| 向量到子空间的距离及其应用 |
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| 引用本文： | 唐建国. 向量到子空间的距离及其应用[J]. 大学数学, 2004, 20(5): 74-79 |
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| 作者姓名： | 唐建国 |
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| 作者单位： | 零陵学院,数学与计算科学系,湖南,永州,425006 |
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| 基金项目： | 湖南省自然科学基金 ( 0 3 JJY3 0 1 4)，湖南省教育厅科研项目 ( 0 2 C3 5 5 ) |
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| 摘 要： | 给出了向量到有限维子空间距离的定义及求法 ,并推广到向量到可数无限维子空间距离 .采用两种方法求距离并比较了它们的运算量 .揭示了 Cholesky分解法与 Schmidt正交化方法的内在联系 .最后利用向量到子空间距离给出了矛盾方程组最小二乘解的求法
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| 关 键 词： | 向量到子空间的距离 Cholesky分解法 Schmidt正交化方法 最小二乘解 |
| 文章编号： | 1672-1454(2004)05-0074-06 |
| 修稿时间： | 2003-07-29 |
Distance from a Given Vector to a Subspace and Its Applications |
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| TANG Jian-guo. Distance from a Given Vector to a Subspace and Its Applications[J]. College Mathematics, 2004, 20(5): 74-79 |
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| Authors: | TANG Jian-guo |
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| Abstract: | A definition of the distance from a given vector to a subspace is presented and its properties are generalized to denumberal infinite-dimensional subspaces. Two methods are adopted to compute the distance and its operations are compared. The relations between Cholesky's decomposition and Schmidt's orthogonalization are revealed essentially. Finally, the method for finding least-square solutions is given. |
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| Keywords: | distance from a given vector to a subspace Cholesky's decomposition Schmidt's orthogonalization (least-square solution) |
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