Stable border bases for ideals of points

Let be a set of points whose coordinates are known with limited accuracy; our aim is to give a characterization of the vanishing ideal independent of the data uncertainty. We present a method to compute, starting from , a polynomial basis of which exhibits structural stability, that is, if is any set of points differing only slightly from , there exists a polynomial set structurally similar to , which is a basis of the perturbed ideal .