On convergence of three iterative methods for solving of the matrix equation X+A∗X-1A+B∗X-1B=Q

In this paper, we give new convergence results for the basic fixed point iteration and its two inversion-free variants for finding the maximal positive definite solution of the matrix equation X + A ∗ X - 1 A + B ∗ X - 1 B = Q , proposed by Long et al. (Bull Braz Math Soc 39:371–386, 2008 ) and Vaezzadeh et al. (Adv Differ Equ 2013 ). The new results are illustrated by numerical examples.