| 反对称正交反对称矩阵反问题的加权最小二乘解 |
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| 引用本文： | 孟国艳,赵青杉,赵俊华.反对称正交反对称矩阵反问题的加权最小二乘解[J].太原师范学院学报(自然科学版),2008,7(1):13-17. |
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| 作者姓名： | 孟国艳 赵青杉 赵俊华 |
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| 作者单位： | 1. 忻州师范学院,计算机系,山西,忻州,034000
2. 太原师范学院数学系,山西,太原,030012 |
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| 基金项目： | 山西省教育厅资助项目，忻州师范学院校科研和教改项目 |
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| 摘 要： | 主要讨论了矩阵方程A^TXA=B的反对称正交反对称最小二乘解,得到了解的一般表达式,并且文章对于任意给定的矩阵X^＊,在最小二乘解集中得到了A的最佳逼近解.
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| 关 键 词： | 矩阵方程 反对称正交反对称矩阵 加权最小二乘解 最佳逼近 |
On Weighted Least-Square Solutions for Inverse Problem of Anti-symmetric Orthogonal Anti-symmetric Matrices |
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| Meng Guoyan,Zhao Qingshan,Zhao Junhua.On Weighted Least-Square Solutions for Inverse Problem of Anti-symmetric Orthogonal Anti-symmetric Matrices[J].Journal of Taiyuan Normal University:Natural Science Edition,2008,7(1):13-17. |
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| Authors: | Meng Guoyan Zhao Qingshan Zhao Junhua |
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| Institution: | Meng Guoyan Zhao Qingshan Zhao Junhua(1.Department of Computer,Xinzhou Teachers′ College,Xinzhou 034000;2.Department of Mathmatics,Taiyuan Normal University,Taiyuan 030012,China) |
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| Abstract: | We discuss the anti-symmetric orthogonal anti-symmetric least square solutions of the matrix equation A^TXA=B.And we obtain the general expressions of the solution.In addition,in solutions set of the equation,the expressions of the optimal approximation to any given matrix X^＊ are derived. |
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| Keywords: | matrix equation anti-symmetric orthogonal anti-symmetric matrix weighted least-square solution optimal approximation |
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