An iterative algorithm is established in this paper for solving the discrete Lyapunov matrix equations. The proposed algorithm contains a tunable parameter, and includes the Smith iteration as a special case, and thus is called the parametric Smith iterative algorithm. Some convergence conditions are developed for the proposed parametric Smith iterative algorithm. Moreover, the optimal parameter for the proposed algorithm to have the fastest convergence rate is also provided for a special case. Finally, numerical examples are employed to illustrate the effectiveness of the proposed algorithm.

中文翻译：

---

离散Lyapunov矩阵方程的参数Smith迭代算法。

本文建立了一种求解离散Lyapunov矩阵方程的迭代算法。所提出的算法包含一个可调参数，并包括Smith迭代作为特例，因此称为参数Smith迭代算法。为拟议的参数Smith迭代算法开发了一些收敛条件。此外，还为特殊情况提供了所提出算法具有最快收敛速度​​的最佳参数。最后，通过算例说明了所提算法的有效性。