Applied numerical linear algebra / James W. Demmel.

Content
1. Introduction
1.1 Basic notation
1.2 Standard problems of numerical linear Algebra
1.3 General techniques
1.4 Example: Polynomial Evaluation
1.5 Floating point Arithmetic
etc

2. Linear equation solving
2.1 Introduction
2.2 Perturbation theory
2.3 Gaussian Elimination
2.4 Error Analysis
2.5 Improving the accuracy of a solution
etc

3. Linear least squares problems
3.1 Introduction
3.2 Matrix Factorization that solve the linear least square problem
3.3 Perturbation Theory for the least square problem
3.4 Orthogonal matrices
3.5 Rank-Deficient least square problems using the SVD
etc

4. Nonsymmetric Eigenvalue problem
4.1 Introduction
4.2 Canonical forms
4.3 Perturbation Theory
4.4 Algorithms for the Nonsymmetric Eigenvalue
4.5 Other Nonsymmetric Eigenvalue problems

5. The symmetric Eigenproblem and Singular value decomposition
5.1 Introduction
5.2 Perturbation theory
5.3 Algorithms for symmetric for Eigenproblem
5.4 Algorithms for singular value decomposition
5.5 Differential equations and Eigenvalue problems
etc

6. Iterative methods for linear systems
6.1 Introduction
6.2 One-line help for alternative methods
6.3 Poisson's Equation
6.4 Summary of ,methods for solving Possion's equation
6.5 Basic iterative methods
etc

7. Iterative methods for Eigenvalue problems
7.1 Introduction
7.2 The Rayleigh-Ritz methods
7.3 The Lanczos Algorithm in exact Arithmetic
7.4 The Lanczos Algorithm in in floating point Arithmetic
7.5 The Lanczos Algorithm in with selective Orthogonalization
etc

Includes bibliographical references (p. 389-408) and index.