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

Sheng-Kun Li and Ting-Zhu Huang

Applied Mathematics and Computation, 2019, vol. 348, issue C, 206-214

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.

Keywords: Stein-like matrix equation; Krylov subspace; Global FOM; Global GMRES (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:348:y:2019:i:c:p:206-214

DOI: 10.1016/j.amc.2018.11.058

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