Intro
Preface to the Second Edition
Preface to the First Edition
Acknowledgments
Contents
About the Authors
1 Preliminaries
1.1 Introduction
1.1.1 Floating Point Numbers in Binary Form
1.1.2 Rounding Errors and Loss of Precision
1.1.3 Effect of Rounding on Numerical Computation
1.1.4 Taylor Series and Tuncation
1.1.5 Effect of Digital Calculations on Iteration
1.2 Mathematical and Computational Modeling
1.3 A Brief Introduction to MATLAB
1.3.1 Programming in MATLAB
1.3.2 Array and Matrices
1.3.3 Loops and Conditional Operations

1.3.4 Graphics
Part I System of Equations and Eigenvalues
2 Solution of Linear Equations
2.1 Analytical Methods of Solving a Set of Linear Equations
2.1.1 Cramer's Rule
2.1.2 Inverse of a Square Matrix
2.2 Preliminaries
2.2.1 Row operations
2.2.2 Some Useful Results
2.2.3 Condition Number of a Matrix
2.2.4 Pivoting
2.2.5 Triangular Matrices
2.3 Gauss Elimination Method
2.4 Gauss Jordan Method of Determining the Inverse Matrix
2.5 LU Decomposition or LU Factorization
2.5.1 Doolittle Decomposition
2.5.2 Crout Decomposition

2.5.3 Cholesky Decomposition
2.6 Tridiagonal Matrix Algorithm
2.6.1 Cholesky Decomposition of a Symmetric Tridiagonal Matrix
2.6.2 General Case of a Tridiagonal Matrix and the TDMA
2.7 QR Factorization
2.7.1 Gram-Schmidt Method
2.7.2 Householder Transformation and QR Factorization
2.7.3 Givens Rotation and QR Factorization
2.8 Iterative Methods of Solution
2.8.1 Jacobi and Gauss-Seidel Methods
2.8.2 Conjugate Gradient Method
3 Computation of Eigenvalues
3.1 Examples of Eigenvalues
3.1.1 Eigenvalue Problem in Geometry

3.1.2 Solution of a Set of Ordinary Differential Equations (ODE)
3.1.3 Standing Waves on a String
3.1.4 Resonance
3.1.5 Natural Frequency of a Spring Mass System
3.2 Preliminaries on Eigenvalues
3.2.1 Some Important Points
3.2.2 Similarity Transformation
3.2.3 More About the 2times2 Case
3.3 Analytical Evaluation of Eigenvalues and Eigenvectors in Simple Cases
3.4 Power Method
3.4.1 Inverse Power Method
3.4.2 Inverse Power Method with Shift
3.5 Rayleigh Quotient Iteration
3.5.1 Deflation of a Matrix
3.6 Eigenvalue Eigenvector Pair by QR Iteration

3.7 Modification of QR Iteration for Faster Convergence
3.7.1 Upper Hessenberg Form
3.7.2 QR Iteration with Shift
4 Solution of Algebraic Equations
4.1 Univariate Non-linear Equation
4.1.1 Plotting Graph: The Simplest Method
4.1.2 Bracketing Methods
4.1.3 Fixed Point Iteration Method
4.1.4 Newton-Raphson Method
4.1.5 Secant Method
4.1.6 Regula Falsi Method
4.2 Multivariate Non-linear Equations
4.2.1 Gauss-Seidel Iteration
4.2.2 Newton-Raphson Method
4.3 Root Finding and Optimization
4.3.1 Search Methods of Optimization: Univariate Case