A numerical algorithm for Lyapunov equations

In this paper, we give a new numerical iterative method for Lyapunov matrix equations, which is called Kronecker products iterative method (KPIM). By means of the Kronecker products we get an iterative convergent sequence from the Lyapunov matrix equations. At the same time we give its algorithms and corresponding improved algorithm in order to reduce the computation cost. Finally we discuss how to choose the optimal parameter of KPIM for the continuous Lyapunov matrix equations in the case of symmetry.