Applications of Mathematics

, Volume 62, Issue 4, pp 333–355

A real-valued block conjugate gradient type method for solving complex symmetric linear systems with multiple right-hand sides

  • Yasunori Futamura
  • Takahiro Yano
  • Akira Imakura
  • Tetsuya Sakurai


We consider solving complex symmetric linear systems with multiple right-hand sides. We assume that the coefficient matrix has indefinite real part and positive definite imaginary part. We propose a new block conjugate gradient type method based on the Schur complement of a certain 2-by-2 real block form. The algorithm of the proposed method consists of building blocks that involve only real arithmetic with real symmetric matrices of the original size. We also present the convergence property of the proposed method and an efficient algorithmic implementation. In numerical experiments, we compare our method to a complex-valued direct solver, and a preconditioned and nonpreconditioned block Krylov method that uses complex arithmetic.


linear system with multiple right-hand sides complex symmetric matrices block Krylov subspace methods 

MSC 2010

65F10 65F50 


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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  • Yasunori Futamura
    • 1
  • Takahiro Yano
    • 1
  • Akira Imakura
    • 1
  • Tetsuya Sakurai
    • 1
  1. 1.University of TsukubaIbarakiJapan

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