The use of a gradient-based iterative technique to solve the generalized coupled Sylvester matrix equations over generalized centro-symmetric matrices

Abstract

In this paper, the generalized coupled Sylvester matrix equations are solved using a gradient-based iterative technique over the generalized centro-symmetric matrices ( . In the case that our investigated matrix equations are consistent, with chosen initial generalized centro-symmetric matrices and , a generalized centro-symmetric solution ( can be found in a finite number of iterations in the absence of round-off errors. Numerical examples are presented in order to support the theoretical results of this paper.