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A simplified PSS preconditioner for non-Hermitian generalized saddle point problems

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  • Shen, Hai-Long
  • Wu, Hong-Yu
  • Shao, Xin-Hui

Abstract

The preconditioner for positive-definite and skew-Hermitian splitting (PSS) iteration method has been used to solve saddle point problems. Firstly, we propose a simplified PSS preconditioner for non-Hermitian generalized saddle point problems, which is much closer to original matrix than other PSS preconditioners. Moreover, the spectral properties of preconditioned matrix are also discussed. Finally, we give an example to illustrate the efficiency of the new preconditioner which is used to accelerate the convergence rate of the Krylov subspace, such as GMRES method, it has an obvious advantage than other preconditioners.

Suggested Citation

  • Shen, Hai-Long & Wu, Hong-Yu & Shao, Xin-Hui, 2021. "A simplified PSS preconditioner for non-Hermitian generalized saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    • Handle: RePEc:eee:apmaco:v:394:y:2021:i:c:s0096300320307633
    DOI: 10.1016/j.amc.2020.125810
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    References listed on IDEAS

    as
    1. Zhang, Ke & Zhang, Ju-Li & Gu, Chuan-Qing, 2017. "A new relaxed PSS preconditioner for nonsymmetric saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 115-129.
    2. Fan, Hong-tao & Zhu, Xin-yun, 2015. "A generalized relaxed positive-definite and skew-Hermitian splitting preconditioner for non-Hermitian saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 36-48.
    3. Ling, Si-Tao & Liu, Qing-Bing, 2017. "New local generalized shift-splitting preconditioners for saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 58-67.
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