A relaxed gradient based iterative algorithm of the generalized Sylvester-conjugate matrix equation over centro-symmetric and centro-Hermitian matrices

Abstract

The main purpose of this paper is to establish two relaxed gradient-based iterative (RGI) algorithms extending the Jacobi and Gauss–Seidel iterations for solving the generalized Sylvester-conjugate matrix equation $A X B + C \bar{X} D = F$ , over centro-symmetric, and centro-Hermitian matrices. It is shown that the iterative methods, respectively, converge to the centro-symmetric and centro-Hermitian solutions for any initial centro-symmetric and centro-Hermitian matrices. We report numerical tests to show the effectiveness of the proposed approaches.

Keywords

generalized Sylvester conjugate matrix equation two relaxed gradient-based algorithms centro-symmetric solution centro-Hermitian solution accuracy

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