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基于约束总体最小二乘方法的近似消逝理想算法

李喆,张树功,董天,刘莉莉   

  1. 吉林大学数学学院, 长春 130012
  • 收稿日期:2010-09-15 修回日期:1900-01-01 出版日期:2010-11-25 发布日期:2010-11-25

李喆;张树功;董天;刘莉莉. 基于约束总体最小二乘方法的近似消逝理想算法[J]. 系统科学与数学, 2010, 30(11): 1478-1490.

LI Zhe;ZHANG Shugong;DONG Tian;LIU Lili. An Approximate Vanishing Ideal Algorithm Based on onstrained Total Least Squares[J]. Journal of Systems Science and Mathematical Sciences, 2010, 30(11): 1478-1490.

An Approximate Vanishing Ideal Algorithm Based on onstrained Total Least Squares

LI Zhe, ZHANG Shugong,DONG Tian, LIU Lili   

  1. School of Mathemathics, Jilin University, Changchun 130012
  • Received:2010-09-15 Revised:1900-01-01 Online:2010-11-25 Published:2010-11-25
提出了基于约束总体最小二乘方法的近似消逝理想算法. 给定经验点集$\mathbb{X}^\varepsilon$, 该算法输出序理想 $\mathcal{O}$和多项式集合$\mathcal{G}$. 当 $\mathcal{O}$ 中单项的个数等于经验点集$\mathbb{X}^\varepsilon$ 的基数时, $\mathcal{G}$ 即为$\mathbb{X}^\varepsilon$ 的近似消逝理想基.该算法充分考虑赋值向量的扰动之间的内在联系,因此在关注向量的数值相关性方面, 算法优于目前其它同类算法.
This paper provides an algorithm of approximate vanishing ideal based on constrained total least squares technique. Given a set of empirical points $\mathbb{X}^\varepsilon$, the algorithm outputs an order ideal $\mathcal{O}$ and a set of polynomials $\mathcal{G}$. If $\#\mathcal{O}=\# \mathbb{X}^\varepsilon$, then $\mathcal{G}$ forms a basis for the approximate vanishing ideal of $\mathbb{X}^\varepsilon$. Since the algorithm pays sufficient attention to the relationship among the perturbations of the evaluation vectors, it gives a better performance than other similar algorithms in the numerical dependence.

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