Perturbation bounds for the matrix equation X + A^* \widehatX^-1 A = Q

2019/02/28 by Hasanov, Vejdi
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1903.00074

Abstract

Consider the matrix equation X+ A^*\widehatX^-1A=Q, where Q is an n × n Hermitian positive definite matrix, A is an mn× n matrix, and \widehatX 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 ‖\widehatX_L^-1A‖≥ 1 a modification of the main result is derived. The theoretical results are illustrated by numerical examples.

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