Strong tractability of integration using scrambled niederreiter points

Rong Xian Yue*, Fred J. Hickernell

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

9 Citations (Scopus)


We study the randomized worst-case error and the randomized error of scrambled quasi-Monte Carlo (QMC) quadrature as proposed by Owen. The function spaces considered in this article are the weighted Hilbert spaces generated by Haar-like wavelets and the weighted Sobolev-Hilbert spaces. Conditions are found under which multivariate integration is strongly tractable in the randomized worst-case setting and the randomized setting, respectively. The ε-exponents of strong tractability are found for the scrambled Niederreiter nets and sequences. The sufficient conditions for strong tractability for Sobolev spaces are more lenient for scrambled QMC quadratures than those for deterministic QMC net quadratures.

Original languageEnglish
Pages (from-to)1871-1893
Number of pages23
JournalMathematics of Computation
Issue number252
Early online date3 Mar 2005
Publication statusPublished - Oct 2005
Externally publishedYes

Scopus Subject Areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Multivariate integration
  • Nets and sequences
  • Quasi-Monte Carlo methods
  • Scrambling


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