From the numerical point of view, given a set X, subset of R^n of s points whose coordinates are known with only limited precision, each set XP 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 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 XP. 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 XP.
Almost vanishing polynomials for sets of limited precision points
FASSINO, CLAUDIA
2010-01-01
Abstract
From the numerical point of view, given a set X, subset of R^n of s points whose coordinates are known with only limited precision, each set XP 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 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 XP. 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 XP.
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