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 XP is any set of points differing only slightly from X, there exists a polynomial set BP structurally similar to B, which is a basis of the perturbed ideal I(XP).

Stable border basis for ideals of points

ABBOTT, JOHN ANTHONY;FASSINO, CLAUDIA;TORRENTE, MARIA LAURA
2008

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 XP is any set of points differing only slightly from X, there exists a polynomial set BP structurally similar to B, which is a basis of the perturbed ideal I(XP).
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/262608
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