An Augmented Subspace Conjugate Gradient

: 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. Key-words: Conjugate Gradient, Krylov subspace, orthogonal projection (R'esum'e : tsvp) * INRIA, UR Rennes, Jocelyne.Erhel@inria.fr, http://www.irisa.fr/aladin/perso/erhel.html ** INRIA, UR Rennes, Frederic.Guyomarch@inria.fr, http://www.irisa...