| On the Hermitian Positive Definite Solutions of the Nonlinear Matrix Equation $X^s-A^*X^{-t}A=Q$ with Perturbation Estimates |
| Received:July 29, 2012 Revised:November 22, 2012 |
| Key Words:
matrix equation Hermitian positive definite solution property existence perturbation bound.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11071079) and the Natural Science Foundation of Zhejiang Province (Grant No.Y6110043). |
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| Abstract: |
| In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation $X^s-A^*X^{-t}A=Q$ are studied, where $Q$ is a Hermitian positive definite matrix, $s$ and $t$ are positive integers. The existence of a Hermitian positive definite solution is proved. A sufficient condition for the equation to have a unique Hermitian positive definite solution is given. Some estimates of the Hermitian positive definite solutions are obtained. Moreover, two perturbation bounds for the Hermitian positive definite solutions are derived and the results are illustrated by some numerical examples. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2013.06.004 |
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