Deflated Iterative Methods for Linear Equations with Multiple Right-Hand Sides

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

A new approach is discussed for solving large nonsymmetric systems of linear equations with multiple right-hand sides. The first system is solved with a deflated GMRES method that generates eigenvector information at the same time that the linear equations are solved. Subsequent systems are solved by combining restarted GMRES with a projection over the previously determined eigenvectors. This approach offers an alternative to block methods, and it can also be combined with a block method. It is useful when there are a limited number of small eigenvalues that slow the convergence. An example is given showing significant improvement for a problem from quantum chromodynamics. The second and subsequent right-hand sides are solved much quicker than without the deflation. This new approach is relatively simple to implement and is very efficient compared to other deflation methods.
13 pages, 5 figures

Keywords

Mathematical Physics, High Energy Physics - Lattice

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/132931

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0707.0505
 http://arxiv.org/abs/0707.0505

Collections

arXiv