Employing an iterative gradient-based approach to solve generalized coupled Sylvester matrix equations over generalized centro-symmetric matrices

Abstract

In this research, we present a different approach to a method for solving coupled generalized Sylvester matrix (GSM) equations  over generalized centro-symmetric matrices (GCSMs) (  using a gradient-based iterative technique. In the absence of round-off errors, a generalized centro-symmetric solution (GCSS) (may be obtained in a small amount of iterations if the matrix equations explored here are compatible with the initial GCSM. The theoretical results of this study are reinforced by numerical examples.