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The MGPBiCG method for solving the generalized coupled Sylvester-conjugate matrix equations

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  • Xie, Ya-Jun
  • Ma, Chang-Feng

Abstract

In this paper, we extend the generalized product-type bi-conjugate gradient (GPBiCG) method for solving the generalized Sylvester-conjugate matrix equations A1XB1+C1Y¯D1=S1,A2X¯B2+C2YD2=S2 by the real representation of the complex matrix and the properties of Kronecker product and vectorization operator. Some numerical experiments demonstrate that the introduced iteration approach is efficient.

Suggested Citation

  • Xie, Ya-Jun & Ma, Chang-Feng, 2015. "The MGPBiCG method for solving the generalized coupled Sylvester-conjugate matrix equations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 68-78.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:68-78
    DOI: 10.1016/j.amc.2015.04.078
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    References listed on IDEAS

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    1. Mehdi Dehghan & Masoud Hajarian, 2012. "The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(8), pages 1580-1590.
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    Cited by:

    1. Yan, Tongxin & Ma, Changfeng, 2021. "An iterative algorithm for generalized Hamiltonian solution of a class of generalized coupled Sylvester-conjugate matrix equations," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    2. Xie, Ya-Jun & Ma, Chang-Feng, 2016. "The accelerated gradient based iterative algorithm for solving a class of generalized Sylvester-transpose matrix equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1257-1269.
    3. Li, Sheng-Kun & Huang, Ting-Zhu, 2019. "Restarted global FOM and GMRES algorithms for the Stein-like matrix equation X+M(X)=C," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 206-214.

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