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Restarted global FOM and GMRES algorithms for the Stein-like matrix equation X+M(X)=C

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  • Li, Sheng-Kun
  • Huang, Ting-Zhu

Abstract

In this paper, we propose the restarted global full orthogonalization method (Gl-FOM) and global generalized minimum residual (Gl-GMRES) method to solve the Stein-like matrix equation X+M(X)=C with M(X)=AXB,M(X)=AX⊤B,M(X)=AX¯B or M(X)=AXHB, respectively, where X is an unknown matrix to be solved. First, by using a real inner product in complex matrix spaces, a generalized global Arnoldi process is given. Then we demonstrate how to employ the restarted Gl-FOM and Gl-GMRES algorithms for solving the Stein-like matrix equation. The proposed algorithms take advantage of the shifted structure of the matrix equation and are implemented by the original coefficient matrices. Finally, some numerical examples are given to illustrate the effectiveness with comparison to some existing methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:348:y:2019:i:c:p:206-214
    DOI: 10.1016/j.amc.2018.11.058
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    References listed on IDEAS

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    1. Chun-Yueh Chiang, 2013. "A Note on the -Stein Matrix Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, August.
    2. 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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