Simple Approximate Varieties for Sets of Empirical Points

Details Simple Approximate Varieties for Sets of Empirical Points Simple Approximate Varieties for Sets of Empirical Points

2010-08-02

arxiv.org/abs/1008.0274v2

Mathematics

Commutative Algebra

27 pages, 2 figures

Scientific paper

We present a symbolic-numeric approach for the analysis of a given set of noisy data, represented as a finite set $\X$ of limited precision points. Starting from $\X$ and a permitted tolerance $\varepsilon$ on its coordinates, our method automatically determines a low degree monic polynomial whose associated variety passes close to each point of $\X$ by less than the given tolerance $\varepsilon$.

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