Approximate computation of zero-dimensional polynomial ideals
نویسندگان
چکیده
The Buchberger-Möller algorithm is a well-known 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 ([11]) to the approximate setting and study the approximate membership problem for zero-dimensional polynomial ideals. The algorithms are then applied to actual industrial problems.
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ورودعنوان ژورنال:
- J. Symb. Comput.
دوره 44 شماره
صفحات -
تاریخ انتشار 2009