A relaxed gradient based iterative algorithm of the generalized Sylvester-conjugate matrix equation over centro-symmetric and centro-Hermitian matrices
Naglaa M. El–Shazly, Mohamed A. Ramadan, Marwa H. El-Sharway · Journal of Vibration and Control · 2022
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 [Formula: see text], 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.