Stable border bases for ideals of points

Authors:
John Abbott;Claudia Fassino;Maria-Laura Torrente
Affiliations:
Dip. di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy;Dip. di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy;Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
Venue:
Journal of Symbolic Computation
Year:
2008

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Abstract

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 I(X) independent of the data uncertainty. We present a method to compute, starting from X, a polynomial basis B of I(X) which exhibits structural stability, that is, if X@? is any set of points differing only slightly from X, there exists a polynomial set B@? structurally similar to B, which is a basis of the perturbed ideal I(X@?).