Improvement of Convergence of Restarted GMRES(k) Method with Iterative Refinement using Minimized Residual Method

Abstract

In this paper we consider how to give the initial approximate solution χ_0 of the restarted GMRES(k) method with iterative refinement process which was proposed by Imakura et al. In this restarted GMRES(k) method, it is crucial to give a reasonable initial approximate solution e_0 of the equation of errors in order to improve the convergence of the restarted GMRES(k) method at the restarted phase. In order to do so, we adopt the higher order Minimal Residual method proposed by Indora et al. Numerical experiments show that the IR-GMRES(k)-MR(4) method works best among several methods.