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On the Number of Random Digits Required in MonteCarlo Integration of Definable Functions

  • César L. Alonso
  • Josè L. Montaña
  • Luis M. Pardo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3618)

Abstract

Semi-algebraic objects are subsets or functions that can be described by finite boolean combinations of polynomials with real coefficients. In this paper we provide sharp estimates for the the precision and the number of trials needed in the MonteCarlo integration method to achieve a given error with a fixed confidence when approximating the mean value of semi-algebraic functions. Our study extends to the functional case the results of P. Koiran ([7]) for approximating the volume of semi-algebraic sets.

Keywords

MonteCarlo algorithms discrepancy bounds learning theory Chebyshev inequalities semi-algebraic geometry 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • César L. Alonso
    • 1
  • Josè L. Montaña
    • 2
  • Luis M. Pardo
    • 2
  1. 1.Centro de Inteligencia ArtificialUniversidad de OviedoGijónSpain
  2. 2.Departamento de Matemáticas, Estadística y Computación, Facultad de CienciasUniversidad de CantabriaSpain

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