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Article Dans Une Revue Electronic Transactions on Numerical Analysis Année : 2017

Varying the s in Your s-step GMRES

Résumé

Krylov subspace methods are commonly used iterative methods for solving large sparse linear systems, however they suffer from communication bottlenecks on parallel computers. Therefore, $s$-step methods have been developed where the Krylov subspace is built block by block, so that $s$ matrix-vector multiplications can be done before orthonormalizing the block. Then Communication-Avoiding algorithms can be used for both kernels. This paper introduces a new variation on $s$-step GMRES in order to reduce the number of iterations necessary to ensure convergence, with a small overhead in the number of communications. Namely, we develop a $s$-step GMRES algorithm, where the block size is variable and increases gradually. Our numerical experiments show a good agreement with our analysis of condition numbers and demonstrate the efficiency of our variable $s$-step approach.
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Dates et versions

hal-01299652 , version 1 (11-04-2016)
hal-01299652 , version 2 (07-07-2016)
hal-01299652 , version 3 (07-12-2017)

Identifiants

  • HAL Id : hal-01299652 , version 3

Citer

David Imberti, Jocelyne Erhel. Varying the s in Your s-step GMRES. Electronic Transactions on Numerical Analysis, 2017, 47, pp.206-230. ⟨hal-01299652v3⟩
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