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GPGCD, an Iterative Method for Calculating Approximate GCD, for Multiple Univariate Polynomials

  • Akira Terui
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6244)

Abstract

We present an extension of our GPGCD method, an iterative method for calculating approximate greatest common divisor (GCD) of univariate polynomials, to multiple polynomial inputs. For a given pair of polynomials and a degree, our algorithm finds a pair of polynomials which has a GCD of the given degree and whose coefficients are perturbed from those in the original inputs, making the perturbations as small as possible, along with the GCD. In our GPGCD method, the problem of approximate GCD is transferred to a constrained minimization problem, then solved with the so-called modified Newton method, which is a generalization of the gradient-projection method, by searching the solution iteratively. In this paper, we extend our method to accept more than two polynomials with the real coefficients as an input.

Keywords

Newton Method Full Rank Great Common Divisor Algebraic Computation Univariate Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Akira Terui
    • 1
  1. 1.Graduate School of Pure and Applied SciencesUniversity of TsukubaTsukubaJapan

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