| 投影方法在线性最小二乘问题中的应用 |
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| 引用本文： | 易华,谢沐玄.投影方法在线性最小二乘问题中的应用[J].井冈山大学学报（自然科学版）,2015(6):21-23. |
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| 作者姓名： | 易华 谢沐玄 |
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| 作者单位： | 井冈山大学数理学院, 江西 吉安 343009,南昌大学建筑工程学院土木工程系, 江西, 南昌 330047 |
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| 基金项目： | 吉安市科技计划项目(吉市科计字[2014]36号13);井冈山大学博士科研启动基金项目(JZB1304) |
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| 摘 要： | 采用正交投影方法推导了最小二乘问题的法方程。首先求出了到最小二乘问题系统矩阵的列空间的正交投影矩阵,然后根据正交投影的性质求出了最小二乘问题的解。该方法可以迁移到带有权重的最小二乘问题。
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| 关 键 词： | 最小二乘问题 加权线性最小二乘问题 正交投影算子 法方程 |
| 收稿时间： | 7/4/2015 12:00:00 AM |
| 修稿时间： | 2015/9/12 0:00:00 |
THE APPLICATION OF PROJECTION METHOD FOR LEAST SQUARES PROBLEMS |
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| YI Hua and XIE Mu-xuan.THE APPLICATION OF PROJECTION METHOD FOR LEAST SQUARES PROBLEMS[J].Journal of Jinggangshan University(Natural Sciences Edition),2015(6):21-23. |
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| Authors: | YI Hua and XIE Mu-xuan |
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| Institution: | School of Mathematics and Physics, Jinggangshan University, Ji'an, Jiangxi 343009, China and Department of Civil Engineering, College of Building Engineering, Nachang University, Nachang, Jiangxi 330047, China |
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| Abstract: | Projection operators or projectors play an important role in numerical linear algebra, particularly in iterative methods for solving various matrix problems. The method of least squares is a standard approach in regression analysis. The projection method is exploited to deduce the normal equation of linear least squares problems. Furthermore, it is easy to use the projection method to solve the weighted linear least squares problems. |
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| Keywords: | least squares problems weighted linear least squares problems orthogonal projection operators normal equation |
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