in scientific research is now of fundamental importance. No modern applied mathematician, physical scientist, or engineer can be properly trained without some understanding of numerical methods. We attempt, in this book, to supply some of the required knowledge. In presenting the material we stress techniques for the development of new methods. This requires knowing why a particular method is effective on some problems but not on others. Hence we are led to the analysis of numerical methods rather than merely their description and listing. Certainly the solving of scientific problems should not be and is not the sole motivation for studying numerical methods. Our opinion is that the analysis of numerical methods is a broad and challenging mathematical activity whose central theme is the effective constructibility of various kinds of approximations. Many numerical methods have been neglected in this book since we do not attempt to be exhaustive. Procedures treated are either quite good and efficient by present standards or else their study is considered instructive (while their use may not be advocated). Unfortunately the limitations of space and our own experience have resulted in the omission of many important topics that we would have liked to include (for example, linear programming, rational approximation, Monte Carlo methods). The present work, it turns out, could be considered a mathematics in selected areas of analysis and matrix theory. Essentially no text Vll

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