Akira IMAKURA,Tomohiro SOGABE,张绍良.An Efficient Variant of the Restarted Shifted GMRES Method for Solving Shifted Linear Systems[J].数学研究及应用,2013,33(2):127~141
An Efficient Variant of the Restarted Shifted GMRES Method for Solving Shifted Linear Systems
An Efficient Variant of the Restarted Shifted GMRES Method for Solving Shifted Linear Systems

DOI：10.3770/j.issn:2095-2651.2013.02.001

 作者 单位 Akira IMAKURA Center for Computational Sciences, University of Tsukuba, 1-1-1, Tennodai Tsukuba-city, Ibaraki 305-8577, Japan Tomohiro SOGABE Graduate School of Information Science and Technology, Aichi Prefectural University, 1522-3 Ibaragabasama, Kumabari, Nagakute-cho, Aichi-gun, Aichi, 480-1198, Japan 张绍良 Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan

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 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.

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.