Counting Roots of a Polynomial in a Convex Compact Region by Means of Winding Number Calculation via Sampling
Counting Roots of a Polynomial in a Convex Compact Region by Means of Winding Number Calculation via Sampling
复制标题
采样绕数计算求凸紧区域多项式的根
DOI：
10.1007/978-3-030-26831-2_29
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Liang Zhao
中科院分区：
文献类型：
--
作者：
Vitaly Zaderman;Liang Zhao
在本文中，我们提出了一种用于计算缠绕数的新型有效算法，旨在计算复杂平面上凸区域中给定多项式的根的数量。该算法可用于在多项式根调格的细分算法中进行计数和排除测试，并且在应用方案中尤其有用，在应用程序方案中很难获得高精度多项式系数，但我们已经成功地通过使用较低的多项式评估来获得多项式评估。精确。我们提供算法的伪代码，证明其正确性以及其复杂性的估计。
In this paper we propose a novel efficient algorithm for calculating winding numbers, aiming at counting the number of roots of a given polynomial in a convex region on the complex plane. This algorithm can be used for counting and exclusion tests in a subdivision algorithms for polynomial root-finding, and would be especially usefull in application scenarios where high-precision polynomial coefficients are hard to obtain but we succeed with counting already by using polynomial evaluation with lower precision. We provide the pseudo code of the algorithm, proof of its correctness as well as estimation of its complexity.
DOI：
10.1007/978-3-319-96418-8_28
发表时间：
2018
期刊：
International Congress on Mathematical Software (ICMS
影响因子：
--
作者：
Imbach, Rémi;Pan, Victor;Yap, Chee
通讯作者：
Yap, Chee