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On the Quality of Some Root-Bounds

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Mathematical Aspects of Computer and Information Sciences (MACIS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9582))

Abstract

Bounds for the maximum modulus of all positive (or all complex) roots of a polynomial are a fundamental building block of algorithms involving algebraic equations. We apply known results to show which are the salient features of the Lagrange (real) root-bound as well as the related bound by Fujiwara. For a polynomial of degree n, we construct a bound of relative overestimation at most 1.72n which overestimates the Cauchy root by a factor of two at most. This can be carried over to the bounds by Kioustelidis and Hong. Giving a very short variant of a recent proof presented by Collins, we sketch a way to further definite, measurable improvement.

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Authors and Affiliations

  1. Institute for Reliable Computing, Hamburg University of Technology, Schwarzenbergstraße 95, 21071, Hamburg, Germany

    Prashant Batra

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  1. Prashant Batra
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Correspondence to Prashant Batra .

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Editors and Affiliations

  1. Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  2. Hamburg University of Technology, Hamburg, Germany

    Siegfried M. Rump

  3. New York University, New York, New York, USA

    Chee K. Yap

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Batra, P. (2016). On the Quality of Some Root-Bounds. In: Kotsireas, I., Rump, S., Yap, C. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2015. Lecture Notes in Computer Science(), vol 9582. Springer, Cham. https://doi.org/10.1007/978-3-319-32859-1_50

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  • DOI: https://doi.org/10.1007/978-3-319-32859-1_50

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32858-4

  • Online ISBN: 978-3-319-32859-1

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