Numerical Analysis, 9th Edition

895 Pages·2010·14.54 MB·English

by  Richard L. Burden

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1st Pass Pages
Numerical Analysis
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Numerical Analysis
NINTH EDITION
Richard L. Burden
Youngstown State University
J. Douglas Faires
Youngstown State University
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • UnitedKingdom • UnitedStates
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NumericalAnalysis, ©2011,2005,2001Brooks/Cole,CengageLearning
NinthEdition
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Contents
Preface ix
1 Mathematical Preliminaries and Error Analysis 1
1.1 ReviewofCalculus 2
1.2 Round-offErrorsandComputerArithmetic 17
1.3 AlgorithmsandConvergence 32
1.4 NumericalSoftware 41
2 Solutions of Equations in OneVariable 47
2.1 TheBisectionMethod 48
2.2 Fixed-PointIteration 56
2.3 Newton’sMethodandItsExtensions 67
2.4 ErrorAnalysisforIterativeMethods 79
2.5 AcceleratingConvergence 86
2.6 ZerosofPolynomialsandMüller’sMethod 91
2.7 SurveyofMethodsandSoftware 101
3 Interpolation and Polynomial Approximation 105
3.1 InterpolationandtheLagrangePolynomial 106
3.2 DataApproximationandNeville’sMethod 117
3.3 DividedDifferences 124
3.4 HermiteInterpolation 136
3.5 CubicSplineInterpolation 144
3.6 ParametricCurves 164
3.7 SurveyofMethodsandSoftware 171
4 Numerical Differentiation and Integration 173
4.1 NumericalDifferentiation 174
4.2 Richardson’sExtrapolation 185
4.3 ElementsofNumericalIntegration 193
v
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vi Contents
4.4 CompositeNumericalIntegration 203
4.5 RombergIntegration 213
4.6 AdaptiveQuadratureMethods 220
4.7 GaussianQuadrature 228
4.8 MultipleIntegrals 235
4.9 ImproperIntegrals 250
4.10 SurveyofMethodsandSoftware 256
5 Initial-Value Problems for Ordinary Differential
Equations 259
5.1 TheElementaryTheoryofInitial-ValueProblems 260
5.2 Euler’sMethod 266
5.3 Higher-OrderTaylorMethods 276
5.4 Runge-KuttaMethods 282
5.5 ErrorControlandtheRunge-Kutta-FehlbergMethod 293
5.6 MultistepMethods 302
5.7 VariableStep-SizeMultistepMethods 315
5.8 ExtrapolationMethods 321
5.9 Higher-OrderEquationsandSystemsofDifferentialEquations 328
5.10 Stability 339
5.11 StiffDifferentialEquations 348
5.12 SurveyofMethodsandSoftware 355
6 Direct Methods for Solving Linear Systems 357
6.1 LinearSystemsofEquations 358
6.2 PivotingStrategies 372
6.3 LinearAlgebraandMatrixInversion 381
6.4 TheDeterminantofaMatrix 396
6.5 MatrixFactorization 400
6.6 SpecialTypesofMatrices 411
6.7 SurveyofMethodsandSoftware 428
7 IterativeTechniques in Matrix Algebra 431
7.1 NormsofVectorsandMatrices 432
7.2 EigenvaluesandEigenvectors 443
7.3 TheJacobiandGauss-SiedelIterativeTechniques 450
7.4 RelaxationTechniquesforSolvingLinearSystems 462
7.5 ErrorBoundsandIterativeRefinement 469
7.6 TheConjugateGradientMethod 479
7.7 SurveyofMethodsandSoftware 495
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