| 矩阵方程X+A~*X~(-n)A=P的Hermite正定解及其扰动分析 |
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| 引用本文： | 尹小艳,刘三阳,房亮.矩阵方程X+A~*X~(-n)A=P的Hermite正定解及其扰动分析[J].计算数学,2008,30(1):37-48. |
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| 作者姓名： | 尹小艳 刘三阳 房亮 |
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| 作者单位： | 西安电子科技大学理学院,西安,710071 |
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| 基金项目： | 国家自然科学基金(60574075) |
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| 摘 要： | 考虑非线性矩阵方程X A~*X~(-n)A=P,其中A是m阶非奇异复矩阵,P是m阶Hermite正定矩阵.本文利用不动点理论讨论了该方程Hermite正定解的存在性及包含区间,给出了极大解的性质及求极大,极小解的迭代算法.研究了极大解的扰动问题,利用微分等方法获得了两个新的一阶扰动界,并给出数值例子对所得结果进行了比较说明.
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| 关 键 词： | 矩阵方程 正定解 不动点理论 范数 扰动 |
| 收稿时间： | 2005-07-15 |
| 修稿时间： | 2006年7月15日 |
SOLUTIONS AND PERTURBATION ESTIMATES FOR THE MATRIX EQUATION X+A~*X~(-n)A=P |
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| Yin Xiaoyan,Liu Sanyang,Fang Liang.SOLUTIONS AND PERTURBATION ESTIMATES FOR THE MATRIX EQUATION X+A~*X~(-n)A=P[J].Mathematica Numerica Sinica,2008,30(1):37-48. |
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| Authors: | Yin Xiaoyan Liu Sanyang Fang Liang |
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| Institution: | Yin Xiaoyan Liu Sanyang Fang Liang (School of Science,Xidian University,Xi'an 710071,China) |
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| Abstract: | The nonlinear matrix equation X+A~*X~(-n)A=P is studied,where A is an m×m nonsingular matrix and P is an m×m Hermite positive definite matrix.The existence of the Hermite positive definite solutions is studied and the properties of the maximal solution are discussed.Moreover,iteration algorithms for the maximal and the minimum solutions are offered.And by means of differential,two new first order perturbation bounds for the maximal solution are obtained.The results are illustrated by several numerical examples. |
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| Keywords: | nonlinear matrix equation positive definite solutions fixed point theorem norm perturbation |
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