Details:
Title  Approximate computation of zerodimensional polynomial ideals  Author(s)  Daniel Heldt, Martin Kreuzer, Sebastian Pokutta, Hennie Poulisse  Type  Article in Journal  Abstract  The Buchberger–Möller algorithm is a wellknown efficient tool for computing the vanishing ideal of a finite set of points. If the coordinates of the points are (imprecise) measured data, the resulting Gröbner basis is numerically unstable. In this paper we introduce a numerically stable Approximate Vanishing Ideal (AVI) Algorithm which computes a set of polynomials that almost vanish at the given points and almost form a border basis. Moreover, we provide a modification of this algorithm which produces a Macaulay basis of an approximate vanishing ideal. We also generalize the Border Basis Algorithm ([Kehrein, A., Kreuzer, M., 2006. Computing border bases. J. Pure Appl. Algebra 205, 279–295]) to the approximate setting and study the approximate membership problem for zerodimensional polynomial ideals. The algorithms are then applied to actual industrial problems.  Keywords  Buchberger–Möller algorithm, Ideal membership, Border basis  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717109000935 
Language  English  Journal  Journal of Symbolic Computation  Volume  44  Number  11  Pages  1566  1591  Year  2009  Note  In Memoriam Karin Gatermann  Edition  0  Translation 
No  Refereed 
No 
