|The Generalized Modified Hermitian and Skew-Hermitian Splitting Method for the Generalized Lyapunov Equation
Juan Zhang* and Huihui Kang
International Journal of Control, Automation, and Systems, vol. 19, no. 1, pp.339-349, 2021
Abstract : 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.
Bilinear systems, controllability, convergence, GMHSS method, IGMHSS method, Hermitian and skew-Hermitian splitting, the generalized Lyapunov equation