Table Of ContentELEMENTARY NUMERICAL ANALYSIS
An Algorithmic Approach
International Series in Pure and Applied Mathematics
G. Springer
rot igdnEitlusnoC
Ahlfors: Complex Analysis
Bender and Orszag: Advanced Mathematical Methods for Scientists and Engineers
Buck: Advanced Calculus
Busacker and Saaty: Finite Graphs and Networks
Cheney: Introduction to Approximation Theory
Chester: Techniques in Partial Differential Equations
Coddington and Levinson: Theory of Ordinary Differential Equations
Conte and de Boor: Elementary Numerical Analysis: An Algorithmic Approach
Dennemeyer: Introduction to Partial Differential Equations and Boundary Value
Problems
Dettman: Mathematical Methods in Physics and Engineering
Hamming: Numerical Methods for Scientists and Engineers
Hildebrand: Introduction to Numerical Analysis
Householder: The Numerical Treatment of a Single Nonlinear Equation
Kalman, Falb, and Arbib: Topics in Mathematical Systems Theory
McCarty: Topology: An Introduction with Applications to Topological Groups
Moore: Elements of Linear Algebra and Matrix Theory
Moursund and Duris: Elementary Theory and Application of Numerical Analysis
Pipes and Harvill: Applied Mathematics for Engineers and Physicists
Ralston and Rabinowitz: A First Course in Numerical Analysis
Ritger and Rose: Differential Equations with Applications
Rudin: Principles of Mathematical Analysis
Shapiro: Introduction to Abstract Algebra
Simmons: Differential Equations with Applications and Historical Notes
Simmons: Introduction to Topology and Modern Analysis
Struble: Nonlinear Differential Equations
ELEMENTARY
NUMERICAL
ANALYSIS
An Algorithmic Approach
drihTnoitidE
S. D. Conte
Purdue University
Carl de Boor
Universiry of Wisconsin—Madison
McGraw-Hill Book Company
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ELEMENTARY NUMERICAL ANALYSIS
An Algorithmic Approach
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yam eb ,decudorper derots ni a laveirter ,metsys ro ,dettimsnart niyna
mrof ro yb yna ,snaem ,cinortcele ,lacinahcem ,gniypocotohp gnidrocerro
,esiwrehto tuohtiw eht roirp nettirw noissimrep fo eht.rehsilbup
234567890 DODO 89876543210
sihT koob saw tes ni semiT namoR yb ecneicS ,srehpargopyT .cnIehT
srotide erew loraC reipaN dna semaJ .S ;ramA eht noitcudorprosivrepus
saw lihP .aelaG ehT sgniward erew enod yb eniF eniL ,snoitartsullI.cnI
.R .R yellennoD & snoS ynapmoC saw retnirp dna.rednib
Library of Congress Cataloging in Publication Data
,etnoC leumaS ,leinaDetad
yratnemelE laciremun .sisylana
lanoitanretnI( seires ni erup dnadeilppa
mathematics)
sedulcnI .xedni
1. Numerical analysis-Data processing.
I . ed ,rooB ,lraC tnioj .rohtua .II.eltiT
QA297.C65 1980 519.4 79-24641
ISBN 0-07-012447-7
CONTENTS
Preface
ix
Introduction
xi
Chapter 1 rebmuN smetsyS dna srorrE 1
1.1 ehT noitatneserpeR fo sregetnI 1
1.2 ehT noitatneserpeR fo snoitcarF 4
1.3 Floating-Point Arithmetic 7
1.4 ssoL fo ecnacifingiS dna rorrE;noitagaporP
Condition and Instability 12
1.5 lanoitatupmoC sdohteM rof rorrE noitamitsE 18
1.6 emoS stnemmoC no ecnegrevnoC fosecneuqeS 19
1.7 Some Mathematical Preliminaries 25
Chapter 2 Interpolation by Polynomial 31
2.1 Polynomial Forms 31
2.2 ecnetsixE dna sseneuqinU fo eht gnitalopretnIlaimonyloP 38
3.2 The Divided-Difference Table 41
*2.4 Interpolation at an Increasing Number of
Interpolation Points 46
2.5 ehT rorrE fo eht gnitalopretnIlaimonyloP 51
6.2 noitalopretnI ni a noitcnuF elbaT desaB noyllauqE
decapS stnioP 55
*2.7 ehT dediviD ecnereffiD sa a noitcnuF fo stIstnemugrA
and Osculatory Interpolation 62
* snoit cdeeSkram htiw na ksiretsa yam eb dett itmuoohtiw ssol f.oytiunitnoc
V
vi CONTETS
Chapter 3 The Solution of Nonlinear Equations 72
3.1 A yevruS fo evitaretIsdohteM 74
3.2 sdohteM evitaretI emoS rof smargorP nartroF 81
3.3 tnioP-dexiF noitaretI 88
3.4 ecnegrevnoC noitareleccA rof tnioP-dexiFnoitaretI 95
*3.5 ecnegrevnoC fo eht notweN dna tnaceSsdohteM 100
