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An Augmented Conjugate Gradient Method for Solving Consecutive Symmetric Positive Definite Linear Systems

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 one 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. Numerical experiments show the efficacy of our method even for quite different right-hand sides.
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Jocelyne Erhel, Frédéric Guyomarc'H. An Augmented Conjugate Gradient Method for Solving Consecutive Symmetric Positive Definite Linear Systems. SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2000, 21 (4), pp.1279-1299. ⟨10.1137/S0895479897330194⟩. ⟨inria-00523682⟩

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