A variant of the IDR(ss) method with the quasi-minimal residual strategy

The IDR(ss) method proposed by Sonneveld and van Gijzen is an effective method for solving nonsymmetric linear systems, but usually with irregular convergence behavior. In this paper, we reformulate the relations of residuals and their auxiliary vectors generated by the IDR(ss) method in matrix form. Then, using this new formulation and motivated by other QMR-type methods, we propose a variant of the IDR(ss) method, called QMRIDR(ss), for overcoming the disadvantage of its irregular convergence behavior. Both fast and smooth convergence behaviors of the QMRIDR(ss) method can be shown. Numerical experiments are reported to show the efficiency of our proposed method.