3.6 sto olRa e:Rsnoitau qlEaimonyloP 110
*3.7 xelpmoC stooR dna s’rellüMdohteM 120
Chapter 4 Matrices and Systems of Linear Equations 128
4.1 seitreporP fosecirtaM 128
4.2 ehT noituloS fo raeniL smetsyS ybnoitanimilE 147
4.3 ehT gnitoviPygetartS 157
4.4 noitazirot craaFlugna ierhTT 160
4.5 smro N;noitulo Setamixorpp An af olaudise Rdn arorrE 169
4.6 rorrE-drawkcaB sisylanA dna evitaretItnemevorpmI 177
*4.7 Determinants 185
8.4* ehT eulavnegiEmelborP 189
Chapter *5 Systems of Equations and Unconstrained
Optimization 208
*5.1 noitazimitpO dna tsepeetStnecseD 209
*5.2 s’notweNdohteM 216
*5.3 sd onhotietM an xodainltae aRtrneitoIP-dexiF 223
Chapter 6 Approximation 235
6.1 mrofinU noitamixorppA ybslaimonyloP 235
2.6 ataDgnittiF 245
*6.3 lanogohtrO slaimonyloP 251
*6.4 serauqS-tsaeL noitamixorppA ybslaimonyloP 259
*6.5 noitamixorppA yb cirtemonogirTslaimonyloP 268
*6.6 smr o rftessinaraFuroTF 277
6.7 laimonyloP-esiweceiPnoitamixorppA 284
Chapter 7 Differentiation and Integration 294
7.1 noitaitneref fliaDciremuN 295
7.2 laciremuN :noitargetnI emoS cisaBseluR 303
7.3 se lnuaRiss u:anGoitarge tlnaIciremuN 311
7.4 seluR etisopmoC :noitargetnI laciremuN 319
7.5 evitpadA erutardauQ 328
l 7.6 tim ie LhonttoitalopartxE 333
l 7.7 grebmoR noitargetnI 340
CONTENTS vii
Chapter 8 The Solution of Differential Equations 346
8.1 lacitamehtaM seiranimilerP 346
8.2 elpmiS ecnereffiDsnoitauqE 349
8.3 laciremuN noitargetnI yb rolyaTseireS 354
8.4 rorrE setamitsE dna ecnegrevnoC fo s’reluEdohteM 359
8.5 sd oahttteuMK-egnuR 362
8.6 eziS-petS lortnoC htiw attuK-egnuRsdohteM 366
8.7 petsitluM salumroF 373
8.8 rotcerroC-rotciderP sdohteM 379
8.9 dohte MnotluoM-smad AehT 382
*8.10 ytilibatS fo laciremuNsdohteM 389
11.8* lortno Cdn anoitagapor ProrrE-ffo-dnuoR 395
*8.12 smetsyS fo laitnereffiDsnoitauqE 398
*8.13 ffitS laitnereffiDsnoitauqE 401
Chapter 9 Boundary Value Problems 406
9.1 etiniF ecnereffiDsdohteM 406
9.2 gnitoohSsdohteM 412
9.3 noitacolloCsdohteM 416
Appendix: Subroutine Libraries 421
References 423
Index 425
PREFACE
sihT si eht driht noitide fo a koob no yratnemele laciremun sisylanahcihw
is designed specifically for the needs of upper-division undergraduate
stneduts ni ,gnireenigne ,scitamehtam dna ecneics ,gnidulcni ni ,ralucitrap
retupmoc .ecneics nO eht ,elohw eht tneduts ohw sah dah a dilosegelloc
calculus sequence should have no difficulty following the material.
decnavdA lacitamehtam ,stpecnoc hcus sa smron dna ,ytilanogohtronehw
yeht era ,desu era decudortni ylluferac ta a level elbatius rofetaudargrednu
students and do not assume any previous knowledge. Some familiarity
htiw secirtam si demussa rof eht retpahc no smetsys fo snoitauqe dnahtiw
laitnereffid snoitauqe rof sretpahC 8 dna .9 sihT noitide seod niatnocemos
snoitces hcihw eriuqer ylthgils erom lacitamehtam ytirutam naht eht-iverp
suo .noitide ,revewoH lla hcus snoitces era dekram htiw sksiretsa dna lla
nac eb dettimo yb eht rotcurtsni htiw on ssol ni.ytiunitnoc
sihT wen noitide sniatnoc a taerg laed fo wen lairetam dnatnacifingis
segnahc ot emos fo eht redlo .lairetam ehT sretpahc evah neebdegnarraer
in what we believe is a more natural order. Polynomial interpolation
(Chapter 2) now precedes even the chapter on the solution of nonlinear
smetsys retpahC( )3 dna si desu yltneuqesbus rof emos fo eht lairetamni
all chapters. The treatment of Gauss elimination (Chapter 4) has been
.deifilpmis nI ,noitidda retpahC 4 won sekam evisnetxe esu fos’nosnikliW
backward error analysis, and contains a survey of many well-known
methods for the eigenvalue-eigenvector problem. Chapter 5 is a new
chapter on systems of equations and unconstrained optimization. It con-
tains an introduction to steepest-descent methods, Newton’s method for
nonlinear systems of equations, and relaxation methods for solving large
raenil smetsys yb .noitareti ehT retpahc no noitamixorppa retpahC( )6 sah
been enlarged. It now treats best approximation and good approximation
ix
