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The GPGCD Algorithm with the Bézout Matrix

Conference paper
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Part of the Lecture Notes in Computer Science book series (LNCS, volume 12291)

Abstract

For a given pair of univariate polynomials with real coefficients and a given degree, we propose a modification of the GPGCD algorithm, presented in our previous research, for calculating approximate greatest common divisor (GCD). In the proposed algorithm, the Bézout matrix is used in transferring the approximate GCD problem to a constrained minimization problem, whereas, in the original GPGCD algorithm, the Sylvester subresultant matrix is used. Experiments show that, in the case that the degree of the approximate GCD is large, the proposed algorithm computes more accurate approximate GCDs than those computed by the original algorithm. They also show that the computing time of the proposed algorithm is smaller than that of the SNTLS algorithm, which also uses the Bézout matrix, with a smaller amount of perturbations of the given polynomials and a higher stability.

Keywords

Approximate GCD GPGCD algorithm Bézout matrix Modified newton method 
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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Graduate School of Pure and Applied SciencesUniversity of TsukubaTsukubaJapan
  2. 2.Faculty of Pure and Applied SciencesUniversity of TsukubaTsukubaJapan

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