Numerical Analysis, 9th Edition

Numerical Analysis, 9th Edition Numerical Analysis, 9th Edition

ISBN: 9780538733519 / 0538733519

Table of Contents

Chapter 1

Mathematical Preliminaries And Error Analysis

1-1 Review of Calculus Exercises p.14
1-2 Round-Off Errors and Computer Arithmetic Exercises p.28
1-3 Algorithms and Convergence Exercises p.39

Chapter 2

Solutions Of Equations In One Variable

2-1 The Bisection Method Exercises p.54
2-2 Fixed-Point Iteration Exercises p.64
2-3 Newton's Method and Its Extensions Exercises p.75
2-4 Error Analysis for Iterative Methods Exercises p.85
2-5 Accelerating Convergence Exercises p.90
2-6 Zeros of Polynomials and Muller's Method Exercises p.100

Chapter 3

Interpolation And Polynomial Approximation

3-1 Interpolation and the Lagarange Polynomial Exercises p.114
3-2 Data Approximation and Neville's Method Exercises p.123
3-3 Divided Differences Exercises p.133
3-4 Hermite Interpolation Exercises p.142
3-5 Cubic Spline Interpolation Exercises p.161
3-6 Parametric Curves Exercises p.170

Chapter 4

Numerical Differentiation And Integration

4-1 Numerical Differentiation Exercises p.182
4-2 Richardson's Extrapolation Exercises p.191
4-3 Elements of Numerical Intergration Exercises p.202
4-4 Composite Numerical Integration Exercises p.210
4-5 Romberg Integration Exercises p.218
4-6 Adaptive Quadrature Methods Exercises p.227
4-7 Gaussian Quadrature Exercises p.234
4-8 Multiple Integrals Exercises p.248
4-9 Improper Integrals Exercises p.254

Chapter 5

Initial-Value Problems For Ordinary Differential Equations

5-1 The Elementary Theory of Initial-Value Problems Exercises p.264
5-2 Euler's Method Exercises p.273
5-3 Higher-Order Taylor Methods Exercises p.281
5-4 Runge-Kutta Methods Exercises p.291
5-5 Error Control and the Runge-Kutta Fehlberg Method Exercises p.300
5-6 Multistep Methods Exercises p.314
5-7 Variable Step-Size Multistep Methods Exercises p.320
5-8 Extrapolation Methods Exercises p.327
5-9 Higher-Order Equations and Systems of Differential Equations Exercises p.337
5-10 Stablity Exercises p.347
5-11 Stiff Differential Equations Exercises p.354

Chapter 6

Direct Methods For Solving Linear Systems

6-1 Linear Systems of Equations Exercises p.368
6-2 Pivoting Strategies Exercises p.379
6-3 Linear Algebra and Matrix Inversion Exercises p.390
6-4 The Determinat of a Matrix Exercises p.399
6-5 Matrix Factorization Exercises p.409
6-6 Special Types of Matrices Exercises p.425

Chapter 7

Iterative Techniques In Matrix Algebra

7-1 Norms of Vectors and Matrices Exercises p.441
7-2 Eigenvalues and Eigenvectors Exercises p.449
7-3 The Jacobi and Gauss-Siedel Iterative Techniques Exercises p.459
7-4 Relaxation Techniques for Solving Linear Systems Exercises p.467
7-5 Error Bounds and Iterative Refinement Exercises p.476
7-6 The Conjugate Gradient Method Exercises p.492

Chapter 8

Approximation Theory

8-1 Discrete Least Squares Approximation Exercises p.506
8-2 Orthogonal Polynomials and Least Squares Approximation Exercises p.518
8-3 Chebyshev Polynomials and Economization of Power Series Exercises p.527
8-4 Rational Function Approximation Exercises p.537
8-5 Trigonometric Polynomial Approximation Exercises p.546
8-6 Fast Fourier Transforms Exercises p.557

Chapter 9

Approximating Eigenvalues

9-1 Linear Algebra and Eigenvalues Exercises p.568
9-2 Orthogonal Matrices and Similarity Transformations Exercises p.573
9-3 The Power Method Exercises p.590
9-4 Householder's Method Exercises p.600
9-5 The QR Algorithm Exercises p.611
9-6 Singular Value Decomposition Exercises p.625

Chapter 10

Numerical Solutions Of Nonlinear Systems Of Equations

10-1 Fixed Points for Functions of Several Variables Exercises p.636
10-2 Newton's Method Exercises p.644
10-3 Quasi-Newton Methods Exercises p.652
10-4 Steepest Descent Techniques Exercises p.659
10-5 Homotopy and Continuation Methods Exercises p.666

Chapter 11

Boundary-Value Problems For Ordinary Differential Equations

11-1 The Linear Shooting Method Exercises p.677
11-2 The Shooting Method for Nonlinear Problems Exercises p.684
11-3 Finite-Difference Methods for Linear Problems Exercises p.689
11-4 Finite-Difference Methods for Nonlinear Problems Exercises p.696
11-5 The Rayleigh-Ritz Method Exercises p.710

Chapter 12

Numerical Solutions To Partial Differential Equations

12-1 Elliptic Partial Differential Equations Exercises p.723
12-2 Parabolic Partial Differential Equations Exercises p.736
12-3 Hyperbolic Partial Differential Equations Exercises p.744
12-4 An Introduction to the Finite-Element Method Exercises p.758
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