The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Digital Nets and Sequences: Discrepancy Theory and Quasi–Monte Carlo Integration
Abstract
Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasi–Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method, quasi–Monte Carlo rules have increased in popularity, with many fruitful applications in mathematical practice. These rules require nodes with good uniform distribution properties, and digital nets and sequences in the sense of Niederreiter are known to be excellent candidates. Besides the classical theory, the book contains chapters on reproducing kernel Hilbert spaces and weighted integration, duality theory for digital nets, polynomial lattice rules, the newest constructions by Niederreiter and Xing and many more. The authors present an accessible introduction to the subject based mainly on material taught in undergraduate courses with numerous examples, exercises and illustrations.
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Cites
An algorithm for the machine calculation of complex Fourier series
Cooley, J. W., & Tukey, J. W. (1965) · Mathematics of Computation · doi:10.1090/s0025-5718-1965-0178586-1 · Cited by 13,154
On the distribution of points in a cube and the approximate evaluation of integrals
Sobol', I. M. (1967) · USSR Computational Mathematics and Mathematical Physics · doi:10.1016/0041-5553(67)90144-9 · Cited by 2,975
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The 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
Metadata
- Authors
- Dick, J., & Pillichshammer, F.
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 2010-09-09
- OpenAlex
- W598051755
- Cited by
- 681
- References
- 2
- FWCI
- 10.72
- Type
- book
- Language
- en
- Open access
- closed
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