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

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Abstract

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.

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Authors and Affiliations

  1. University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8577, Japan

    Yasunori Futamura, Takahiro Yano, Akira Imakura & Tetsuya Sakurai

Authors
  1. Yasunori Futamura
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  2. Takahiro Yano
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  3. Akira Imakura
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  4. Tetsuya Sakurai
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Corresponding author

Correspondence to Yasunori Futamura.

Additional information

This work was supported in part by JST/CREST, JST/ACT-I (Grant No. JPMJPR16U6), MEXT KAKENHI (Grant Nos. 25286097, 17K12690), and University of Tsukuba Basic Research Support Program Type A.

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Futamura, Y., Yano, T., Imakura, A. et al. A real-valued block conjugate gradient type method for solving complex symmetric linear systems with multiple right-hand sides. Appl Math 62, 333–355 (2017). https://doi.org/10.21136/AM.2017.0023-17

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