Iterative solution of two matrix equations

We study iterative methods for finding the maximal Hermitian positive defin ite solutions of the matrix equations X + A*X-1 A = Q and X - A*X-1 A = Q, where Q is Hermitian positive definite. General convergence results are giv en for the basic fixed point iteration for both equations. Newton's method and inversion free variants of the basic fixed point iteration are discusse d in some detail for the first equation. Numerical results are reported to illustrate the convergence behaviour of various algorithms.