| 关于非线性矩阵方程$X^s-A^*X^{-t}A=Q$的Hermitian正定解及其扰动估计 |
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| 引用本文： | 蔡静.关于非线性矩阵方程$X^s-A^*X^{-t}A=Q$的Hermitian正定解及其扰动估计[J].数学研究及应用,2013,33(6):673-682. |
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| 作者姓名： | 蔡静 |
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| 作者单位： | 湖州师范学院理学院, 浙江 湖州 313000 |
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| 基金项目： | 国家自然科学基金(Grant No.11071079), 浙江省自然科学基金(Grant No.Y6110043). |
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| 摘 要： | In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X^s - A^＊X^-tA = 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.
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| 关 键 词： | Hermite正定解 非线性矩阵方程 扰动估计 埃尔米特 解的存在性 正定矩阵 条件方程 正整数 |
| 收稿时间： | 2012/7/29 0:00:00 |
| 修稿时间： | 2012/11/22 0:00:00 |
On the Hermitian Positive Definite Solutions of the Nonlinear Matrix Equation $X^s-A^*X^{-t}A=Q$ with Perturbation Estimates |
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| Jing CAI.On the Hermitian Positive Definite Solutions of the Nonlinear Matrix Equation $X^s-A^*X^{-t}A=Q$ with Perturbation Estimates[J].Journal of Mathematical Research with Applications,2013,33(6):673-682. |
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| Authors: | Jing CAI |
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| Institution: | School of Science, Huzhou Teachers College, Zhejiang 313000, P. R. China |
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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. |
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| Keywords: | matrix equation Hermitian positive definite solution property existence perturbation bound |
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