Introduction to Applied Numerical Analysis

356 Pages·1989·10.138 MB·English

by  Richard W. Hamming

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. (0-486-47220-5)
INTRODUCTION TO DIFFERENTIABLE MANIFOLDS, Louis Auslander and Robert E.
MacKenzie. (0-486-47172-1)
PROBLEM SOLVING THROUGH RECREATIONAL MATHEmatics, Bonnie Averbach and Orin
Chein. (0-486-40917-1)
THEORY OF LINEAR OPERATIONS, Stefan Banach. Translated by F. Jellett.
(0-486-46983-2)
Vector CatcuLus, Peter Baxandall and Hans Liebeck. (0-486-46620-5)
INTRODUCTION TO VECTORS AND TENSORS: SECOND EDITION—T'Wo VoLUMES BouNnD AS ONE,
Ray M. Bowen and C.-C. Wang. (0-486-46914-X)
ADVANCED TRIGONOMETRY, C. V. Durell and A. Robson. (0-486-43229-7)
FourIER ANALYSIS IN SEVERAL COMPLEX VARIABLES, Leon Ehrenpreis. (0-486-44975-0)
THE THIRTEEN BOOKS OF THE ELEMENTS, VOL. 1, Euclid. Edited by Thomas L. Heath.
(0-486-60088-2)
THE THIRTEEN BOOKS OF THE ELEMENTS, VOL. 2, Euclid. (0-486-60089-0)
THE THIRTEEN BOOKS OF THE ELEMENTS, VOL. 3, Euclid. Edited by Thomas L. Heath.
(0-486-60090-4)
AN INTRODUCTION TO DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, Stanley J.
Farlow. (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,