On the relaxed gradient-based iterative methods for the generalized coupled Sylvester-transpose matrix equations

In this paper, we propose the full-rank and reduced-rank relaxed gradient-based iterative algorithms for solving the generalized coupled Sylvester-transpose matrix equations. We provide analytically the necessary and sufficient condition for the convergence of the proposed iterative algorithm and give explicitly the optimal step size such that the convergence rate of the algorithm is maximized. Some numerical examples are examined to confirm the feasibility and efficiency of the proposed algorithms. (c) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

This paper proposes full-rank and reduced-rank relaxed gradient-based iterative algorithms for solving the generalized coupled Sylvester-transpose matrix equations. The necessary and sufficient condition for the convergence of the proposed iterative algorithm is analytically provided, and the optimal step size is explicitly given to maximize the convergence rate of the algorithm. Numerical examples are examined to confirm the feasibility and efficiency of the proposed algorithms.