On two perturbation estimates of the extreme solutions to the equations X ± A*X−1A = Q

Two perturbation estimates for maximal positive definite solutions of equations X + A*X−1A = Q and X − A*X−1A = Q are considered. These estimates are proved in [Hasanov et al., Improved perturbation Estimates for the Matrix Equations X ± A*X−1A = Q, Linear Algebra Appl. 379 (2004) 113–135]. We derive new perturbation estimates under weaker restrictions on coefficient matrices of the equations. The theoretical results are illustrated by numerical examples.