The NMHSS Iterative Method for the Standard Lyapunov Equation

Based on the previous research results, a new modified-Hermitian and skew-Hemitian splitting iteration method (NMHSS) is presented for solving the standard Lyapunov equation in this paper. At the same time, the corresponding inexact new modified-Hermitian and skew-Hemitian splitting algorithm are given from the perspective of the application. Moreover, some convergence results of the presented NMHSS iterative method and the inexact NMHSS algorithm are established. The numerical experiments are provided to compare the new method with the existing methods, and the improvement effect is obvious. The feasibility and effectiveness of the proposed method are proved from the two aspects of theory and calculation.