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The accelerated gradient based iterative algorithm for solving a class of generalized Sylvester-transpose matrix equation

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  • Xie, Ya-Jun
  • Ma, Chang-Feng

Abstract

In this paper, we present an accelerated gradient based algorithm by minimizing certain criterion quadratic function for solving the generalized Sylvester-transpose matrix equation AXB+CXTD=F. The idea is from (Ding and Chen, 2005; Niu et al., 2011; Wang et al., 2012) in which some efficient algorithms were developed for solving the Sylvester matrix equation and the Lyapunov matrix equation. On the basis of the information generated in the previous half-step, we further introduce a relaxation factor to obtain the solution of the generalized Sylvester-transpose matrix equation. We show that the iterative solution converges to the exact solution for any initial value provided that some appropriate assumptions. Finally, some numerical examples are given to illustrate that the introduced iterative algorithm is efficient.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:1257-1269
    DOI: 10.1016/j.amc.2015.07.022
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    1. 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.
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    Cited by:

    1. Baohua Huang & Changfeng Ma, 2019. "The least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint," Journal of Global Optimization, Springer, vol. 73(1), pages 193-221, January.

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