| 线性流形上反对称正交对称矩阵反问题的最小二乘解 |
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| 引用本文： | 于蕾,张凯院,史忠科.线性流形上反对称正交对称矩阵反问题的最小二乘解[J].数学物理学报(A辑),2006,26(B12):1031-1038. |
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| 作者姓名： | 于蕾 张凯院 史忠科 |
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| 作者单位： | [1]西北工业大学理学院应用数学系,西安710072 [2]西北工业大学自动化学院,西安710072 |
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| 基金项目： | 国家自然科学基金重点项目（60134010）资助 |
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| 摘 要： | 该文讨论了线性流形上矩阵方程AX=B反对称正交对称反问题的最小二乘解及其最佳逼近问题．给出了最小二乘问题解集合的表达式，得到了给定矩阵的最佳逼近问题的解，最后给出计算任意矩阵的最佳逼近解的数值方法及算例．
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| 关 键 词： | 矩阵方程 线性流形 反对称正交对称矩阵 最佳逼近 |
| 收稿时间： | 2005-12-08 |
| 修稿时间： | 2006-06-20 |
Least-Squares Solutions of Inverse Problems for Anti-Symmetric Ortho-Symmetric Matrices on the Linear Manifold |
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| Yu Lei .Zhang Kaiyuan.Shi Zhongke.Least-Squares Solutions of Inverse Problems for Anti-Symmetric Ortho-Symmetric Matrices on the Linear Manifold[J].Acta Mathematica Scientia,2006,26(B12):1031-1038. |
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| Authors: | Yu Lei Zhang KaiyuanShi Zhongke |
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| Abstract: | This paper discusses the least-squares solutions of matrix equation AX = B for anti-symmetric ortho-symmetric matrices on the linear manifold and its optimal approximation problems. The general expression of the least-squares solution set is given.In addition,the expression of the optimal approximation solution to the given matrix is obtained.Numerical methods of the optimal approximation to a given matrix and numerical experiments are described. |
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| Keywords: | Matrix equation Linear manifold Anti-symmetric ortho-symmetric matrix Optimal approximation |
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