An Augmented Conjugate Gradient Method for Solving Consecutive Symmetric Positive Definite Linear Systems
Jocelyne Erhel, Frédéric Guyomarc'h · SIAM Journal on Matrix Analysis and Applications · 2000
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.