A Low-Rank Global Krylov Squared Smith Method for Solving Large-Scale Stein Matrix Equation

Abstract

This paper deals with the numerical solution of the large-scale Stein and discrete-time Lyapunov matrix equations. Based on the global Arnoldi process and the squared Smith iteration, we propose a low-rank global Krylov squared Smith method for solving large-scale Stein and discrete-time Lyapunov matrix equations, and estimate the upper bound of the error and the residual of the approximate solutions for the matrix equations. Moreover, we discuss the restarting of the low-rank global Krylov squared Smith method and provide some numerical experiments to show the efficiency of the proposed method.

Funding

Innovative Research Group Project of the National Natural Science Foundation of China(No.11571171)