New averaging technique for approximating weighted integrals

L. Plaskota, G. W. Wasilkowski, Y. Zhao

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We consider a new averaging technique for studying the complexity of weighted multivariate integration problems. While the standard averaging requires that ∫D K (x, x) ρ (x) d x < ∞, our new technique works under a less restrictive condition ∫D sqrt(K (x, x)) ρ (x) d x < ∞. It allows us to conclude the existence of algorithms with the worst case errors bounded by O (n- 1 / 2) for a wider class of problems than the techniques used so far. It also leads to more refined sufficient conditions for tractability of the multivariate integration problems, as well as a new class of randomized algorithms with errors bounded by O (n- 1 sqrt(ln (ln (n)))).

Original languageEnglish
Pages (from-to)268-291
Number of pages24
JournalJournal of Complexity
Issue number3
StatePublished - Jun 2009

Bibliographical note

Funding Information:
The first author was partially supported by the Polish Ministry of Science and Higher Education under Grant 1 P03A 039 28. The second author was partially supported by the National Science Foundation under Grant DMS-0609703.


  • Multivariate weighted integration
  • Randomized setting
  • Tractability
  • Worst case setting

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • Mathematics (all)
  • Control and Optimization
  • Applied Mathematics


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