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arXiv · 1209.2480

Solutions and improved perturbation analysis for the matrix equation X-A^{*}X^{-p}A=Q (p>0)

Jing Li
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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 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.

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Jing Li. 2012-09-12. Solutions and improved perturbation analysis for the matrix equation X-A^{*}X^{-p}A=Q (p>0). https://arxiv.org/abs/1209.2480

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