This book is a comprehensive survey of matrix perturbation theory, a topic of interest to numerical analysts, statisticians, physical scientists, and engineers. In particular, the authors cover perturbation theory of linear systems and least square problems, the eignevalue problem, and the generalized eignevalue problem as wellas a complete treatment of vector and matrix norms, including the theory of unitary invariant norms.

This book is the second volume in a projected five-volume survey of numerical linear algebra and matrix algorithms. This volume treats the numerical solution of dense and large-scale eigenvalue problems with an emphasis on algorithms and the theoretical background required to understand them. Stressing depth over breadth, Professor Stewart treats the derivation and implementation of the more important algorithms in detail. The notes and references sections contain pointers to other methods along with historical comments. The book is divided into two parts: dense eigenproblems and large eigenproblems. The first part gives a full treatment of the widely used QR algorithm, which is then applied to the solution of generalized eigenproblems and the computation of the singular value decomposition. The second part treats Krylov sequence methods such as the Lanczos and Arnoldi algorithms and presents a new treatment of the Jacobi-Davidson method. The volumes in this survey are not intended to be encyclopedic. By treating carefully selected topics in depth, each volume gives the reader the theoretical and practical background to read the research literature and implement or modify new algorithms. The algorithms treated are illustrated by pseudocode that has been tested in MATLAB implementations.

There are many textbooks to choose from when teaching an introductory numerical analysis course, but there is only one Afternotes on Numerical Analysis. This book presents the central ideas of modern numerical analysis in a vivid and straightforward fashion with a minimum of fuss and formality. Stewart designed this volume while teaching an upper-division course in introductory numerical analysis. To clarify what he was teaching, he wrote down each lecture immediately after it was given. The result reflects the wit, insight, and verbal craftmanship which are hallmarks of the author. Simple examples are used to introduce each topic, then the author quickly moves on to the discussion of important methods and techniques. With its rich mixture of graphs and code segments, the book provides insights and advice that help the reader avoid the many pitfalls in numerical computation that can easily trap an unwary beginner.