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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Strong tractability of integration using scrambled Niederreiter points
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by Rong-Xian Yue and Fred J. Hickernell PDF
Math. Comp. 74 (2005), 1871-1893 Request permission


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 $\varepsilon$-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.
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Additional Information
  • Rong-Xian Yue
  • Affiliation: Division of Scientific Computation, E-Institute of Shanghai Universities, 100 Guilin Road, Shanghai 200234, People’s Republic of China
  • Email:
  • Fred J. Hickernell
  • Affiliation: Department of Applied Mathematics, Shanghai Normal University, Shanghai, People’s Republic of China
  • Address at time of publication: Department of Applied Mathematics, Illinois Institute of Technology, 10 West 32nd Street, E1 Building, Room 208, Chicago, Illinois 60616-3793
  • ORCID: 0000-0001-6677-1324
  • Email:,
  • Received by editor(s): November 24, 2003
  • Received by editor(s) in revised form: July 6, 2004
  • Published electronically: March 3, 2005
  • Additional Notes: This work was partially supported by Hong Kong Research Grants Council grant HKBU/2020/02P, National Science Foundation of China grant 10271078, E-Institute of Shanghai Municipal Education Commission (E03004), and the Special Funds for Major Specialties of the Shanghai Education Committee
  • © Copyright 2005 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 1871-1893
  • MSC (2000): Primary 65C05, 65D30
  • DOI:
  • MathSciNet review: 2164101