| D反对称矩阵反问题的最小二乘解 |
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| 引用本文： | 张忠志,周富照,胡锡炎.D反对称矩阵反问题的最小二乘解[J].中南大学学报(自然科学版),2001,32(5):545-548. |
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| 作者姓名： | 张忠志 周富照 胡锡炎 |
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| 作者单位： | 湖南大学应用数学系, |
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| 基金项目： | 国家自然科学基金资助项目(19971024) |
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| 摘 要： | 为了研究约束矩阵方程问题,提出了D反对称矩阵的概念,研究了D反对称矩阵反问题的最小二乘解及其最佳逼近问题;采用矩阵奇异值分解、分块降阶等方法,获得了D反对称矩阵反问题的最小二乘解一般表达式及最佳逼近解的表达式,并对其逆特值问题、线性约束方程问题给出了有解的充分必要条件,推广了文献1]中的相关结果及应用范围.
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| 关 键 词： | D反对称矩阵 矩阵范数 最佳逼近 |
| 文章编号： | 1005-9792(2001)05-0545-04 |
| 修稿时间： | 2001年4月4日 |
Least-square solutions to inverse problems for D-antisymmetric matrices |
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| ZHANG Zhong-zhi,ZHOU Fu zhao,HU Xi yan.Least-square solutions to inverse problems for D-antisymmetric matrices[J].Journal of Central South University:Science and Technology,2001,32(5):545-548. |
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| Authors: | ZHANG Zhong-zhi ZHOU Fu zhao HU Xi yan |
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| Abstract: | A concept of D antisysmmetric matrices was put out. The least square solutions of inverse problems for D antisymmetric matrices and their optimal approximation are considered. A general representation of the solutions of the least square problem and the expression of the optimal approximation solution by exploiting a matrix factorization or a dimension decreasing method was given. Necessary and sufficient conditions for the solvability of inverse eigenvalue problem and linear constraints matrix equation problem are proposed. The theorem of the conference was extended. |
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| Keywords: | D untisymmetric matrices matrix norm optimal approximation |
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