@Article{IJNAM-2-2,
author = {},
title = {A Variable Preconditioning Using the SOR Method for GCR-Like Methods},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2005},
volume = {2},
number = {2},
pages = {147--162},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/2005-IJNAM-926},
url = {https://global-sci.com/article/83852/a-variable-preconditioning-using-the-sor-method-for-gcr-like-methods}
}