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TitleAlmost vanishing polynomials for sets of limited precision points
Author(s) Claudia Fassino
TypeArticle in Journal
AbstractFrom the numerical point of view, given a set X ⊂ R^n 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 ˜ .
KeywordsVanishing ideal, Border and Gröbner bases, Limited precision data
URL http://www.sciencedirect.com/science/article/pii/S0747717109001084
JournalJournal of Symbolic Computation
Pages19 - 37
Translation No
Refereed No