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

Authors:
Jocelyne Erhel;Frédéric Guyomarc'h
Affiliations:
-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2000

Citing 0
Cited 6

Restarted block-GMRES with deflation of eigenvalues

Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Choice of initial guess in iterative solution of series of systems arising in fluid flow simulations

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Multiple right-hand side techniques for the numerical simulation of quasistatic electric and magnetic fields

Journal of Computational and Applied Mathematics
Restarted block-GMRES with deflation of eigenvalues

Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Deflated and Restarted Symmetric Lanczos Methods for Eigenvalues and Linear Equations with Multiple Right-Hand Sides

SIAM Journal on Scientific Computing
Computing and Deflating Eigenvalues While Solving Multiple Right-Hand Side Linear Systems with an Application to Quantum Chromodynamics

SIAM Journal on Scientific Computing

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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.