| 矩阵不等式约束下矩阵方程AX=B的双对称解 |
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| 引用本文： | 李姣芬,彭振赟,彭靖静. 矩阵不等式约束下矩阵方程AX=B的双对称解[J]. 计算数学, 2013, 35(2): 137-150 |
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| 作者姓名： | 李姣芬 彭振赟 彭靖静 |
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| 作者单位： | 桂林电子科技大学数学与计算科学学院, 广西桂林 541004 |
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| 基金项目： | 国家自然科学基金资助项目，广西自然科学基金资助项目 |
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| 摘 要： | 本文讨论矩阵不等式CXD≥E 约束下矩阵方程AX=B的双对称解,即给定矩阵A,B,C,D和 E, 求双对称矩阵X, 使得AX=B 和 CXD≥E, 其中CXD≥E表示矩阵CXD-E非负.本文将问题转化为矩阵不等式最小非负偏差问题,利用极分解理论给出了求其解的迭代方法,并结合相关矩阵理论说明算法的收敛性.最后给出数值算例验证算法的有效性.
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| 关 键 词： | 矩阵不等式 矩阵方程 双对称矩阵 迭代法 极分解 |
| 收稿时间： | 2012-06-24; |
THE BISYMMETRIC SOLUTION OF MATRIX EQUATION AX =B OVER A MATRIX INEQUALITY CONSTRAINT |
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| Li Jiaofen , Peng Zhenyun , Peng Jingjing. THE BISYMMETRIC SOLUTION OF MATRIX EQUATION AX =B OVER A MATRIX INEQUALITY CONSTRAINT[J]. Mathematica Numerica Sinica, 2013, 35(2): 137-150 |
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| Authors: | Li Jiaofen Peng Zhenyun Peng Jingjing |
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| Affiliation: | School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, Guangxi, China |
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| Abstract: | We consider the bisymmetric solution of the matrix equation AX=B over linear inequality CXD≥E constraint. That is, given matrices A,B,C,D and E, find a bisymmetric matrix X such that AX=B and CXD≥E, where CXD≥E means that matrix CXD-E nonnegative. We transform the problem into a matrix inequality smallest nonnegative deviation problem, and then combined with the polar decomposition theory, we propose an iterative method for solving this transformed problem. The convergence analysis of the proposed method are given and numerical experiments are proposed to show that the iterative method is feasible and effective. |
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| Keywords: | Matrix inequality matrix equation bisymmetric matrix iteration method polar decomposition |
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