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 | References | Similar Articles | Additional Information
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 -star discrepancy and
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
Email:
fred@hkbu.edu.hk
DOI:
https://doi.org/10.1090/S0025-5718-98-00894-1
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