BIT Numerical Mathematics

, Volume 34, Issue 2, pp 288–294 | Cite as

Optimal stochastic quadrature formulas for convex functions

  • E. Novak
  • K. Petras
Article

Abstract

We study optimal stochastic (or Monte Carlo) quadrature formulas for convex functions. While nonadaptive Monte Carlo methods are not better than deterministic methods, we prove that adaptive Monte Carlo methods are much better.

AMS subject classification

41A55 65C05 65D30 

Key words

numerical integration convex functions adaptive integration Monte Carlo methods 

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Copyright information

© the BIT Foundation 1994

Authors and Affiliations

  • E. Novak
    • 1
  • K. Petras
    • 2
  1. 1.Mathematisches InstitutUniversität Erlangen-NürnbergErlangenGermany
  2. 2.Institut für Angewandte MathematikTechnische Universität BraunschweigBraunschweigGermany

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