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

ISBN: 9780538733519 / 0538733519

### 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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