| 奇异值分解求线性最小二乘解的理论分析 |
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| 引用本文： | 徐文华,孙学栋.奇异值分解求线性最小二乘解的理论分析[J].贵阳金筑大学学报,2009(4). |
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| 作者姓名： | 徐文华 孙学栋 |
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| 作者单位： | 贵州师范大学数学与计算机科学学院; |
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| 摘 要： | 最小二乘问题在数据拟合、参数估计和控制理论等方面有着广泛的作用。本文将利用奇异值分解给出了线性方程Ax=b的最小二乘解的通解表达式以及广义逆的表达式,并对最小线性二乘问题的条件数进行了论证,指出了当矩阵A为方阵时怎样估算该方程组的是否是病态的方法。
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| 关 键 词： | 最小二乘解 奇异值 广义逆和条件数 |
A Theoretical Analysis of Linear Least Square based on Singular Value Decomposition |
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| XU Wen-hua SUN Xue-dong.A Theoretical Analysis of Linear Least Square based on Singular Value Decomposition[J].Journal of Jinzhu University of Guiyang,2009(4). |
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| Authors: | XU Wen-hua SUN Xue-dong |
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| Institution: | XU Wen-hua SUN Xue-dong(School of Mathematical and Computer Science,Guizhou Normal University,Guiyang Guizhou 550001,China) |
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| Abstract: | The method of linear least square is widely applied extensively in data fitting,parameter estimation,control theory,etc.This paper gives the general expressions of least square and generalized inverse in the equation Ax=b by means of singular value decomposition,proves the condition number of the linear least square and gives the method of how to judge if the equation is ill-conditioned,when matrix A is square. |
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| Keywords: | least square singular value decomposition generalized inverse and condition number |
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