8 Approximation Theory 497 1 Discrete Least Squares Approximation 498 8.2 Orthogonal Polynomials and Least Squares Approximation 510 8.3 Chebyshev Polynomials and Economization of Power Series 518 8.4 Rational Function Approximation 528 8.5 Trigonometric Polynomial Approximation 538 8.6 Fast fourier transforms 547 8.7 Survey of Methods and Software 558 9 Approximating Eigenvalues 561 9.1 Linear Algebra and Eigenvalues 562 9.2 Orthogonal Matrices and Similarity Transformations 570 9.3 The Power Method 576 9. 4 Householder's Method 593 9.5 The QR Algorithm 601 Singular Value Decomposition 614 9.7 Survey of Methods and Software 626 10 Numerical Solutions of Nonlinear Systems of quations 629 E 10.1 Fixed Points for Functions of several variables 630 10.2 Newtons Method 638 10.3 Quasi-Newton Methods 647 10.4 Steepest Descent Techniques 6.54 10.5 Homotopy and Continuation Methods 660 10.6 Survey of Methods and Software 668 11 Boundary-Value Problems for Ordinary Differential quations 671 11.1 The Linear Shooting method 672 11.2 The Shooting Method for Nonlinear Problems 678 11. 3 Finite-Difference Methods for Linear problems 684 11.4 Finite-Difference methods for Nonlinear problems 691 11. 5 The Rayleigh-Ritz Method 696 11.6 Survey of Methods and Software 711 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 vii 8 ApproximationTheory 497 8.1 Discrete Least Squares Approximation 498 8.2 Orthogonal Polynomials and Least Squares Approximation 510 8.3 Chebyshev Polynomials and Economization of Power Series 518 8.4 Rational Function Approximation 528 8.5 Trigonometric Polynomial Approximation 538 8.6 Fast Fourier Transforms 547 8.7 Survey of Methods and Software 558 9 Approximating Eigenvalues 561 9.1 Linear Algebra and Eigenvalues 562 9.2 Orthogonal Matrices and Similarity Transformations 570 9.3 The Power Method 576 9.4 Householder’s Method 593 9.5 The QR Algorithm 601 9.6 Singular Value Decomposition 614 9.7 Survey of Methods and Software 626 10 Numerical Solutions of Nonlinear Systems of Equations 629 10.1 Fixed Points for Functions of Several Variables 630 10.2 Newton’s Method 638 10.3 Quasi-Newton Methods 647 10.4 Steepest Descent Techniques 654 10.5 Homotopy and Continuation Methods 660 10.6 Survey of Methods and Software 668 11 Boundary-Value Problems for Ordinary Differential Equations 671 11.1 The Linear Shooting Method 672 11.2 The Shooting Method for Nonlinear Problems 678 11.3 Finite-Difference Methods for Linear Problems 684 11.4 Finite-Difference Methods for Nonlinear Problems 691 11.5 The Rayleigh-Ritz Method 696 11.6 Survey of Methods and Software 711 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