| 矩阵最小剩余问题及其最优近似问题的对称解 |
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| 引用本文： | 尹凤,黄光鑫.矩阵最小剩余问题及其最优近似问题的对称解[J].成都理工大学学报(自然科学版),2008,35(2):212-215. |
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| 作者姓名： | 尹凤 黄光鑫 |
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| 作者单位： | 四川理工学院数学系,四川自贡,643000;成都理工大学"数学地质"四川省重点实验室,成都,610059 |
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| 基金项目： | 成都理工大学校科研和教改项目
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成都理工大学信息管理学院重点基金 |
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| 摘 要： | 主要给出了矩阵的最小剩余问题及其最优近似问题的对称解.首先,分别给出了与矩阵最小剩余问题及其最优近似问题等价的线性方程;其次,用广义奇异值分解得到了与最小剩余问题等价的线性方程的对称解,即最小剩余问题的对称解;最后,通过寻求与最优近似问题等价的线性方程的对称解,从而得到了矩阵的最优近似问题的最优近似解.
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| 关 键 词： | 广义奇异值分解 最小剩余问题 最优近似问题 对称解 最小二乘解 |
| 文章编号： | 1671-9727(2008)02-0212-04 |
| 修稿时间： | 2006年10月23 |
Symmetric matrix solutions of the matrix minimum residual problem and the matrix optimal approximation problem |
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| YIN Feng,HUANG Guang-xin.Symmetric matrix solutions of the matrix minimum residual problem and the matrix optimal approximation problem[J].Journal of Chengdu University of Technology: Sci & Technol Ed,2008,35(2):212-215. |
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| Authors: | YIN Feng HUANG Guang-xin |
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| Institution: | YIN Feng1,HUANG Guang-xin21.Mathematics Department of Sichuan College of Science , Engineering,Zigong 643000,China,2.Key Laboratory of Geomathematics of Sichuan,Chengdu University of Technology,Chengdu 610059 |
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| Abstract: | This paper gives the precise symmetric matrix solutions of the matrix minimum residual problem and the matrix optimal approximation problem.Firstly,it gives the linear equation equivalent to the minimum residual problem.Then,by the generalized singular value decomposition,a general symmetric solution of the minimum residual problem is obtained.Lastly,for the matrix optimal approximation problem,an unique optimal approximate solution is given by first finding the general symmetric solution of linear equation... |
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| Keywords: | generalized singular value decomposition minimum residual problem optimal approximation problem symmetric solution least squares solution |
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