James Weldon Demmel is a professor in the Computer Science Division and Mathematics Department at the University of California, Berkeley.

Preface; Chapter 1: Introduction. Basic Notation; Standard Problems of Numerical Linear Algebra; General Techniques; Example: Polynomial Evaluation; Floating Point Arithmetic; Polynomial Evaluation Revisited; Vector and Matrix Norms; References and Other Topics for Chapter 1; Questions for Chapter 1; Chapter 2: Linear Equation Solving. Introduction; Perturbation Theory; Gaussian Elimination; Error Analysis; Improving the Accuracy of a Solution; Blocking Algorithms for Higher Performance; Special Linear Systems; References and Other Topics for Chapter 2; Questions for Chapter 2; Chapter 3: Linear Least Squares Problems. Introduction; Matrix Factorizations That Solve the Linear Least Squares Problem; Perturbation Theory for the Least Squares Problem; Orthogonal Matrices; Rank Deficient Least Squares Problems; Performance Comparison of Methods for Solving Least Squares Problems; Reference and Other Topics for Chapter 3; Questions for Chapter 3; Chapter 4: Nonsymmetric Eigenvalue Problems. Introduction; Canonical Forms; Perturbation Theory; Algorithms for the Nonsymmetric Eigenproblem; Other Nonsymmetric Eigenvalue Problems; Summary; References and Other Topics for Chapter 4; Questions for Chapter 4; Chapter 5: The Symmetric Eigenproblem and Singular Value Decomposition. Introduction; Perturbation Theory; Algorithms for the Symmetric Eigenproblem; Algorithms for the Singular Value Decomposition; Differential Equations and Eigenvalue Problems; References and Other Topics for Chapter 5; Questions for Chapter 5; Chapter 6: Iterative Methods for Linear Systems. Introduction; On-line Help for Iterative Methods; Poisson's Equation; Summary of Methods for Solving Poisson's Equation; Basic Iterative Methods; Krylov Subspace Methods; Fast Fourier Transform; Block Cyclic Reduction; Multigrid; Domain Decomposition; References and Other Topics for Chapter 6; Questions for Chapter 6; Chapter 7: Iterative Methods for Eigenvalue Problems. Introduction. The Rayleigh-Ritz Method; The Lanczos Algorithm in Exact Arithmetic; The Lanczos Algorithm in Floating Point Arithmetic; The Lanczos Algorithm with Selective Orthogonalization; Beyond Selective Orthogonalization; Iterative Algorithms for the Nonsymmetric Eigenproblem; References and Other Topics for Chapter 7; Questions for Chapter 7; Bibliography; Index.