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Additive Complexity

  • Peter Bürgisser
  • Michael Clausen
  • Mohammad Amin Shokrollahi
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 315)

Abstract

We prove Khovanskii’s theorem [300] which gives an upper bound on the number of non-degenerate real solutions of a system of n polynomial equations in n variables which depends only on n and the number of distinct terms occurring in the polynomials. This result is in fact a consequence of a more general result dealing with certain systems of transcendental equations. A variant of Rolle’s theorem and Bézout’s inequality enter in the proof. As a consequence we deduce Grigoriev’s and Risler’s lower bound [209, 438] on the additive complexity of a univariate real polynomial in terms of the number of its real roots.

Keywords

Real Root Regular Point Additive Complexity Univariate Polynomial Positive Real Root 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Peter Bürgisser
    • 1
  • Michael Clausen
    • 2
  • Mohammad Amin Shokrollahi
    • 2
    • 3
  1. 1.Institut für Mathematik Abt. Angewandte MathematikUniversität Zürich-IrchelZürichSwitzerland
  2. 2.Institut für Informatik VUniversität BonnBonnGermany
  3. 3.International Computer Science InstituteBerkeleyUSA

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