Perturbation bounds for the matrix equation X + A^* X^-1 A = Q
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Consider the matrix equation X+ A^*X^-1A=Q, where Q is an n × n Hermitian positive definite matrix, A is an mn× n matrix, and X is the m× m block diagonal matrix with X on its diagonal. In this paper, a perturbation bound for the maximal positive definite solution X_L is obtained. Moreover, in case of X_L^-1A> 1 a modification of the main result is derived. The theoretical results are illustrated by numerical examples.
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