On strong tractability of weighted multivariate integration

Fred J. Hickernell, Ian H. Sloan, Grzegorz W. Wasilkowski

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We prove that for every dimension s and every number n of points, there exists a point-set Pn,s whose γ-weighted unanchored L discrepancy is bounded from above by C(b)/n1/2-b independently of s provided that the sequence γ = {γk} has ∑k=1 γka for some (even arbitrarily large) a. Here 6 is a positive number that could be chosen arbitrarily close to zero and C(b) depends on b but not on s or n. This result yields strong tractability of the corresponding integration problems including approximation of weighted integrals ∫Df(x)ρ(x)dx over unbounded domains such as D = ℝs. It also supplements the results that provide an upper bound of the form C√s/n when γk ≡ 1.

Original languageEnglish
Pages (from-to)1903-1911
Number of pages9
JournalMathematics of Computation
Issue number248
StatePublished - Oct 2004


  • Low discrepancy points
  • Tractability
  • Weighted integration
  • quasi-Monte Carlo methods

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics


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