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A generalization of the Hermitian and skew-Hermitian splitting iteration method for solving Sylvester equations

Author

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  • Zhou, Rong
  • Wang, Xiang
  • Tang, Xiao-Bin

Abstract

This paper is concerned with a generalization of the Hermitian and skew-Hermitian splitting (HSS) iteration method for solving large sparse continuous Sylvester equations. The analysis shows that the GHSS iteration method will converge under certain assumptions. Numerical results show that this new method is more efficient and robust than the existing ones.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:609-617
    DOI: 10.1016/j.amc.2015.09.027
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    Cited by:

    1. Kai Jiang & Jianghao Su & Juan Zhang, 2022. "A Data-Driven Parameter Prediction Method for HSS-Type Methods," Mathematics, MDPI, vol. 10(20), pages 1-24, October.
    2. Dehghan, Mehdi & Shirilord, Akbar, 2019. "A generalized modified Hermitian and skew-Hermitian splitting (GMHSS) method for solving complex Sylvester matrix equation," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 632-651.
    3. 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.
    4. Fu, Chunhong & Chen, Jiajia & Xu, Qingxiang, 2021. "Upper bounds and lower bounds for the Frobenius norm of the solution to certain structured Sylvester equation," Applied Mathematics and Computation, Elsevier, vol. 399(C).

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