Analysis of Augmented Krylov Subspace Methods

Authors:
Yousef Saad
Affiliations:
-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
1997

Citing 0
Cited 10

Restarted block-GMRES with deflation of eigenvalues

Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Simultaneous solution of large-scale linear systems and eigenvalue problems with a parallel GMRES method

Journal of Computational and Applied Mathematics
A family of physics-based preconditioners for solving elliptic equations on highly heterogeneous media

Applied Numerical Mathematics
An analysis of Laplacian methods for value function approximation in MDPs

IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Restarted block-GMRES with deflation of eigenvalues

Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Toward memory-efficient linear solvers

VECPAR'02 Proceedings of the 5th international conference on High performance computing for computational science
Deflated and Restarted Symmetric Lanczos Methods for Eigenvalues and Linear Equations with Multiple Right-Hand Sides

SIAM Journal on Scientific Computing
Flexible GMRES with Deflated Restarting

SIAM Journal on Scientific Computing
GMRES with adaptively deflated restarting and its performance on an electromagnetic cavity problem

Applied Numerical Mathematics
A Flexible Generalized Conjugate Residual Method with Inner Orthogonalization and Deflated Restarting

SIAM Journal on Matrix Analysis and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

Residual norm estimates are derived for a general class of methods based on projection techniques on subspaces of the form $ K_m + {\cal W}$, where $K_m$ is the standard Krylov subspace associated with the original linear system and ${\cal W}$ is some other subspace. These "augmented Krylov subspace methods" include eigenvalue deflation techniques as well as block-Krylov methods. Residual bounds are established which suggest a convergence rate similar to one obtained by removing the components of the initial residual vector associated with the eigenvalues closest to zero. Both the symmetric and nonsymmetric cases are analyzed.