The Generalized Modified Hermitian and Skew-Hermitian Splitting Method for the Generalized Lyapunov Equation
The Generalized Modified Hermitian and Skew-Hermitian Splitting Method for the Generalized Lyapunov Equation
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DOI：
10.1007/s12555-020-0053-1
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发表时间：
2020-09
期刊：
影响因子：
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通讯作者：
Juan Zhang;Huihui Kang
中科院分区：
文献类型：
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作者：
Juan Zhang;Huihui Kang
本文提出了计算广义李雅普诺夫方程的广义修正厄米和斜厄米分裂（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，不精确版本的GMHSS（IGMHSS）的方法制定，以改善GMHSS方法。最后，通过数值实验验证了本文方法的有效性和竞争力
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