| 线性流形上矩阵方程B^TXB=D的加权最小二乘对称解和解的最佳逼近 |
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| 引用本文： | 周立平.线性流形上矩阵方程B^TXB=D的加权最小二乘对称解和解的最佳逼近[J].数学理论与应用,2008,28(1):78-81. |
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| 作者姓名： | 周立平 |
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| 作者单位： | 湖南科技学院数学与计算机科学系 永州，425000 |
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| 摘 要： | 本文利用矩阵的奇异值分解（SVD）,给出了在一流形上矩阵方程B^TXB=D的加权最小二乘对称解的通解表达式,并解决了加权最小二乘对称解的最佳逼近问题。
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| 关 键 词： | 线性流形 加权 最小二乘 最佳逼近 |
The Weighted Least Squares Symmetric Solutions of Matrix Equation B~TXB=D and its Optimal Approximation on A Linear Manifold |
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| Zhou Liping.The Weighted Least Squares Symmetric Solutions of Matrix Equation B~TXB=D and its Optimal Approximation on A Linear Manifold[J].Mathematical Theory and Applications,2008,28(1):78-81. |
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| Authors: | Zhou Liping |
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| Affiliation: | Zhou Liping (Department of Mathematics and Computational Science,Hunan University of Science and Engineering, Yongzhou, 425000) |
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| Abstract: | The expression of the weighted least squares symmetric solutions of ma trix equation BTXB=D on a linear manifold is derived by the use of matrix singular value decomposition (SVD).Meanwhile,the optimal approximation solution is also obtained. |
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| Keywords: | Linear manifold weighted least squares optimal approximation |
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