New results of the IO iteration algorithm for solving Sylvester matrix equation

Abstract

In this paper, the IO iteration algorithm proposed in Tian et al. [3] is further investigated, and some new results for solving the Sylvester matrix equation are obtained. At first, a new convergence property of the IO iteration algorithm is given for a wider convergence region associated with the parameter γ. Under the new convergence condition, a corresponding comparison result is established for the IO iteration algorithm compared with the Smith method. Moreover, if the matrices A,B in the Sylvester matrix equation are nonnegative, the IO iteration algorithm is proved to be convergent for any inner iteration number lk≥1 with 0<γ<1. Finally, three numerical examples are implemented to confirm the validity of the new results.