From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules. (English) Zbl 1335.11063
The paper under review is a survey about van der Corput sequences and their generalizations in commemoration of 125th birthday of J.G. van der Corput. The authors give results on uniform distribution modulo 1 of the van der Corput sequence, generalizations and variants of the van der Corput sequence, and moreover multi-dimensional generalizations of the van der Corput sequence. The paper contains a comprehensive references list of earlier studies derived from van der Corput’s idea.
Reviewer: Yukio Ohkubo (Kagoshima)
MSC:
| 11K38 | Irregularities of distribution, discrepancy |
| 11K45 | Pseudo-random numbers; Monte Carlo methods |
| 11-02 | Research exposition (monographs, survey articles) pertaining to number theory |
Keywords:
van der Corput sequence; uniform distribution; discrepancy; generalized Halton sequence; \((t,s)\)-sequence; Niederreiter sequenceSoftware:
MinTReferences:
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