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Mathematics of Computation

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A Generalized Discrepancy and
Quadrature Error Bound

Author: Fred J. Hickernell
Journal: Math. Comp. 67 (1998), 299-322
MSC (1991): Primary 65D30, 65D32
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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Additional Information

Fred J. Hickernell
Affiliation: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

Keywords: Figure of merit, multidimensional integration, number-theoretic nets and sequences, quasi-random sets, variation
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
Article copyright: © Copyright 1998 American Mathematical Society