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Old and New Nearly Optimal Polynomial Root-Finders

  • Victor Y. PanEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11661)

Abstract

Univariate polynomial root-finding has been studied for four millennia and still remains the subject of intensive research. Hundreds if not thousands of efficient algorithms for this task have been proposed and analyzed. Two nearly optimal solution algorithms have been devised in 1995 and 2016, based on recursive factorization of a polynomial and subdivision iterations, respectively, but both of them are superseded in practice by Ehrlich’s functional iterations. By combining factorization techniques with Ehrlich’s and subdivision iterations we devise a variety of new root-finders. They match or supersede the known algorithms in terms of their estimated complexity for root-finding on the complex plane, in a disc, and in a line segment and promise to be practically competitive.

Keywords

Polynomial root-finding Deflation Polynomial factorization Functional iterations Subdivision Real root-finding 

2000 Math. Subject Classification

65H05 26C10 30C15 

Notes

Acknowledgements

This research has been supported by NSF Grants CCF–1563942 and CCF–1733834 and PSC CUNY Award 69813 00 48.

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Copyright information

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Authors and Affiliations

  1. 1.Department of Computer ScienceLehman College of the City University of New YorkBronxUSA
  2. 2.Ph.D. Programs in Mathematics and Computer ScienceThe Graduate Center of the City University of New YorkNewYorkUSA

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