# Stable Border Bases for Ideals of Points - Mathematics > Commutative Algebra

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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 \$IX\$ independentof the data uncertainty. We present a method to compute a polynomial basis \$B\$of \$IX\$ which exhibits structural stability, that is, if \$\widetilde X\$ isany set of points differing only slightly from \$X\$, there exists a polynomialset \$\widetilde B\$ structurally similar to \$B\$, which is a basis of theperturbed ideal \$ I\widetilde X\$.

Autor: John Abbott, Claudia Fassino, Maria-Laura Torrente

Fuente: https://arxiv.org/