Quasi-minimal residual smoothing technique for the IDR($s$) method

Abstract

The IDR($s$) proposed by Sonneveld and Gijzen is an efficient method for solving large nonsymmetric linear systems. In this paper, QMRIDR($s$), a new variant of the IDR($s$) method is presented. In this method, the irregular convergence behavior of IDR($s$) is remedied and both the fast and smooth convergence behaviors are expected. Numerical experiments are reported to show the performance of our method.