| 矩阵方程$X A^*X^{-q}A=Q~(q\geq 1)$的Hermite正定解 |
| |
| 引用本文： | 刘巍,廖安平,段雪峰.矩阵方程$X A^*X^{-q}A=Q~(q\geq 1)$的Hermite正定解[J].数学研究及应用,2009,29(5):831-838. |
| |
| 作者姓名： | 刘巍 廖安平 段雪峰 |
| |
| 作者单位： | 长沙学院信息与计算科学系, 湖南 长沙 410003; 湖南大学数学与计量经济学院, 湖南 长沙 410082;;湖南大学数学与计量经济学院, 湖南 长沙 410082;;湖南大学数学与计量经济学院, 湖南 长沙 410082; 桂林电子科技大学数学与计算机科学学院, 广西 桂林 541004 |
| |
| 基金项目： | 湖南省自然科学基金(No.09JJ6012). |
| |
| 摘 要： | In this paper, Hermitian positive definite solutions of the nonlinear matrix equation X ＋ A^＊X^-qA = Q （q≥1） are studied. Some new necessary and sufficient conditions for the existence of solutions are obtained. Two iterative methods are presented to compute the smallest and the quasi largest positive definite solutions, and the convergence analysis is also given. The theoretical results are illustrated by numerical examples.
|
| 关 键 词： | 矩阵方程 质量保证 充要条件 迭代方法 整合分析 非线性 正定解 半正定 |
| 收稿时间： | 2007/10/17 0:00:00 |
| 修稿时间： | 2008/5/21 0:00:00 |
Hermitian Positive Definite Solutions of the Matrix Equation $X A^*X^{-q}A=Q~(q\geq 1)$ |
| |
| LIU Wei,LIAO An Ping and DUAN Xue Feng.Hermitian Positive Definite Solutions of the Matrix Equation $X A^*X^{-q}A=Q~(q\geq 1)$[J].Journal of Mathematical Research with Applications,2009,29(5):831-838. |
| |
| Authors: | LIU Wei LIAO An Ping and DUAN Xue Feng |
| |
| Institution: | Department of Information and Computing Science, Changsha University, Hunan 410003, China; College of Mathematics and Econometrics, Hunan University, Hunan 410082, China;College of Mathematics and Econometrics, Hunan University, Hunan 410082, China;;College of Mathematics and Econometrics, Hunan University, Hunan 410082, China; School of Mathematics & Computational Science, Guilin University of Electronic Technology, Guangxi 541004, China |
| |
| Abstract: | In this paper, Hermitian positive definite solutions of the nonlinear matrix equation $X+A^*X^{-q}A=Q\ (q\geq 1)$ are studied. Some new necessary and sufficient conditions for the existence of solutions are obtained. Two iterative methods are presented to compute the smallest and the quasi largest positive definite solutions, and the convergence analysis is also given. The theoretical results are illustrated by numerical examples. |
| |
| Keywords: | nonlinear matrix equations positive definite solution iterative method |
| 本文献已被 维普 万方数据 等数据库收录！ |
| 点击此处可从《数学研究及应用》浏览原始摘要信息 |
| 点击此处可从《数学研究及应用》下载免费的PDF全文 |
|
