Douglas-Rachford iterations for the HSS splitting

Abstract In this paper, we study a variation of the HSS Iteration method. This variation is based on a method introduced by Douglas and Rachford and has been called the Douglas-Rachford iterative method throughout the literature. A convergence criteria is given for positive definite matrices which is similar to the convergence criteria for the HSS iterative method. Examples are given to illustrate numerical differences of these two iterative methods.