In this work, we present an iterative algorithm to solve a class of generalized coupled Sylvester-conjugate matrix equations over the generalized Hamiltonian matrices. We show that if the equations are consistent, a generalized Hamiltonian solution can be obtained within finite iteration steps in the absence of round-off errors for any initial generalized Hamiltonian matrix by the proposed iterative algorithm. Furthermore, we can obtain the minimum-norm generalized Hamiltonian solution by choosing the special initial matrices. Finally, numerical examples show that the iterative algorithm is effective.

中文翻译：

---

一类广义耦合西尔维斯特-共轭矩阵方程广义哈密顿解的迭代算法

在这项工作中，我们提出了一种迭代算法来求解广义哈密顿矩阵上的一类广义耦合 Sylvester 共轭矩阵方程。我们表明，如果方程是一致的，则可以通过所提出的迭代算法在任何初始广义哈密顿矩阵没有舍入误差的情况下，在有限迭代步骤内获得广义哈密顿解。此外，我们可以通过选择特殊的初始矩阵来获得最小范数广义哈密顿解。最后，数值例子表明迭代算法是有效的。