2009 Volume 19 Issue 4 Pages 551-564
In 1986, the GMRES method and its restarted version, GMRES(m) method, were proposed by Saad and Schultz for solving nonsymmetric linear systems. In this paper, we investigate the restart of the GMRES(m) method. The main goal of this paper is to propose an extension of the GMRES(m) method based on a new framework of the restart. A mathematical background of the extension is analyzed based on the error equations. The numerical results are presented to show a potential efficiency in our framework.