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The Four-Parameter PSS Method for Solving the Sylvester Equation

Author

Listed:
  • Hai-Long Shen

    (Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, China)

  • Yan-Ran Li

    (Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, China)

  • Xin-Hui Shao

    (Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, China)

Abstract

In order to solve the Sylvester equations more efficiently, a new four parameters positive and skew-Hermitian splitting (FPPSS) iterative method is proposed in this paper based on the previous research of the positive and skew-Hermitian splitting (PSS) iterative method. We prove that when coefficient matrix A and B satisfy certain conditions, the FPPSS iterative method is convergent in the parameter’s value region. The numerical experiment results show that compared with previous iterative method, the FPPSS iterative method is more effective in terms of iteration number IT and runtime.

Suggested Citation

  • Hai-Long Shen & Yan-Ran Li & Xin-Hui Shao, 2019. "The Four-Parameter PSS Method for Solving the Sylvester Equation," Mathematics, MDPI, vol. 7(1), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:105-:d:199310
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    References listed on IDEAS

    as
    1. Zhou, Duanmei & Chen, Guoliang & Cai, Qingyou, 2015. "On modified HSS iteration methods for continuous Sylvester equations," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 84-93.
    2. Zhou, Rong & Wang, Xiang & Tang, Xiao-Bin, 2015. "A generalization of the Hermitian and skew-Hermitian splitting iteration method for solving Sylvester equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 609-617.
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