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

Motivated by a recent method of Freund [SIAM J. Sci. Comput., 14 (1993), pp. 470–482], who introduced a quasi-minimal residual (QMR) version of the conjugate gradients squared (CGS) algorithm, a QMR variant of the biconjugate gradient stabilized (Bi-CGSTAB) algorithm of van der Vorst that is called QMRCGSTAB, is proposed for solving nonsymmetric linear systems. The motivation for both QMR variants is to obtain smoother convergence behavior of the underlying method. The authors illustrate this by numerical experiments that also show that for problems on which Bi-CGSTAB performs better than CGS, the same advantage carries over to QMRCGSTAB.