A quasi-minimal residual variant of IDRstab using the residual smoothing technique

Quasi-Minimal Residual (QMR)-type methods have been developed for improving the oscillations in the residual norms of the Bi-Conjugate Gradient (Bi-CG) method and the hybrid Bi-CG methods. The IDRstab method, which combines the Induced Dimension Reduction (IDR)(s) method with higher-order stabilizing polynomials, is often more effective than IDR(s) and the hybrid Bi-CG methods, but the residual norms oscillate. In this paper, we design a QMR variant of IDRstab by using a residual smoothing technique in order to obtain smoother convergence behavior. Numerical experiments show the effectiveness of our QMR variant of IDRstab.