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An Augmented Subspace Conjugate Gradient

Jocelyne Erhel 1 Frédéric Guyomarc'H 1
1 ALADIN - Algorithms Adapted to Intensive Numerical Computing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : Many scientific applications require to solve successively linear systems Ax=b with different right-hand sides b and a symmetric positive definite matrix A. The Conjugate Gradient method applied to the first system generates a Krylov subspace which can be efficiently recycled thanks to orthogonal projections in subsequent systems. A modified Conjugate Gradient method is then applied with a specific initial guess and initial descent direction and a modified descent direction during the iterations. This paper gives new theoretical results for this method and proposes a new version which seems robust as far as loss of orthogonality is concerned. Numerical experiments show the efficacy of our method even for quite different right-hand sides.
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https://hal.inria.fr/inria-00073411
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 12:44:20 PM
Last modification on : Thursday, February 11, 2021 - 2:48:03 PM
Long-term archiving on: : Sunday, April 4, 2010 - 11:45:39 PM

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  • HAL Id : inria-00073411, version 1

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Jocelyne Erhel, Frédéric Guyomarc'H. An Augmented Subspace Conjugate Gradient. [Research Report] RR-3278, INRIA. 1997. ⟨inria-00073411⟩

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