Contents
Preface .................................. ix
1 Mathematical Preliminaries and Error Analysis 1
1.1 Introduction . . .............................. 1
1.2 ReviewofCalculus............................ 1
1.3 Round-off Error and Computer Arithmetic .............. 17
1.4 Errors in Scientific Computation .................... 25
1.5 ComputerSoftware............................ 34
2 Solutions of Equations of One Variable 39
2.1 Introduction . . .............................. 39
2.2 The Bisection Metho d .......................... 39
2.3 The Secant Method ............................ 47
2.4 Newton’s Metho d ............................. 55
2.5 Error Analysis and Accelerating Convergence ............. 64
2.6 M¨uller’sMethod ............................. 70
2.7 SurveyofMethodsandSoftware .................... 77
3 Interpolation and Polynomial Approximation 79
3.1 Introduction . . .............................. 79
3.2 Lagrange Polynomials .......................... 81
3.3 Divided Differences ............................ 95
3.4 Hermite Interpolation ..........................104
3.5 Spline Interpolation ...........................111
3.6 ParametricCurves ............................124
3.7 SurveyofMethodsandSoftware ....................131
4 Numerical Integration and Differentiation 133
4.1 Introduction . . ..............................133
4.2 BasicQuadratureRules .........................134
4.3 Comp osite Quadrature Rules ......................144
4.4 Romberg Integration ...........................155
4.5 GaussianQuadrature...........................164
4.6 AdaptiveQuadrature...........................170
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