通过推广求解矩阵方程AX=b或AX+XB=C的递推迭代算法和基于递阶辩识原理的思想，给出了求解广义耦合矩阵方程的梯度迭代算法。并证明了迭代算法的收敛性。分析表明，若矩阵方程有唯一解，则对任意的初始值该算法给出的迭代解都能快速的收敛到其精确解。数值实例验证了该算法的有效性。%This paper presents a gradient iterative algorithm for solving the generalized coupled matrix equations based on the hierarchical identification principle and extending of the iterative algorithm for the AX=b or AX+XB=C, and the convergence of this method is also given. The analysis shows that if the matrix equation has an unique solution, then the iterative solutions converge fast to the exact one for any initial value. Giving numerical example demonstrates the effectiveness of the proposed algorithm.
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