A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems

Motivated by a recent method of Freund [3], who introduced a quasi-minimal residual (QMR) version of the CGS algorithm, we propose a QMR variant of the Bi-CGSTAB algorithm of van der Vorst, which we call QMRCGSTAB for solving nonsymmetric linear systems. The motivation for both QMR variants is to obtain smoother convergence behavior of the underlying method. We illustrate this by numerical experiments, which also show that for problems on which Bi-CGSTAB performs better than CGS, the same advantage carries over to QMRCGSTAB.