Stable border bases for ideals of points

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.