Solutions and improved perturbation analysis for the matrix equation X-A^{*}X^{-p}A=Q (p>0)
Abstract
In this paper the nonlinear matrix equation X-A^{*}X^{-p}A=Q with p>0 is investigated. We consider two cases of this equation: the case p>1 and the case 0<p<1. In the case p>1, a new sufficient condition for the existence of a unique positive definite solution for the matrix equation is obtained. A perturbation estimate for the positive definite solution is derived. Explicit expressions of the condition number for the positive definite solution are given. In the case 0<p<1, a new sharper perturbation bound for the unique positive definite solution is evaluated. A new backward error of an approximate solution to the unique positive definite solution is obtained. The theoretical results are illustrated by numerical examples.
Keywords
Cite
@article{arxiv.1209.2480,
title = {Solutions and improved perturbation analysis for the matrix equation X-A^{*}X^{-p}A=Q (p>0)},
author = {Jing Li},
journal= {arXiv preprint arXiv:1209.2480},
year = {2012}
}
Comments
17 pages. arXiv admin note: substantial text overlap with arXiv:1208.3672, arXiv:1208.3518