Almost vanishing polynomials for sets of limited precision points

Abstract

AbstractFrom the numerical point of view, given a set X⊂Rn of s points whose coordinates are known with only limited precision, each set X˜ of s points whose elements differ from those of X of a quantity less than data uncertainty can be considered equivalent to X. We present an algorithm that, given X and a tolerance ε on the data error, computes a set G of polynomials such that each element of G is “almost vanishing” at X and at all its equivalent sets X˜. The set G is not, in the general case, a basis of the vanishing ideal I(X). Nevertheless G can determine geometrical configurations simultaneously characterizing the set X and all its equivalent sets X˜