Integration of Multivariate Haar Wavelet Series

  • Stefan Heinrich
  • Fred J. Hickernell
  • Rong-Xian Yue
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2251)


This article considers the error of integrating multivariate Haar wavelet series by quasi-Monte Carlo rules using scrambled digital nets. Both the worst-case and random-case errors are analyzed. It is shown that scrambled net quadrature has optimal order. Moreover, there is a simple formula for the worst-case error.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Stefan Heinrich
    • 1
  • Fred J. Hickernell
    • 2
  • Rong-Xian Yue
    • 3
  1. 1.FB InformatikUniversität KaiserslauternKaiserslauternGermany
  2. 2.Department of MathematicsHong Kong Baptist UniversityKowloon TongHong Kong SAR, China
  3. 3.College of Mathematical ScienceShanghai Normal UniversityShanghaiChina

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