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Remarks on Eigenvalue Computations
Contents
Index
Generalized Hermitian Eigenvalue Problems
Subsections
Introduction
Overview of Available Algorithms.
Summary of Choices.
Application.
Orthogonalization.
Eigenvalues Sought.
Storage and Work.
Transformation to Standard Problem
Direct Methods
Single- and Multiple-Vector Iterations
M. Gu
Power Method.
Inverse Iteration.
Rayleigh Quotient Iteration.
Lanczos Methods
A. Ruhe
Algorithm.
Lanczos Algorithm with SI.
Convergence Properties.
Multiple Eigenvalues.
Software Availability.
Numerical Example.
Jacobi-Davidson Methods
G. Sleijpen and H. van der Vorst
Stability and Accuracy Assessments
Z. Bai and R. Li
Positive Definite
Residual Vector.
Transfer Residual Error to Backward Error.
Error Bounds for Computed Eigenvalues.
Error Bounds for Computed Eigenvectors.
Remarks on Clustered Eigenvalues.
Some Combination of
and
is Positive Definite
Residual Vector.
Transfer Residual Error to Backward Error.
Error Bound for Computed Eigenvalues.
Error Bound for Computed Eigenvectors.
Remarks on Clustered Eigenvalues.
Susan Blackford 2000-11-20
and