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

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Book cover Mathematical Foundations of Computer Science 1977 (MFCS 1977)

Part of the book series: Lecture Notes in Computer Science ((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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References

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Authors and Affiliations

  1. Fachbereich Mathematik der Universität Frankfurt, Rob. Mayer-Str. 10, 6000, Frankfurt am Main

    C. P. Schnorr

Authors
  1. C. P. Schnorr
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Jozef Gruska

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© 1977 Springer-Verlag Berlin Heidelberg

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Schnorr, C.P. (1977). Improved lower bounds on the number of multiplications/divisions which are necessary to evaluate polynomials. In: Gruska, J. (eds) Mathematical Foundations of Computer Science 1977. MFCS 1977. Lecture Notes in Computer Science, vol 53. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08353-7_133

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  • DOI: https://doi.org/10.1007/3-540-08353-7_133

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08353-5

  • Online ISBN: 978-3-540-37285-1

  • eBook Packages: Springer Book Archive

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