A New Double-Step Iteration Method for Solving a Class of Complex Continuous Sylvester Equations

Abstract

In this paper, a new double-step (NDS) iteration method is proposed for solving a broad class of complex continuous Sylvester equations. Some sufficient conditions guaranteeing the convergence of the NDS iteration method are studied and the quasi-optimal parameter is given. Moreover, to reduce the computational cost, an inexact NDS (INDS) iteration method is established and the corresponding convergence results are also obtained in detail. Numerical experiments illustrate the superiorities of the NDS and INDS iteration methods.