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Towards More Accurate Separation Bounds of Empirical Polynomials II

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Computer Algebra in Scientific Computing (CASC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3718))

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Abstract

We study the problem of bounding a polynomial which is absolutely irreducible, away from polynomials which are not absolutely irreducible. These separation bounds are useful for testing whether an empirical polynomial is absolutely irreducible or not, for the given tolerance or error bound of its coefficients. In the former paper, we studied some improvements on Kaltofen and May’s method which finds applicable separation bounds using an absolute irreducibility criterion due to Ruppert. In this paper, we study the similar improvements on the method using the criterion due to Gao and Rodrigues for sparse polynomials satisfying Newton polytope conditions, by which we are able to find more accurate separation bounds, for such bivariate polynomials. We also discuss a concept of separation bound continuations for both dense and sparse polynomials.

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References

  1. Nagasaka, K.: Towards more accurate separation bounds of empirical polynomials. SIGSAM/CCA 38, 119–129 (2004)

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Author information

Authors and Affiliations

  1. Faculty of Human Development, Kobe University, Japan

    Kosaku Nagasaka

Authors
  1. Kosaku Nagasaka
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Editor information

Editors and Affiliations

  1. Institute of Informatics, Technische Universität München, Boltzmannstr. 3, 85748, Garching, Germany

    Victor G. Ganzha  & Ernst W. Mayr  & 

  2. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2005 Springer-Verlag Berlin Heidelberg

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Nagasaka, K. (2005). Towards More Accurate Separation Bounds of Empirical Polynomials II. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2005. Lecture Notes in Computer Science, vol 3718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11555964_27

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  • DOI: https://doi.org/10.1007/11555964_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28966-1

  • Online ISBN: 978-3-540-32070-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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