Perturbation bounds for the matrix equation
V Hasanov - arXiv preprint arXiv:1903.00074, 2019 - arxiv.org
V Hasanov
arXiv preprint arXiv:1903.00074, 2019•arxiv.orgConsider the matrix equation $ X+ A^*\widehat {X}^{-1} A= Q $, where $ Q $ is an $ n\times n
$ Hermitian positive definite matrix, $ A $ is an $ mn\times n $ matrix, and $\widehat {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 $\|\widehat {X_L^{-1}} A\|\ge 1$ a modification of the main result is derived. The
theoretical results are illustrated by numerical examples.
$ Hermitian positive definite matrix, $ A $ is an $ mn\times n $ matrix, and $\widehat {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 $\|\widehat {X_L^{-1}} A\|\ge 1$ a modification of the main result is derived. The
theoretical results are illustrated by numerical examples.
Consider the matrix equation , where is an Hermitian positive definite matrix, is an matrix, and is the block diagonal matrix with on its diagonal. In this paper, a perturbation bound for the maximal positive definite solution is obtained. Moreover, in case of a modification of the main result is derived. The theoretical results are illustrated by numerical examples.
arxiv.org