An Efficient Variant of the GMRES(m) Method Based on the Error Equations
Akira Imakura 1*, Tomohiro Sogabe 2, Shao-Liang Zhang 11 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
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.
Email: email@example.com (A. Imakura), sogabe@ ist.aichi-pu.ac.jp (T. Sogabe),