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Improved lower bounds on the number of multiplications/divisions which are necessary to evaluate polynomials

  • C. P. Schnorr
Invited Lectures
Part of the Lecture Notes in Computer Science book series (LNCS, volume 53)

Abstract

We improve some lower bounds which have been obtained by Strassen and Lipton. In particular there exist polynomials of degree n with 0–1 coefficients that cannot be evaluated with less than \(\sqrt {n/}\)(4 log n) nonscalar multiplications/divisions. The evaluation of \(p(x) = \sum\limits_{\delta \doteq o}^n {e^{2\pi i/2^\delta } } x^\delta\)requires at least n/(12 log n) multiplications/divisions and at least \(\sqrt {n/ (8 log n)}\)nonscalar multiplications/divisions. We specify polynomials with algebraic coefficients that require n/2 multiplications/divisions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • C. P. Schnorr
    • 1
  1. 1.Fachbereich Mathematik der Universität FrankfurtFrankfurt am Main

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