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Efficiency of Quasi-Monte Carlo Algorithms for High Dimensional Integrals

  • Henryk Woźniakowski
Conference paper

Abstract

This paper reports recent progress and presents a few new results on the efficiency of quasi-Monte Carlo algorithms that use n function values for approximation of multivariate integration of high dimension d. We consider the worst case error of a quasi-Monte Carlo algorithm over the unit ball of a normed space of functions of d variables. We indicate for which spaces of functions there exist quasi-Monte Carlo algorithms whose worst case errors go to zero polynomially in n -1 and are independent of d or polynomially dependent on d.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Henryk Woźniakowski
    • 1
    • 2
  1. 1.Department of Computer ScienceColumbia UniversityNew YorkUSA
  2. 2.Institute of Applied Mathematics and MechanicsUniversity of WarsawWarszawaPoland

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