Convergence analysis of some iterative methods for a nonlinear matrix equation

We study iterative methods for finding the largest Hermitian positive definite solution of the matrix equation X+∑i=1mAi∗X−1Ai=Q. Convergence rates of the basic fixed point iteration, inversion free variants of the basic fixed point iteration, and Stein iteration are considered. Some numerical examples are presented to illustrate the convergence behaviour of the various algorithms.