Stable border bases for ideals of points

被引：27
|
作者：
Abbott, John [1 ]
Fassino, Claudia [1 ]
Torrente, Maria-Laura [2 ]
机构：
[1] Univ Genoa, Dip Matemat, I-16146 Genoa, Italy
[2] Scuola Normale Super Pisa, I-56126 Pisa, Italy
来源：
JOURNAL OF SYMBOLIC COMPUTATION | 2008年 / 43卷 / 12期
关键词：
Empirical points; Vanishing ideal; Border bases;
D O I：
10.1016/j.jsc.2008.05.002
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Let X be a set of points whose coordinates are known with limited accuracy; our aim is to give a characterization of the vanishing ideal l(X) independent of the data uncertainty. We present a method to compute, starting from X, a polynomial basis B of l(X) which exhibits structural stability, that is, if (X) over tilde is any set of points differing only slightly from X, there exists a polynomial set (B) over tilde structurally similar to B, which is a basis of the perturbed ideal l((X) over tilde). (c) 2008 Elsevier Ltd. All rights reserved.
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页码：883 / 894
页数：12
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