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 | 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