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East Asian Journal on Applied Mathematics, 2 (2012), pp. 19-32. |
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An Efficient Variant of the GMRES(m) Method Based on the Error Equations Akira Imakura 1*, Tomohiro Sogabe 2, Shao-Liang Zhang 1 1 Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan.2 Aichi Prefectural University, 1522-3 Ibaragabasama, Kumabari, Nagakute-cho, Aichi-gun, Aichi, 480-1198, Japan. Received 28 June 2011; Accepted (in revised version) 3 September 2011 Available online 10 February 2012 doi:10.4208/eajam.280611.030911a Abstract The GMRES(m) method proposed by Saad and Schultz is one of the most successful Krylov subspace methods for solving nonsymmetric linear systems. In this paper, we investigate how to update the initial guess to make it converge faster, and in particular propose an efficient variant of the method that exploits an unfixed update. The mathematical background of the unfixed update variant is based on the error equations, and its potential for efficient convergence is explored in some numerical experiments. AMS subject classifications: 65F10 Key words: Nonsymmetric linear systems, GMRES($m$) method, restart, error equations. *Corresponding author. Email: a-imakura@na.cse.nagoya-u.ac.jp (A. Imakura), sogabe@ ist.aichi-pu.ac.jp (T. Sogabe), |