Next:
Introduction
Up:
book
Previous:
Related Problems J.
Contents
Index
Non-Hermitian Eigenvalue Problems
Subsections
Introduction
Balancing Matrices
T. Chen and J. Demmel
Direct Balancing
Krylov Balancing Algorithms
Accuracy of Eigenvalues Computed after Balancing
Direct Methods
Single- and Multiple-Vector Iterations
M. Gu
Power Method
Inverse Iteration
Subspace Iteration
Software Availability
Arnoldi Method
Y. Saad
Basic Algorithm
Variants
Explicit Restarts
Deflation
Implicitly Restarted Arnoldi Method
R. Lehoucq and D. Sorensen
Arnoldi Procedure in GEMV Form
Implicit Restart
Convergence Properties
Numerical Stability
Computational Costs and Tradeoffs
Deflation and Stopping Rules
Orthogonal Deflating Transformation
Locking or Purging a Single Eigenvalue.
Locking
.
Purging
.
Stability of
.
Locking and Purging in IRAM.
Eigenvector Computation with Spectral Transformation
Software Availability
Block Arnoldi Method
R. Lehoucq and K. Maschhoff
Block Arnoldi Reductions
Practical Algorithm
Block Size.
Stopping Criterion.
Deflation.
Restarting a Block Arnoldi Reduction.
Software Availability
Notes and References
Lanczos Method
Z. Bai and D. Day
Algorithm
Convergence Properties
Multiple Eigenvalues.
Software Availability
Notes and References
Block Lanczos Methods
Z. Bai and D. Day
Basic Algorithm
An Adaptively Blocked Lanczos Method
Storage Requirements and Floating Point Operations.
Software Availability
Notes and References
Band Lanczos Method
R. Freund
Deflation
Basic Properties
Algorithm
Application to Reduced-Order Modeling
Variants
Lanczos Method for Complex Symmetric Eigenproblems
R. Freund
Properties of Complex Symmetric Matrices
Properties of the Algorithm
Algorithm
Solving the Reduced Eigenvalue Problems
Software Availability
Notes and References
Jacobi-Davidson Methods
G. Sleijpen and H. van der Vorst
Generalization of Hermitian Case
Schur Form and Restart
Computing Interior Eigenvalues
Software Availability
Numerical Example
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
.
.