A proposal of Multi-Restarts type of Look-Back GMRES(k) method

Abstract

In 2009, Imakura et al. proposed the Look-Back GMRES(k) method which determines an initial guess by an approximate solution vector obtained at the previous one restart. Numerical experiments clarified that convergence rate of the Look-Back GMRES(k) method is much better than that of the original GMRES(k) method. In this paper, we extend their Look-Back GMRES(k) method by using approximate solution vectors obtained at the previous multi-restarts for determining an initial guess, and improve convergence rate of the Look-Back GMRES(k) method. Numerical results will be presented in order to show effectiveness of the proposed method.