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A generalized discrepancy and quadrature error bound
Open accessAbstract
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 Lp-star discrepancy and Pα that arises in the study of lattice rules.
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Cited by
Hickernell, F. J. (2005) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess4085.pub2 · Cited by 21
Self-citationThe Trio Identity for Quasi-Monte Carlo Error
Hickernell, F. J. (2018) · Springer Proceedings in Mathematics & Statistics · doi:10.1007/978-3-319-91436-7_1 · Cited by 9
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Metadata
- Authors
- Hickernell, F.
- Venue
- Mathematics of Computation
- Publisher
- American Mathematical Society (AMS)
- Published
- 1998
- Volume
- 67
- Issue
- 221
- Pages
- 299-322
- ISSN
- 0025-5718 (ISSN-L)
- 1088-6842
- OpenAlex
- W2040396531
- Cited by
- 724
- References
- 0
- FWCI
- 15.01
- Type
- journal article
- Language
- en
- Open access
- bronze
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