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Templates for the Solution of Algebraic Eigenvalue Problems:

a Practical Guide

Edited by Zhaojun Bai, James Demmel, Jack Dongarra, Axel Ruhe, and Henk van der Vorst

List of Contributors
How to Use This Book
How to Cite This Book
Acknowledgments
Contents
List of Symbols and Acronyms
- Symbols
- Acronyms
List of Direct Algorithms
List of Figures
List of Tables
Introduction
- Why Eigenvalue Templates?
- Intended Readership
- Using the Decision Tree to Choose a Template
- What Is a Template?
- Organization of the Book
A Brief Tour of Eigenproblems
- Introduction
  - Numerical Stability and Conditioning
- Hermitian Eigenproblems
  J. Demmel
- Generalized Hermitian Eigenproblems
  J. Demmel
- Singular Value Decomposition
  J. Demmel
- Non-Hermitian Eigenproblems
  J. Demmel
- Generalized Non-Hermitian Eigenproblems
  J. Demmel
- More Generalized Eigenproblems
- Nonlinear Eigenproblems
  J. Demmel
An Introduction to Iterative Projection Methods
- Introduction
- Basic Ideas
  Y. Saad
- Spectral Transformations
  R. Lehoucq and D. Sorensen
Hermitian Eigenvalue Problems
- Introduction
- Direct Methods
- Single- and Multiple-Vector Iterations
  M. Gu
- Lanczos Method
  A. Ruhe
- Implicitly Restarted Lanczos Method
  R. Lehoucq and D. Sorensen
- Band Lanczos Method
  R. Freund
- Jacobi-Davidson Methods
  G. Sleijpen and H. van der Vorst
- Stability and Accuracy Assessments
  Z. Bai and R. Li
Generalized Hermitian Eigenvalue Problems
- Introduction
- Transformation to Standard Problem
- Direct Methods
- Single- and Multiple-Vector Iterations
  M. Gu
- Lanczos Methods
  A. Ruhe
- Jacobi-Davidson Methods
  G. Sleijpen and H. van der Vorst
- Stability and Accuracy Assessments
  Z. Bai and R. Li
  - Positive Definite
  - Some Combination of and is Positive Definite
Singular Value Decomposition
- Introduction
- Direct Methods
- Iterative Algorithms
  J. Demmel
- Related Problems
  J. Demmel
Non-Hermitian Eigenvalue Problems
- Introduction
- Balancing Matrices
  T. Chen and J. Demmel
- Direct Methods
- Single- and Multiple-Vector Iterations
  M. Gu
- Arnoldi Method
  Y. Saad
- Implicitly Restarted Arnoldi Method
  R. Lehoucq and D. Sorensen
- Block Arnoldi Method
  R. Lehoucq and K. Maschhoff
- Lanczos Method
  Z. Bai and D. Day
- Block Lanczos Methods
  Z. Bai and D. Day
- Band Lanczos Method
  R. Freund
- Lanczos Method for Complex Symmetric Eigenproblems
  R. Freund
- Jacobi-Davidson Methods
  G. Sleijpen and H. van der Vorst
- Stability and Accuracy Assessments
  Z. Bai and R. Li
Generalized Non-Hermitian Eigenvalue Problems
- Introduction
- Direct Methods
- Transformation to Standard Problems
- Jacobi-Davidson Method
  G. Sleijpen and H. van der Vorst
- Rational Krylov Subspace Method
  A. Ruhe
- Symmetric Indefinite Lanczos Method
  Z. Bai, T. Ericsson, and T. Kowalski
- Singular Matrix Pencils
  B. Kågström
- Stability and Accuracy Assessments
  Z. Bai and R. Li
Nonlinear Eigenvalue Problems
- Introduction
- Quadratic Eigenvalue Problems
  Z. Bai, G. Sleijpen, and H. van der Vorst
- Higher Order Polynomial Eigenvalue Problems
- Nonlinear Eigenvalue Problems with Orthogonality Constraints
  R. Lippert and A. Edelman
Common Issues
- Sparse Matrix Storage Formats
  J. Dongarra
- Matrix-Vector and Matrix-Matrix Multiplications
  J. Dongarra, P. Koev, and X. Li
- A Brief Survey of Direct Linear Solvers
  J. Demmel, P. Koev, and X. Li
- A Brief Survey of Iterative Linear Solvers
  H. van der Vorst
- Parallelism
  J. Dongarra and X. Li
Preconditioning Techniques
- Introduction
- Inexact Methods
  K. Meerbergen and R. Morgan
- Preconditioned Eigensolvers
  A. Knyazev
Bibliography
Index
About this document ...

Susan Blackford 2000-11-20