Almost vanishing polynomials for sets of limited precision points

作者：Fassino Claudia^*

来源：Journal of Symbolic Computation, 2010, 45(1): 19-37.

DOI：10.1016/j.jsc.2009.06.002

• Vanishing ideal
• Border and Grobner bases
• Limited precision data

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 (X) over tilde 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 epsilon 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) over tilde. The set g, is not, in the general case, a basis of the vanishing ideal l(X). Nevertheless g, can determine geometrical configurations simultaneously characterizing the set X and all its equivalent sets (X) over tilde.

• 出版日期2010-1