| 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(6): 1031 |
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| 作者姓名： | 于蕾 张凯院 史忠科 |
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| 作者单位： | 西北工业大学理学院应用数学系; 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(6): 1031 |
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| Authors: | Yu Lei Zhang Kaiyuan Shi Zhongke |
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| Affiliation: | School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi'an 710072 College of Automation, Northwestern Polytechnical University, Xi'an 710072 |
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| Abstract: | This paper discusses the least-squares solutions of matrix equation AX=Bfor 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 equationzz Linear manifoldzz Anti-symmetric ortho-symmetric matrixzz Optimal approximationzz |
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