Counting Roots of a Polynomial in a Convex Compact Region by Means of Winding Number Calculation via Sampling

  • Vitaly Zaderman
  • Liang ZhaoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11661)


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 useful 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 as well as a proof of its correctness.


Polynomial root-finding Winding number 



Our research has been supported by the NSF Grant CCF–1563942, NSF Grant CCF-1733834, and the PSC CUNY Award 69813 00 48.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Ph.D. Program in MathematicsThe Graduate Center of the City University of New YorkNew YorkUSA
  2. 2.Department of Computer ScienceThe Graduate Center of the City University of New YorkNew YorkUSA

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