Hasanov, Vejdi I. Perturbation bounds for the matrix equation \(X + A^\ast X^{-1}A=Q\). (English) Zbl 1451.15011 Appl. Comput. Math. 19, No. 1, 20-33 (2020). Summary: Consider the matrix equation \(X + A^\ast X^{-1}A=Q\), where \(Q\) is an \(n\times n\) Hermitian positive definite matrix, \(A\) is an \(mn\times n\) matrix, and \(X\) is the \(m\times m\) 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 modification of the main result is derived. The theoretical results are illustrated by numerical examples. MSC: 15A24 Matrix equations and identities 47H14 Perturbations of nonlinear operators 65H05 Numerical computation of solutions to single equations Keywords:nonlinear matrix equation; positive definite solutions; maximal solution; perturbation PDFBibTeX XMLCite \textit{V. I. Hasanov}, Appl. Comput. Math. 19, No. 1, 20--33 (2020; Zbl 1451.15011) Full Text: arXiv Link