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Error Bound for Computed
Contents
Index
Generalized Non-Hermitian Eigenvalue Problems
Subsections
Introduction
Direct Methods
Transformation to Standard Problems
Invert
.
Split-and-invert
.
Shift-and-Invert.
Jacobi-Davidson Method
G. Sleijpen and H. van der Vorst
Basic Theory
Deflation and Restart
Deflation.
Restart.
Algorithm
Software Availability
Numerical Example
Rational Krylov Subspace Method
A. Ruhe
Symmetric Indefinite Lanczos Method
Z. Bai, T. Ericsson, and T. Kowalski
Some Properties of Symmetric Indefinite Matrix Pairs
Algorithm
Stopping Criteria and Accuracy Assessment
Singular
Software Availability
Numerical Examples
Example 8.6.1.
Example 8.6.2.
Example 8.6.3.
Notes and References
Singular Matrix Pencils
B. Kågström
Regular Versus Singular Problems
Kronecker Canonical Form
Generic and Nongeneric Kronecker Structures
Ill-Conditioning
Generalized Schur-Staircase Form
GUPTRI Algorithm
A
Singular Pencil in GUPTRI Form.
Criterion for Determining the Numerical Rank.
The GUPTRI Form of a Regularized Problem.
Software Availability
More on GUPTRI and Numerical Examples
Robustness of Computed GUPTRI Form and Error Bounds.
Arithmetic and Space Complexity.
MATLAB Interface to GUPTRI.
Example in MATLAB.
Notes and References
Stability and Accuracy Assessments
Z. Bai and R. Li
Residual Vectors.
Transfer Residual Errors to Backward Errors.
Error Bound for Computed Eigenvalues.
Error Bound for Computed Eigenvectors.
Susan Blackford 2000-11-20
.
Singular Pencil in GUPTRI Form.