Transcription of ELEMENTARY NUMERICAL ANALYSIS
1 ELEMENTARY NUMERICAL ANALYSISAn Algorithmic ApproachInternational Series in Pure and Applied MathematicsG. SpringerConsulting EditorAhlfors: Complex AnalysisBender and Orszag: Advanced Mathematical Methods for Scientists and EngineersBuck: Advanced CalculusBusacker and Saaty: Finite Graphs and NetworksCheney: Introduction to Approximation TheoryChester: Techniques in Partial differential EquationsCoddington and Levinson: Theory of Ordinary differential EquationsConte and de Boor: ELEMENTARY NUMERICAL ANALYSIS : An Algorithmic ApproachDennemeyer.
2 Introduction to Partial differential equations and Boundary ValueProblemsDettman: Mathematical Methods in Physics and EngineeringHamming: NUMERICAL Methods for Scientists and EngineersHildebrand: Introduction to NUMERICAL AnalysisHouseholder: The NUMERICAL Treatment of a Single Nonlinear EquationKalman, Falb, and Arbib: Topics in Mathematical Systems TheoryMcCarty: Topology: An Introduction with Applications to Topological GroupsMoore: Elements of Linear Algebra and Matrix TheoryMoursund and Duris: ELEMENTARY Theory and Application of NUMERICAL AnalysisPipes and Harvill: Applied Mathematics for Engineers and PhysicistsRalston and Rabinowitz: A First Course in NUMERICAL AnalysisRitger and Rose: differential equations with ApplicationsRudin: Principles of Mathematical AnalysisShapiro: Introduction to Abstract AlgebraSimmons: differential equations with Applications and Historical NotesSimmons.
3 Introduction to Topology and Modern AnalysisStruble: Nonlinear differential EquationsELEMENTARYNUMERICALANALYSISAn Algorithmic ApproachThird EditionS. D. ContePurdue UniversityCarl de BoorUniversiry of Wisconsin MadisonMcGraw-Hill Book CompanyNew York St. Louis San Francisco Auckland Bogot HamburgJohannesburg London Madrid Mexico Montreal New DelhiPanama Paris S o Paulo Singapore Sydney Tokyo TorontoELEMENTARY NUMERICAL ANALYSISAn Algorithmic ApproachCopyright 1980, 1972, 1965 by McGraw-Hill, inc.
4 All rights in the United States of America. No part of this publicationmay be reproduced, stored in a retrieval system, or transmitted, in anyform or by any means, electronic, mechanical, photocopying, recording orotherwise, without the prior written permission of the DODO 89876543210 This book was set in Times Roman by Science Typographers, Inc. Theeditors were Carol Napier and James S. Amar; the production supervisorwas Phil Galea. The drawings were done by Fine Line Illustrations, R.
5 Donnelley & Sons Company was printer and of Congress Cataloging in Publication DataConte, Samuel Daniel, dateElementary NUMERICAL ANALYSIS .(International series in pure and appliedmathematics)Includes NUMERICAL ANALYSIS -Data Boor, Carl, joint author. II. 0-07-012447-7 CONTENTSC hapter 1 1 4 * * Systems and ErrorsThe Representation of IntegersThe Representation of FractionsFloating-Point ArithmeticLoss of Significance and Error Propagation.
6 Condition and InstabilityComputational Methods for Error EstimationSome Comments on Convergence of SequencesSome Mathematical PreliminariesInterpolation by PolynomialPolynomial FormsExistence and Uniqueness of the Interpolating PolynomialThe Divided-Difference TableInterpolation at an Increasing Number ofInterpolation PointsThe Error of the Interpolating PolynomialInterpolation in a Function Table Based on EquallySpaced PointsThe Divided Difference as a Function of Its Argumentsand Osculatory Interpolation* Sections marked with an asterisk may be omitted without loss of CONTETSC hapter 3 The Solution of Nonlinear Survey of Iterative Programs for Some Iterative Acceleration for Fixed-Point Iteration95* of the Newton and Secant equations .
7 Real Roots110* Roots and M ller s Method120 Chapter 4 Matrices and Systems of Linear of Solution of Linear Systems by Pivoting Triangular and Residual of an Approximate Solution; ANALYSIS and Iterative Improvement* * Eigenvalue ProblemChapter *5 Systems of equations and UnconstrainedOptimization* and Steepest Descent* s Method* Iteration and Relaxation MethodsChapter Approximation by Fitting* Polynomials* Approximation by Polynomials* by Trigonometric Polynomials* Fourier ApproximationChapter and IntegrationNumerical DifferentiationNumerical Integration: Some Basic RulesNumerical Integration: Gaussian RulesNumerical Integration.
8 Composite RulesAdaptive QuadratureExtrapolation to the LimitRomberg Integration12812814715716016917718518920 8209216223235235245251259268277284294295 303311319328333340 CONTENTS viiChapter * * * * PreliminariesSimple Difference EquationsThe Solution of differential EquationsNumerical Integration by Taylor SeriesError Estimates and Convergence of Euler s MethodRunge-Kutta MethodsStep-Size Control with Runge-Kutta MethodsMultistep FormulasPredictor-Corrector MethodsThe Adams-Moulton MethodStability of NUMERICAL MethodsRound-off-Error Propagation and ControlSystems of differential EquationsStiff differential EquationsChapter 9 Boundary Value Difference Shooting Collocation MethodsAppendix.
9 Subroutine Libraries421 References423 Index42534634634935435936236637337938238 9395398401406406412416 PREFACEThis is the third edition of a book on ELEMENTARY NUMERICAL ANALYSIS whichis designed specifically for the needs of upper-division undergraduatestudents in engineering, mathematics, and science including, in particular,computer science. On the whole, the student who has had a solid collegecalculus sequence should have no difficulty following the mathematical concepts, such as norms and orthogonality, whenthey are used, are introduced carefully at a level suitable for undergraduatestudents and do not assume any previous knowledge.
10 Some familiaritywith matrices is assumed for the chapter on systems of equations and withdifferential equations for Chapters 8 and 9. This edition does contain somesections which require slightly more mathematical maturity than the previ-ous edition. However, all such sections are marked with asterisks and allcan be omitted by the instructor with no loss in new edition contains a great deal of new material and significantchanges to some of the older material.
