| 子矩阵约束下矩阵方程ATXA=B的实矩阵解及其最佳逼近 |
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| 引用本文： | 龚丽莎,胡锡炎,张磊. 子矩阵约束下矩阵方程ATXA=B的实矩阵解及其最佳逼近[J]. 工程数学学报, 2007, 24(5): 913-918 |
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| 作者姓名： | 龚丽莎 胡锡炎 张磊 |
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| 作者单位： | 电子科技大学应用数学学院,成都,610054;湖南大学数学与计量经济学院,长沙,410082 |
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| 摘 要： | 本文讨论了子矩阵约束下一类矩阵方程的实矩阵解问题。基于矩阵的奇异值分解和广义奇异值分解方法,给出了该问题有解的充要条件和解的一般表达式。并证明了对任一给定的实矩阵,在上述解集合中必存在唯一的最佳逼近解,给出了最佳逼近解的形式。
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| 关 键 词： | 矩阵方程 子矩阵 矩阵范数 最佳逼近 |
| 文章编号： | 1005-3085（2007）05-0913-06 |
| 修稿时间： | 2005-09-02 |
The Real Solutions and its Optimal Approximation of Matrix Equation ATXA=B under a Submatrix Constraint |
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| GONG Li-sha,HU Xi-yan,ZHANG Lei. The Real Solutions and its Optimal Approximation of Matrix Equation ATXA=B under a Submatrix Constraint[J]. Chinese Journal of Engineering Mathematics, 2007, 24(5): 913-918 |
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| Authors: | GONG Li-sha HU Xi-yan ZHANG Lei |
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| Affiliation: | 1. School of Applied Mathematics,University of Electronic Science and Technology of China, Chengdu 610054; 2. College of Mathematics and Econometrics, Hunan University, Changsha 410082 |
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| Abstract: | The problem of finding real matrix solutions for a class of matrix equation under a subma- trix constraint is discussed.Based on the singular value decomposition and generalized singular value decomposition methods,the necessary and sufficient conditions for the existence of solutions and their general expression are given.Moreover,for a given real matrix,we prove a unique optimal approxima- tion solution exists in the above previous solution set,and the expression of the optimal approximation solution is also derived. |
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| Keywords: | matrix equation submatrix matrix norm optimal approximation |
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