ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0 Online Edition Research Article
David Imberti,
Jocelyne Erhel
S. 206 - 230 doi:10.1553/etna_vol47s206 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol47s206
Abstract: Krylov subspace methods are commonly used iterative methods for solving largesparse linear systems. However, they suffer from communication bottlenecks onparallel computers.Therefore, $s$-step methods have been developed, where the Krylov subspace isbuilt block by block so that $s$ matrix-vector multiplications can be donebefore orthonormalizing the block.Then Communication-Avoiding algorithms can be used for both kernels.This paper introduces a new variation on the $s$-step GMRES method in order toreduce the number of iterations necessary to ensure convergence with a smalloverhead in the number of communications.Namely, we develop an $s$-step GMRES algorithm, where the block size isvariable and increases gradually.Our numericalexperiments show a good agreement with our analysis of condition numbersand demonstratethe efficiency of our variable $s$-step approach. Keywords: Communication-Avoiding, s-step Krylov subspace method, GMRES algorithm, variable s-step Published Online: 2018/02/13 13:46:25 Document Date: 2018/02/13 13:38:00 Object Identifier: 0xc1aa5576 0x00375bc6 Rights: . Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613. …
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |