An Efficient Variant of the Restarted Shifted GMRES Method for Solving Shifted Linear Systems

We investigate the restart of the Restarted Shifted GMRES method for solving shifted linear systems. Recently the variant of the GMRES($m$) method with the {\it unfixed update} has been proposed to improve the convergence of the GMRES($m$) method for solving linear systems, and shown to have an efficient convergence property. In this paper, by applying the unfixed update to the Restarted Shifted GMRES method, we propose a variant of the Restarted Shifted GMRES method. We show a potentiality for efficient convergence within the variant by some numerical results.