| 矩阵方程X+A~*X~2A=P的Hermite正定解及扰动分析 |
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| 引用本文： | 李磊,刘国栋.矩阵方程X+A~*X~2A=P的Hermite正定解及扰动分析[J].山东科技大学学报(自然科学版),2009,28(1):96-98. |
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| 作者姓名： | 李磊 刘国栋 |
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| 作者单位： | 1. 中国石油大学,数学与计算科学学院,山东,东营,257061
2. 山东科技大学,理学院,山东,青岛,266510 |
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| 基金项目： | 国家自然科学数学天元青年基金 |
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| 摘 要： | 考虑非线性矩阵方程X＋A·X^2A=P，其中A是一个n×n阶的复矩阵，P是一个n×n阶的Hermite正定矩阵，A＊表示矩阵A的共轭转置。推导出矩阵方程的Hermite解的存在及唯一性条件，同时给出唯一解的存在区间。最后对该唯一解进行扰动分析，给出不依赖于扰动解的扰动边界。
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| 关 键 词： | 矩阵方程 正定解 扰动边界 Hermite矩阵 |
Perturbation Analysis of the Hermitian Positive Definite Solutions of the Matrix Equation X+A~*X~2A=P |
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| LI Lei,LIU Guo-dong.Perturbation Analysis of the Hermitian Positive Definite Solutions of the Matrix Equation X+A~*X~2A=P[J].Journal of Shandong Univ of Sci and Technol: Nat Sci,2009,28(1):96-98. |
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| Authors: | LI Lei LIU Guo-dong |
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| Institution: | 1.College of Math.and Computing Sci.;China University of Petroleum;Dongying;Shandong 257061;China;2.College of Science;SUST;Qingdao;Shandong 266510;China |
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| Abstract: | The nonlinear matrix equation X＋A·X^2A=P is considered,where A is the n×n complex matrix,P is the n×n hermitian positive matrix. In this paper, the conditions of existence and uniqueness about hermitian positive definite solutions for the equation are discussed in detail,and the range about unique solution is given.In the end,we derive a perturbation bound which does not depend on the perturbation solution for the unique solution. |
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| Keywords: | matrix equation positive definite solution perturbation bound Hermitian matrix |
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