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Notes on two perturbation estimates of the extreme solutions to the equations X±A * X -1 A=Q. (English) Zbl 1222.15020
Summary: 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 V. I. Hasanov and I. G. Ivanov [Linear Algebra Appl. 413, No. 1, 81–92 (2006; Zbl 1087.15016)]. The conditions X L -1 A 2 <1 and X + -1 A 2 <1 in [loc. cit.] are not always satisfied. We replace this conditions by PX L -1 AP -1 2 <1 and PX + -1 AP -1 2 <1 respective, where P is positive definite matrix. The theoretical results are illustrated by numerical examples.
15A24Matrix equations and identities
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