Solution of generalized shifted linear systems with complex symmetric matrices

  • Authors:

  • Tomohiro Sogabe;Takeo Hoshi;Shao-Liang Zhang;Takeo Fujiwara

  • Affiliations:

  • Graduate School of Information Science and Technology, Aichi Prefectural University, 1522-3 Ibaragabasama, Kumabari, Nagakute-cho, Aichi-gun, Aichi 480-1198, Japan;Department of Applied Mathematics and Physics, Tottori University, Tottori 680-8550, Japan and Core Research for Evolutional Science and Technology, Japan Science and Technology Agency (CREST-JST) ...;Department of Computational Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan;Core Research for Evolutional Science and Technology, Japan Science and Technology Agency (CREST-JST), 4-1-8 Honcho, Kawaguchi-shi, Saitama 332-0012, Japan and Center for Research and Development ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

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Abstract

We develop the shifted COCG method [R. Takayama, T. Hoshi, T. Sogabe, S.-L. Zhang, T. Fujiwara, Linear algebraic calculation of Green's function for large-scale electronic structure theory, Phys. Rev. B 73 (165108) (2006) 1-9] and the shifted WQMR method [T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, On a weighted quasi-residual minimization strategy of the QMR method for solving complex symmetric shifted linear systems, Electron. Trans. Numer. Anal. 31 (2008) 126-140] for solving generalized shifted linear systems with complex symmetric matrices that arise from the electronic structure theory. The complex symmetric Lanczos process with a suitable bilinear form plays an important role in the development of the methods. The numerical examples indicate that the methods are highly attractive when the inner linear systems can efficiently be solved.