Multi-Iterative Factors Gradient Algorithm for the Coupled Sylvester-Transpose Matrix Equations

本文研究了耦合Sylvester转置矩阵方程的数值求解问题。通过充分利用方程的耦合性，引入了多个参数，并提出了多迭代因子梯度(MGI)算法。此外，还推导出了确保算法生成的迭代解对于任意初始矩阵都收敛到精确解的充要条件。最后，通过一个数值例子验证了所提算法的有效性。This paper investigates the numerical solution of coupled Sylvester-transpose matrix equations. By fully exploiting the coupling of the equations, several parameters are introduced, and an multi-iterative factors gradient algorithm is proposed. Additionally, the necessary and sufficient conditions that ensure the convergence of the iterative solutions generated by the algorithm to the exact solution for any initial matrix are derived. Finally, the effectiveness of the proposed algorithm has been verified through a numerical example.