基于约束总体最小二乘方法的近似消逝理想算法

AN APPROXIMATE VANISHING IDEAL ALGORITHM BASED ON CONSTRAINED TOTAL LEAST SQUARES

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X~ε,该算法输出序理想O和多项式集合G.当O中单项的个数等于经验点集X~ε的基数时,G即为X~ε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 X~ε,the algorithm outputs an order idealO and a set of polynomialsG.If #O = #X~ε,thenG forms a basis for the approximate vanishing ideal of X~ε.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.