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Reports (Research Report) Year : 1997

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.


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Dates and versions

inria-00073411 , version 1 (24-05-2006)


  • HAL Id : inria-00073411 , version 1


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