Notes on two perturbation estimates of the extreme solutions to the equations X +/- A*X(-1)A = Q

Two perturbation estimates of the maximal positive definite solutions to the matrix equations X + A*X(-1)A = Q and X - A*X(-1)A = Q are considered. These estimates are like to the estimates discussed by Hasanov and Ivanov [8]. The conditions parallel to X(L)(-1)A parallel to(z) < 1 parallel to X(+)(-1)A parallel to(2) <1 in [8] are not always satisfied. We replace this conditions by parallel to PX(L)(-1)AP(-1)parallel to(2) < 1 and parallel to PX(+)(-1)AP(-1)parallel to(2) <1 respective, where P is positive definite matrix. The theoretical results are illustrated by numerical examples. (C) 2010 Elsevier Inc. All rights reserved.