Simple varieties for limited precision points
Simple varieties for limited precision points
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DOI：
10.1016/j.tcs.2012.10.024
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发表时间：
2013-04
期刊：
影响因子：
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通讯作者：
C. Fassino;M. Torrente
中科院分区：
文献类型：
--
作者：
C. Fassino;M. Torrente
给定一个有限集合X的分和宽容ε表示最大误差在每一个点的坐标,我们解决计算问题的一个简单的多项式zero-locus Z的f (f)“几乎”包含X的点,我们提出一个symbolic-numerical方法,从X和ε的知识,决定了一个多项式f的严格程度有限元素的最小程度的理想X然后消失,在定理4.3中,给出了证明Z(f)离X的每一点的距离小于ε的充分条件。该方法的有效性依赖于计算机代数和数值分析的经典结果的结合；通过若干实例说明了其有效性。
Given a finite set X of points and a tolerance ε representing the maximum error on the coordinates of each point, we address the problem of computing a simple polynomial f whose zero-locus Z(f) “almost” contains the points of X. We propose a symbolic–numerical method that, starting from the knowledge of X and ε, determines a polynomial f whose degree is strictly bounded by the minimal degree of the elements of the vanishing ideal of X. Then, in Theorem 4.3, we state the sufficient conditions for proving that Z(f) lies close to each point of X by less than ε. The validity of the proposed method relies on a combination of classical results of Computer Algebra and Numerical Analysis; its effectiveness is illustrated with a number of examples.