In this paper, we propose the generalized modified Hermitian and skew-Hermitian splitting (GMHSS) approach for computing the generalized Lyapunov equation. The GMHSS iteration is convergent to the unique solution of the generalized Lyapunov equation. Moreover, we discuss the convergence analysis of the GMHSS algorithm. Further, the inexact version of the GMHSS (IGMHSS) method is formulated to improve the GMHSS method. Finally, some numerical experiments are carried out to demonstrate the effectiveness and competitiveness of the derived methods

中文翻译：

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广义Lyapunov方程的广义修正Hermitian和Skew-Hermitian分裂方法

在本文中，我们提出了用于计算广义 Lyapunov 方程的广义修正 Hermitian 和 skew-Hermitian 分裂 (GMHSS) 方法。GMHSS 迭代收敛于广义李雅普诺夫方程的唯一解。此外，我们讨论了 GMHSS 算法的收敛性分析。此外，制定了 GMHSS (IGMHSS) 方法的不精确版本以改进 GMHSS 方法。最后，进行了一些数值实验，以证明导出方法的有效性和竞争力