This book is a guide to the numerical solution of eigenvalue problems. It attempts to present the many available methods in an organized fashion, to make it easier for you to identify the most promising methods.

Large-scale problems of engineering and scientific computing often require solutions of eigenvalue and related problems. This book gives a unified overview of theory, algorithms, and practical software for eigenvalue problems. It organizes this large body of material to make it accessible for the first time to experts as well as many nonexpert users who need to choose the best state-of-the-art algorithms and software for their problems. Using an informal decision tree, just enough theory is introduced to identify the relevant mathematical structure that determines the best algorithm for each problem.

The algorithms and software at the "leaves" of the decision tree range from the classical QR algorithm, which is most suitable for small dense matrices, to iterative algorithms for very large generalized eigenvalue problems. Algorithms are presented in a unified style as templates,with different levels of detail suitable for readers ranging from beginning students to experts. The authors' comprehensive treatment includes a treasure of further bibliographic information.

List of Symbols and Acronyms

List of Iterative Algorithm Templates

List of Direct Algorithms

List of Figures

List of Tables

1 Introduction

 1.1 Why Eigenvalue Templates？

 1.2 Intended Readership

 1.3 Using the Decision Tree to Choose a Template

 1.4 What Is a Template？

 1.5 Organization of the Book

 A Brief Tour of Eigenproblems

2 A Brief Tour of Eigenproblems

3 An Introduction to Iterative Projection Methods

4 Hermitian Eigenvalue Problems

5 Generalized Hermitian Eigenvalue Problems

6 Singular Value Decomposition

7 Non-Hermitian Eigenvalue Problems

8 Generalized Non-Hermitian Eigenvalue Problems

9 Nonlinear Eigenvalue Problems

10 Common Issues

11 Preconditioning Techniques

Appendix,Of Things Not Treated

Bibliography

Index