ON QUASI-MINIMAL RESIDUAL APPROACH OF ITERATIVE ALGORITHMS FOR SOLVING NONSYMMETRIC LINEAR-SYSTEMS

Many iterative algorithms, for example the BCG algorithm, the CGS algo rithm etc., for solving nonsymmetric linear systems have the erratic c onvergence behavior. Recently, Freund et al. [6] proposed a BCG-like a pproach, the Quasi-minimal residual (QMR) method, that remedies this p roblem for BCG and produces smooth convergence curves. The QMR approac h is also applied to CGS and BI-CGSTAB to obtain smoothly convergent v ariants of these algorithms [7, 5, 12]. In this paper, we propose a si mple but universal QMR approach which can be applied with unified mann er to any iterative algorithm to construct smoothly convergent variant s, provided this algorithm includes two-term recurrence for the approx imate solutions. The resulting QMR algorithms can be implemented very easily by changing only a few lines in the original iterative algorith m. We compare the performance of our QMR approach with that of other Q MR methods presented in [5], [7] and [12]. Finally, numerical examples are given.