Stable Border Bases for Ideals of Points

Details Stable Border Bases for Ideals of Points Stable Border Bases for Ideals of Points

2007-06-15

arxiv.org/abs/0706.2316v2

Journal of Symbolic Computation, 43, 2008, 883--894

Mathematics

Commutative Algebra

This is an update version of "Notes on stable Border Bases" and it is submitted to JSC. 16 pages, 0 figures

Scientific paper

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 a polynomial basis $B$ of $I(X)$ which exhibits structural stability, that is, if $\widetilde X$ is any set of points differing only slightly from $X$, there exists a polynomial set $\widetilde B$ structurally similar to $B$, which is a basis of the perturbed ideal $ I(\widetilde X)$.

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