Notes on two perturbation estimates of the extreme solutions to the equations X±A∗X-1A=Q

Two perturbation estimates of the maximal positive definite solutions to the matrix equations X+A∗X-1A=Q and X-A∗X-1A=Q are considered. These estimates are like to the estimates discussed by Hasanov and Ivanov [8]. The conditions XL-1A2<1 and X+-1A2<1 in [8] are not always satisfied. We replace this conditions by PXL-1AP-12<1 and ‖PX+-1AP-1‖2<1 respective, where P is positive definite matrix. The theoretical results are illustrated by numerical examples.