The generalized and modified Halton sequences in Cantor bases
Dušan Bednařík , Poj Lertchoosakul , Diego Marques , Pavel Trojovský
AbstractThis paper aims to generalize results that have appeared in Atanassov (Math Balk New Ser 18(1–2):15–32, 2004). We consider here variants of the Halton sequences in a generalized numeration system, called the Cantor expansion, with respect to arbitrary sequences of permutations of the Cantor base. We first show that they provide a wealth of low-discrepancy sequences by giving an estimate of (star) discrepancy bound of the generalized Halton sequence in bounded Cantor bases. Then we impose certain conditions on the sequences of permutations of the Cantor base which are analogous, but not straightforward, to the modified Halton sequence introduced by E.I. Atanassov. We show that this modified Halton sequence in Cantor bases attains a better estimate of the (star) discrepancy bound than the generalized Halton sequence in Cantor bases.
|Journal series||Monatshefte Fur Mathematik, ISSN 0026-9255, (A 25 pkt)|
|Publication size in sheets||1.4|
|Keywords in English||Halton sequence, van der Corput sequence, Hammersley point set, low-discrepancy sequence, pseudorandom number, Cantor expansion|
|License||Other; published final; ; with publication|
|Score|| = 25.0, 22-01-2019, ArticleFromJournal|
= 25.0, 22-01-2019, ArticleFromJournal
|Publication indicators||: 2016 = 0.716 (2) - 2016=0.632 (5)|
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