Restarted block-GMRES with deflation of eigenvalues

Authors:
Ronald B. Morgan
Affiliations:
Department of Mathematics, Baylor University, Waco, TX 76798-7328, USA
Venue:
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Year:
2005

Citing 29
Cited 7

GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems

SIAM Journal on Scientific and Statistical Computing
An iterative solution method for solving f(A)x=b, using Krylov subspace information obtained for the symmetric positive definite matrix A

Journal of Computational and Applied Mathematics
Sparse matrix test problems

ACM Transactions on Mathematical Software (TOMS)
Implicit application of polynomial filters in a k-step Arnoldi method

SIAM Journal on Matrix Analysis and Applications
BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems

SIAM Journal on Scientific and Statistical Computing
Quasi-kernel polynomials and their use in non-Hermitian matrix iterations

Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems

SIAM Journal on Scientific Computing
The superlinear convergence behaviour of GMRES

Journal of Computational and Applied Mathematics
An iterative method for nonsymmetric systems with multiple right-hand sides

SIAM Journal on Scientific Computing
Variable Block CG Algorithms for Solving Large Sparse Symmetric Positive Definite Linear Systems on Parallel Computers, I: General Iterative Scheme

SIAM Journal on Matrix Analysis and Applications
A Restarted GMRES Method Augmented with Eigenvectors

SIAM Journal on Matrix Analysis and Applications
On restarting the Arnoldi method for large nonsymmetric eigenvalue problems

Mathematics of Computation
Restarted GMRES preconditioned by deflation

Journal of Computational and Applied Mathematics
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration

SIAM Journal on Matrix Analysis and Applications
Analysis of Augmented Krylov Subspace Methods

SIAM Journal on Matrix Analysis and Applications
Analysis of Projection Methods for Solving Linear Systems with Multiple Right-Hand Sides

SIAM Journal on Scientific Computing
The symmetric eigenvalue problem

The symmetric eigenvalue problem
Adaptively Preconditioned GMRES Algorithms

SIAM Journal on Scientific Computing
ABLE: An Adaptive Block Lanczos Method for Non-Hermitian Eigenvalue Problems

SIAM Journal on Matrix Analysis and Applications
A Deflated Version of the Conjugate Gradient Algorithm

SIAM Journal on Scientific Computing
Implicitly Restarted GMRES and Arnoldi Methods for Nonsymmetric Systems of Equations

SIAM Journal on Matrix Analysis and Applications
An Augmented Conjugate Gradient Method for Solving Consecutive Symmetric Positive Definite Linear Systems

SIAM Journal on Matrix Analysis and Applications
A Lanczos-type method for multiple starting vectors

Mathematics of Computation
A block GMRES method augmented with eigenvectors

Applied Mathematics and Computation
GMRES with Deflated Restarting

SIAM Journal on Scientific Computing
A Krylov--Schur Algorithm for Large Eigenproblems

SIAM Journal on Matrix Analysis and Applications
Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems

SIAM Journal on Matrix Analysis and Applications
Truncation Strategies for Optimal Krylov Subspace Methods

SIAM Journal on Numerical Analysis
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems

A family of physics-based preconditioners for solving elliptic equations on highly heterogeneous media

Applied Numerical Mathematics
Deflated block Krylov subspace methods for large scale eigenvalue problems

Journal of Computational and Applied Mathematics
A thick-restarted block Arnoldi algorithm with modified Ritz vectors for large eigenproblems

Computers & Mathematics with Applications
Deflated and Restarted Symmetric Lanczos Methods for Eigenvalues and Linear Equations with Multiple Right-Hand Sides

SIAM Journal on Scientific Computing
A new family of global methods for linear systems with multiple right-hand sides

Journal of Computational and Applied Mathematics
Restarting the Nonsymmetric Lanczos Algorithm for Eigenvalues and Linear Equations Including Multiple Right-Hand Sides

SIAM Journal on Scientific Computing
Flexible Variants of Block Restarted GMRES Methods with Application to Geophysics

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Block-GMRES is an iterative method for solving nonsymmetric systems of linear equations with multiple right-hand sides. Restarting may be needed, due to orthogonalization expense or limited storage. We discuss how restarting affects convergence and the role small eigenvalues play. Then a version of restarted block-GMRES that deflates eigenvalues is presented. It is demonstrated that deflation can be particularly important for block methods.