A Look-Back-type restart for the restarted Krylov subspace methods for solving non-Hermitian linear systems

Abstract

In this paper, we investigate the restarted Krylov subspace methods, as typified by the GMRES(m) method and the FOM(m) method, for solving non-Hermitian linear systems. We have recently focused on the restart of the GMRES(m) method and proposed the extension of the GMRES(m) method based on the error equations. The main purpose of this paper is to apply the extension to other restarted Krylov subspace methods, and propose a specific restart technique for the restarted Krylov subspace method. The specific restart technique is named as the Look-Back-type restart, and is based on an implicit residual polynomial reconstruction via the initial guess. The comparison analysis based on the residual polynomials and some numerical experiments indicate that the Look-Back-type restart achieves more efficient convergence results than the traditional restarted Krylov subspace methods.