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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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A generalized discrepancy and quadrature error bound
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by Fred J. Hickernell PDF
Math. Comp. 67 (1998), 299-322 Request permission


An error bound for multidimensional quadrature is derived that includes the Koksma-Hlawka inequality as a special case. This error bound takes the form of a product of two terms. One term, which depends only on the integrand, is defined as a generalized variation. The other term, which depends only on the quadrature rule, is defined as a generalized discrepancy. The generalized discrepancy is a figure of merit for quadrature rules and includes as special cases the ${\mathcal L}^p$-star discrepancy and $P_\alpha$ that arises in the study of lattice rules.
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Additional Information
  • Fred J. Hickernell
  • Affiliation: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
  • ORCID: 0000-0001-6677-1324
  • Email:
  • Received by editor(s): April 5, 1996
  • Received by editor(s) in revised form: September 4, 1996
  • Additional Notes: This research was supported by a Hong Kong RGC grant 94-95/38 and HKBU FRG grant 95-96/II-01
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 299-322
  • MSC (1991): Primary 65D30, 65D32
  • DOI:
  • MathSciNet review: 1433265