Year: 2005
International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 2 : pp. 147–162
Abstract
We propose a variant of variable preconditioning for Generalized Conjugate Residual (CCR)-like methods. The preconditioning is carried out by roughly solving $Az = v$ by an iterative method to a certain degree of accuracy instead of computing $Kz = v$ in a conventional preconditioned algorithm. In our proposal, the number of iterations required for computing $Az = v$ is changed at each iteration by establishing a stopping criterion. This enables the use of a stationary iterative method when applying different preconditioners. The proposed procedure is incorporated into GCR, and the mathematical convergence is proved. In numerical experiments, we employ the Successive Over-Relaxation (SOR) method for computing $Az = v$, and we demonstrate that GCR with the variable preconditioning using SOR is faster and more robust than GCR with an incomplete LU preconditioning, and the FGMRES and GMRESR methods with the variable preconditioning using the Generalized Minimal Residual (GMRES) method. Moreover, we confirm that different preconditioners are applied at each iteration.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2005-IJNAM-926
International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 2 : pp. 147–162
Published online: 2005-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: linear systems generalized conjugate residual method generalized minimal residual method variable preconditioning inner-loop and outer-loop.