A generalized discrepancy and quadrature error bound

Hickernell, Fred

doi:10.1090/S0025-5718-98-00894-1

A generalized discrepancy and quadrature error bound

Author: Fred J. Hickernell
Journal: Math. Comp. 67 (1998), 299-322
MSC (1991): Primary 65D30, 65D32
DOI: https://doi.org/10.1090/S0025-5718-98-00894-1
MathSciNet review: 1433265
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Abstract: 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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