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Approximate GCD in a Bernstein Basis

  • Robert M. Corless
  • Leili Rafiee SevyeriEmail author
Conference paper
  • 61 Downloads
Part of the Communications in Computer and Information Science book series (CCIS, volume 1125)

Abstract

We adapt Victor Y. Pan’s root-based algorithm for finding approximate GCD to the case where the polynomials are expressed in Bernstein bases. We use the numerically stable companion pencil of Guðbjörn Jónsson to compute the roots, and the Hopcroft-Karp bipartite matching method to find the degree of the approximate GCD. We offer some refinements to improve the process.

Keywords

Bernstein basis Approximate GCD Maximum matching Bipartite graph Root clustering Companion pencil 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Ontario Research Centre for Computer Algebra, School of Mathematical and Statistical SciencesWestern UniversityLondonCanada

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