On two perturbation estimates of the extreme solutions to the equations \(X \pm A^*X^{-1}A = Q\) (Q817638)

\textit{V. I. Hasanov, I. G. Ivanov} and \textit{F. Uhlig} [Linear Algebra Appl. 379, 113--135 (2004; Zbl 1039.15005)] have presented perturbation estimates for the maximal positive definite solutions to the equations \(X\pm A^*X^{-1}A=Q\) (the matrices are \(n\times n\), \(Q\) is Hermitian positive definite, \(A^*\) is the conjugate transpose of \(A\)). Here the authors consider these estimates, and they give new perturbation estimates under weaker restrictions on the coefficient matrices of the equations. The results are illustrated by numerical experiments.