Almost vanishing polynomials for sets of limited precision points

From the numerical point of view, given a set X ⊂ Rn of s points whose coordinates are known with only limited precision, each set e X of s points whose elements differ from those of X of a quantity less than the 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 “almost vanishing” at X and at all its equivalent sets e X. Even if G is not, in the general case, a basis of the vanishing ideal I(X), we show that, differently from the basis of I(X) that can be greatly influenced by the data uncertainty, G can determine a geometrical configuration simultaneously characterizing the set X and all its equivalent sets e X.