RICHARD W. HAMMING Introduction o Applied Numerical Analysis DOVER BOOKS ON MATHEMATICS HANDBOOK OF MATHEMATICAL FUNCTIONS: WITH FORMULAS, GRAPHS, AND MATHEMATICAL Tastes, Edited by Milton Abramowitz and Irene A. Stegun. (0-486-61272-4) ABSTRACT AND CONCRETE CATEGORIES: THE Joy OF Cats, Jiri Adamek, Horst Herrlich, George E. Strecker. (0-486-46934-4) NONSTANDARD METHODS IN STOCHASTIC ANALYSIS AND MATHEMATICAL Puysics, Sergio Albeverio, Jens Erik Fenstad, Raphael Hgegh-Krohn and Tom Lindstrom. (0-486-46899-2) Matuematics: Its ConTENT, METHops AND Meaninc, A. D. Aleksandrov, A. N. Kolmogorov, and M. A. Lavrent’ev. (0-486-40916-3) COLLEGE GEOMETRY: AN INTRODUCTION TO THE MODERN GEOMETRY OF THE TRIANGLE AND THE Circe, Nathan Altshiller-Court. (0-486-45805-9) THe Works oF ARCHIMEDES, Archimedes. Translated by Sir Thomas Heath. (0-486-42084-1) REAL VARIABLES WITH Basic METRIC Space Topotocy, Robert B. Ash. 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(0-486-44595-X) PARTIAL DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS, Stanley J. Farlow. (0-486-67620-X) StocHastic DIFFERENTIAL EQUATIONS AND APPLICATIONS, Avner Friedman. (0-486-45359-6) ADVANCED CaLcuLus, Avner Friedman. (0-486-45795-8) Point SET Topotocy, Steven A. Gaal. (0-486-47222-1) DiscovERING MATHEmatics: THE ArT oF InvesTIGATION, A. Gardiner. (0-486-45299-9) Lattice THEORY: First CoNcEPTS AND DistRipuTivE Lattices, George Gratzer. (0-486-47173-X) ORDINARY DIFFERENTIAL Equations, Jack K. Hale. (0-486-47211-6) METHOps OF APPLIED MATHEMatics, Francis B. Hildebrand. (0-486-67002-3) Basic ALcesrA I: SEconp Epition, Nathan Jacobson. (0-486-47189-6) Basic ALGEBRA II: Seconp Epition, Nathan Jacobson. (0-486-47187-X) NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS BY THE FINITE ELEMENT METHOD, Claes Johnson. (0-486-46900-X) ADVANCED EUCLIDEAN GeomeTRY, Roger A. Johnson. (0-486-46237-4) GEOMETRY AND Convexity: A Stupy in MatHematTicaL METHops, Paul J. Kelly and Max L. Weiss. (0-486-46980-8) TRIGONOMETRY REFRESHER, A, Albert Klaf. (0-486-44227-6) (continued on back flap) a) : > tt a 7 a’ " Richard WY, Moin ne a“ a sy —s Le Po * Me og id Av! ia * , . ry A # ¢ s é ie teal » - ’ % be ® = = 4° ‘, « 4 - | ed » ass a ie : 7 i ‘ is 7 7 ’ ( Kd : oa ‘ mt 7 —S | : free 4 > A 7 é = 4 he nc U e7 e < P, arone ceT aelnetn s Wehr ti toeer 6 : a ee i ee ok: el ry me 4 A # » ‘G2 ry Tes ‘ ‘ ridye J La a ? FY ata en a er wGeaee. Rrhae nh Bopeo i e ; on. = 2 Ratna i. oe Ye Vie * =, 7 | Caer Wily v “a neal od ’ a " a % ® ? —- a coe , 7 ; a Preps, ror He DES oF Ce O — ? af me e .z o_ e { A 1 7 oT S a jareen > tee eure a ’ “= 7s a ’ "i 7 ahs, oy fy are Conadyne ; APES POG ey s- ct a tam (a4) ‘al or a. Eines: Cx: nr meas J Satay ieee) < oe Coet Tine. See Cams © mef ol ien rer os ’ cary, Criiged ot. ; : i 9 rhe - 7 » Paes Sn EO ts, Sepev em Sa = een a tie “— aa “© ye © © wel bates paged Pre wa vets | oayy _ re <_G rae Re a oo mesons cae a.e n! : ov il Sues Coy a os a. & - sit 7 7. nr Pana, esac oy sno age Introduction to APPLIED NUMERICAL ANALYSIS Richard W. Hamming DOVER PUBLICATIONS, INC. Mineola, New Yor k Copyright Copyright © 1989 by Richard W. Hamming All rights reserved. Bibliographical Note This Dover edition, first published in 2012, is an unabridged republication of the edition published in 1989 by Hemisphere Publishing Corporation, New York. The work was originally published in 1971 by the McGraw-Hill Book Company, Inc., New York. Library of Congress Cataloging-in-Publication Data Hamming, R. W. (Richard Wesley), 1915-1998. Introduction to applied numerical analysis / Richard W. Hamming. — Dover ed. p. cm. Originally published: New York : Hemisphere Pub., 1989. Summary: “This book is appropriate for an applied numerical analysis course for upper-level undergraduate and graduate students as well as com- puter science students. Actual programming is not covered, but an extensive range of topics includes round-off and function evaluation, real zeros of a function, integration, ordinary differential equations, optimization, orthogo- nal functions, Fourier series, and much more. 1989 edition”’— Provided by publisher. Includes index. ISBN-13: 978-0-486-48590-4 (pbk.) ISBN-10: 0-486-48590-0 (pbk.) 1. Numerical analysis—Data processing. I. Title. QA297.H275 1989 518.0285—de23 2011032722 Manufactured in the United States by Courier Corporation 48590001 www.doverpublications.com contents vii Preface ale 1 Roundoff and function evaluation 2. 33 Real zeros of a function 2 57 Complex zeros 4. 81 Zeros of polynomials 5. 105 Simultaneous linear equations and matrices 6. 143 Interpolation and roundoff estimation 7. 175 Integration 8. 199 Ordinary differential equations 9. 221 Optimization 10. 247 Least squares vi CONTENTS i: 261 Orthogonal functions ied: 283 Fourier series 13. 297 Chebyshev approximation 14, 309 Random processes 15. 325 Design of a library 329 Index preface to the reprint edition It is curious that after 17 years and all the improvements in computing machines, the basics of numerical analysis remain much the same. The great change occurred when we went from hand computing to machines. The further steps to the current super computers have produced more courses in computing and more specialized knowledge, but the fundamen- tals common to most of computing remain unchanged. The same simple problems arise again and again. Thus, were I to try to rewrite the book, there seems to be little that I would, or should, change. richard w. hamming vii noiibs tnihqe1 shit of sostsiq cies man « ~ : : : riiita yran ar eioomavengns st the banes asiryT i softbs aiee con 7 i 7 off uses of) Aon nism zieylean beucisown Yo natant:o t aoa anea > | atioken ot gertegns Inte ment thaw sw asbteT O G >s ails 7 an dgaatieg awed srstuqmae Faga tears. aq oa)o t eee - -egrnebnt adr rot oghstwond besilarsega stoutb as iti os i: = wren bape eod iane gnisogrine 10 Om 0) 06 wo ep * : pneu Oh et ot totew aut? “nig banw hee ett i ssaientpr it aux {Eliade 10b isS he ade - : sd ie ney - ors t el) on,