Optimal quadrature for haar wavelet spaces

Stefan Heinrich*, Fred J. Hickernell, Rong Xian Yue

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

20 Citations (Scopus)


This article considers the error of the scrambled equidistribution quadrature rules in the worst-case, random-case, and average-case settings. The underlying space of integrands is a Hilbert space of multidimensional Haar wavelet series, ℋwav. The asymptotic orders of the errors are derived for the case of the scrambled (λ, t, m, s)-nets and (t, s)-sequences. These rules are shown to have the best asymptotic convergence rates for any random quadrature rule for the space of integrands ℋ wav.

Original languageEnglish
Pages (from-to)259-277
Number of pages19
JournalMathematics of Computation
Issue number245
Publication statusPublished - Jan 2004
Externally publishedYes

Scopus Subject Areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • High dimensional integration
  • Lower bounds
  • Monte Carlo methods
  • Quasi-Monte Carlo methods


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