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

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 AXB + C (X) over barD = 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.

Automated summary

This paper establishes two relaxed gradient-based iterative algorithms for solving the generalized Sylvester-conjugate matrix equation. Numerical tests are conducted to demonstrate the effectiveness of the proposed approaches.