The full-rank JGI algorithm for the generalized coupled Sylvester-transpose matrix equations

In this paper, we focus on the iterative solutions of the generalized coupled Sylvester-transpose matrix equations. Based on the Jacobi iterative algorithm and the principle of hierarchical identification, the full-row rank Jacobi gradient based iterative (RRJGI) algorithm and the full-column rank Jacobi gradient based iterative (CRJGI) algorithm are proposed. It is proved that the proposed algorithms converge to the exact solutions for any initial matrices when the parameter factor µ satisfies certain conditions and the sufficient and necessary conditions for the convergence of the new algorithms are given. Finally, an example is provided to demonstrate the effectiveness and superiority of the presented algorithms.