Implementations of a New Theorem for Computing Bounds for Positive Roots of Polynomials

  • Authors:

  • A. Akritas;A. Strzeboński;P. Vigklas

  • Affiliations:

  • Department of Computer and Communication Engineering,  , 37 Glavani and 28th October, 38221, Volos, Greece;Wolfram Research, Inc, 100 Trade Center Drive, 61820-7237, Champaign, IL, USA;Department of Computer and Communication Engineering,  , 37 Glavani and 28th October, 38221, Volos, Greece

  • Venue:
  • Computing
  • Year:
  • 2006

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Abstract

Finding an upper bound for the positive roots of univariate polynomials is an important step of the continued fractions real root isolation algorithm. The revived interest in this algorithm has highlighted the need for better estimations of upper bounds of positive roots. In this paper we present a new theorem, based on a generalization of a theorem by D. Stefanescu, and describe several implementations of it – including Cauchy's and Kioustelidis' rules as well as two new rules recently developed by us. From the empirical results presented here we see that applying various implementations of our theorem – and taking the minimum of the computed values – greatly improves the estimation of the upper bound and hopefully that will affect the performance of the continued fractions real root isolation method.