Perturbation anaysis for the matrix equation $X=I-A^{*}X^{-1}A+B^{*}X^{-1}B$

Hosoo Lee

doi:10.11568/kjm.2014.22.1.123

Korean J. Math. Vol. 22 No. 1 (2014) pp.123-131
DOI: https://doi.org/10.11568/kjm.2014.22.1.123

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Published: Mar 27, 2014

Mathematics Subject Classification:

15A24, 65F35

Hosoo Lee

Louisiana State University

Abstract

The purpose of this paper is to study the perturbation analysis of the matrix equation

X = I - A^{*} X^{- 1} A + B^{*} X^{- 1} B .

Based on the matrix differentiation, we give a precise perturbation bound for the positive definite solution. A numerical example is presented to illustrate the shrpness of the perturbation bound.

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