Verification of a low-degree polynomial vanishing at empirical points
Verification of a low-degree polynomial vanishing at empirical points
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DOI：
10.1016/j.apnum.2018.08.004
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发表时间：
2018-12
影响因子：
2.8
通讯作者：
Zhe Li;Zhe Li;Kai Zheng;Shugong Zhang
中科院分区：
文献类型：
--
作者：
Zhe Li;Zhe Li;Kai Zheng;Shugong Zhang
在Fassino和Torrente提出的LDP算法的基础上，给出了一种验证算法，该算法计算一个多项式，一个具有验证误差界的可容许摄动点集，从而保证多项式在计算的误差界内的一个微容许摄动点集消失。通过几个算例验证了算法的有效性。
Given a set of distinct empirical points with uniform tolerance, based on the LDP algorithm proposed by Fassino and Torrente, we provide a verification algorithm that computes a polynomial, an admissible perturbed point set with verified error bound, such that the polynomial is guaranteed to vanish at a slightly admissible perturbed point set within computed error bound. The effectiveness of our algorithm is demonstrated in several examples.