The generalized and modified Halton sequences in Cantor bases

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

The generalized and modified Halton sequences in Cantor bases

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

The generalized and modified Halton sequences in Cantor bases

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Monatshefte für Mathematik

ISSN

0026-9255

e-ISSN

—

Svazek periodika

188

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

AT - Rakouská republika

Počet stran výsledku

29

Strana od-do

1-29

Kód UT WoS článku

000454836600001

EID výsledku v databázi Scopus

2-s2.0-85059487852