Contents Preface ix 1 Mathematical Preliminaries and Error Analysis 1 2 Round-off Errors and Computer Arithmetic 17 1.3 Algorithms and Convergence 32 1.4 Numerical Softy 41 2 Solutions of Equations in One Variable 47 2.1 The Bisection Method 48 2.2 Fixed-Point Iteration 56 2. 3 Newtons Method and Its Extensions 67 2.4 Error Analysis for Iterative Methods 79 2.6 Zeros of Polynomials and Muiller's Method 91 2.7 Survey of Methods and Software 101 3 Interpolation and Polynomial Approximation 105 nd the Lagrange Polynomial 106 3.2 Data Approximation and Neville's Method 117 3.3 Divided Differences 124 3.4 Hermite Interp 3.5 Cubic Spline Interpolation 144 6 Parame 164 3.7 Survey of Methods and Software 171 4 Numerical Differentiation and Integration 173 4.2 Richardson's Extrapolation 185 4.3 Elements of Numerical Integration 193 Copyright 2010 Cengage Learning. All Rights t materially affect the overall leaming eaperience Cengage Learning reserves the right to remo rty commen may be suppressed from the eBook andor eChaptert'sh. May no be copied, scanned, or duplicated, in whole or in part Due toContents Preface ix 1 Mathematical Preliminaries and Error Analysis 1 1.1 Review of Calculus 2 1.2 Round-off Errors and Computer Arithmetic 17 1.3 Algorithms and Convergence 32 1.4 Numerical Software 41 2 Solutions of Equations in One Variable 47 2.1 The Bisection Method 48 2.2 Fixed-Point Iteration 56 2.3 Newton’s Method and Its Extensions 67 2.4 Error Analysis for Iterative Methods 79 2.5 Accelerating Convergence 86 2.6 Zeros of Polynomials and Müller’s Method 91 2.7 Survey of Methods and Software 101 3 Interpolation and Polynomial Approximation 105 3.1 Interpolation and the Lagrange Polynomial 106 3.2 Data Approximation and Neville’s Method 117 3.3 Divided Differences 124 3.4 Hermite Interpolation 136 3.5 Cubic Spline Interpolation 144 3.6 Parametric Curves 164 3.7 Survey of Methods and Software 171 4 Numerical Differentiation and Integration 173 4.1 Numerical Differentiation 174 4.2 Richardson’s Extrapolation 185 4.3 Elements of Numerical Integration 193 v Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it