Details:
Title  Almost vanishing polynomials for sets of limited precision points  Author(s)  Claudia Fassino  Type  Article in Journal  Abstract  From 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 ˜ .  Keywords  Vanishing ideal, Border and Gröbner bases, Limited precision data  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717109001084 
Language  English  Journal  Journal of Symbolic Computation  Volume  45  Number  1  Pages  19  37  Year  2010  Edition  0  Translation 
No  Refereed 
No 
