An Augmented Conjugate Gradient Method for Solving Consecutive Symmetric Positive Definite Linear Systems SIAM Journal on Matrix Analysis and Applications Volume 21, Number 4 pp. 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.
65F35 PII .