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East Asian Journal on Applied Mathematics, 1 (2011), pp. 97-107. |
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An Extension of the COCR Method to Solving Shifted Linear Systems with Complex Symmetric Matrices Tomohiro Sogabe 1*, Shao-Liang Zhang 1 1 Graduate School of Information Science and Technology,2 Department of Computational Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Received 26 April 2010; Accepted (in revised version) 24 May 2010 Available online 7 April 2011 doi:10.4208/eajam.260410.240510a Abstract The Conjugate Orthogonal Conjugate Residual (COCR) method [T. Sogabe and S.-L. Zhang, JCAM, 199 (2007), pp. 297-303.] has recently been proposed for solving complex symmetric linear systems. In the present paper, we develop a variant of the COCR method that allows the efficient solution of complex symmetric shifted linear systems. Some numerical examples arising from large-scale electronic structure calculations are presented to illustrate the performance of the variant. Key words: Shifted linear systems, complex symmetric matrices, COCR, *Corresponding author. Email: sogabe@ist.aichi-pu.ac.jp (T. Sogabe), zhang@na.cse. nagoya-u.ac.jp (S.-L. Zhang) |