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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.
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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.
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Krylov methods for solving linear systems
Purpose of the methods
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