Overview
ABSTRACT
Krylov methods for solving linear systems are generally used with a preconditioner which accelerates the convergence. They only require matrix multiplication by a vector, scalar products and vector additions. This article explains these methods and their different aims. An in-depth analysis of the Krylov methods is then provided: construction of the basis, GMRES and FOM methods, conjugate gradient, BiCG and BiCGstab or QMR methods. An example of methods concludes this article.
Read this article from a comprehensive knowledge base, updated and supplemented with articles reviewed by scientific committees.
Read the articleAUTHOR
-
Gérard MEURANT : CEA/DIF (Bruyères le Chatel)
INTRODUCTION
This dossier presents the state of the art for solving large hollow linear systems using iterative Krylov methods. These methods only require multiplications of the system matrix by a vector, scalar products and vector additions. They are generally used in conjunction with a preconditioner to accelerate convergence.
Exclusive to subscribers. 97% yet to be discovered!
Already subscribed? Log in!
Krylov methods for solving linear systems
Purpose of the methods
Exclusive to subscribers. 97% yet to be discovered!
Already subscribed? Log in!
Article included in this offer
"Mathematics"
(
168 articles
)
Updated and enriched with articles validated by our scientific committees
A set of exclusive tools to complement the resources
