The generalized and modified Halton sequences in Cantor bases

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F19%3A50015458" target="_blank" >RIV/62690094:18470/19:50015458 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s00605-018-1225-4" target="_blank" >https://link.springer.com/article/10.1007/s00605-018-1225-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00605-018-1225-4" target="_blank" >10.1007/s00605-018-1225-4</a>

Result language
angličtina
Original language name
The generalized and modified Halton sequences in Cantor bases
Original language description
This 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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