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

AbstractTwo 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