Notes on Stable Border Bases
نویسندگان
چکیده
Given X, a set of points whose coordinates are perturbed by errors, we want to determine a “numerically stable” basis B of the vanishing ideal I(X), i.e. for any permitted perturbation X̃ of the original set of points X, only slight changes to the coefficients in B are needed to produce a basis B̃ for the perturbed vanishing ideal I(X̃). We use border bases because they exhibit good numerical stability.
منابع مشابه
Stable normal forms for polynomial system solving
This paper describes and analyzes a method for computing border bases of a zero-dimensional ideal I . The criterion used in the computation involves specific commutation polynomials and leads to an algorithm and an implementation extending the one provided in [29]. This general border basis algorithm weakens the monomial ordering requirement for Gröbner bases computations. It is up to date the ...
متن کاملModule Border Bases
In this paper, we generalize the notion of border bases of zerodimensional polynomial ideals to the module setting. To this end, we introduce order modules as a generalization of order ideals and module border bases of submodules with finite codimension in a free module as a generalization of border bases of zero-dimensional ideals in the first part of this paper. In particular, we extend the d...
متن کاملMoment matrices, border bases and real radical computation
In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is finte. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and semi-definite programming. While the border basis algorithms of [17] are efficient and numerically stable for computing ...
متن کاملComprehensive Border Bases for Zero Dimensional Parametric Polynomial Ideals
In this paper, we extend the idea of comprehensive Gröbner bases given by Weispfenning (1992) to border bases for zero dimensional parametric polynomial ideals. For this, we introduce a notion of comprehensive border bases and border system, and prove their existence even in the cases where they do not correspond to any term order. We further present algorithms to compute comprehensive border b...
متن کاملComputing Border Bases without using a Term Ordering
Border bases, a generalization of Gröbner bases, have actively been researched during recent years due to their applicability to industrial problems. In [6] Kehrein and Kreuzer formulated the so called Border Basis Algorithm, an algorithm which allows the computation of border bases that relate to a degree compatible term ordering. In this paper we extend the original Border Basis Algorithm in ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008