A good permutation for one-dimensional diaphony

Florian Pausinger; Wolfgang Ch Schmid

doi:10.1515/MCMA.2010.015

A good permutation for one-dimensional diaphony

Florian Pausinger^*, Wolfgang Ch Schmid

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

In this article we focus on two aspects of one-dimensional diaphony F(S ^σ _b, N) of generalised van der Corput sequences in arbitrary bases. First we give a permutation with the best distribution behaviour concerning the diaphony known so far. We improve a result of Chaix and Faure from 1993 from a value of 1.31574... for a permutation in base 19 to 1.13794... for our permutation in base 57. Moreover for an infinite sequence X and its symmetric version X̃, we analyse the connection between the diaphony F(X, N) and the L ₂-discrepancy L ₂(X̃, N) using another result of Chaix and Faure. Therefore we state an idea how to get a lower bound for the diaphony of generalised van der Corput sequences in arbitrary base b.

Original language	English
Pages (from-to)	307-322
Number of pages	16
Journal	Monte Carlo Methods and Applications
Volume	16
Issue number	3-4
DOIs	https://doi.org/10.1515/MCMA.2010.015
Publication status	Published - Dec 2010
Externally published	Yes

Keywords

Diaphony
Generalised van der Corput sequence

ASJC Scopus subject areas

Statistics and Probability
Applied Mathematics

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10.1515/MCMA.2010.015

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title = "A good permutation for one-dimensional diaphony",

abstract = "In this article we focus on two aspects of one-dimensional diaphony F(S σ b, N) of generalised van der Corput sequences in arbitrary bases. First we give a permutation with the best distribution behaviour concerning the diaphony known so far. We improve a result of Chaix and Faure from 1993 from a value of 1.31574... for a permutation in base 19 to 1.13794... for our permutation in base 57. Moreover for an infinite sequence X and its symmetric version {\~X}, we analyse the connection between the diaphony F(X, N) and the L 2-discrepancy L 2({\~X}, N) using another result of Chaix and Faure. Therefore we state an idea how to get a lower bound for the diaphony of generalised van der Corput sequences in arbitrary base b.",

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author = "Florian Pausinger and Schmid, \{Wolfgang Ch\}",

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AU - Pausinger, Florian

AU - Schmid, Wolfgang Ch

PY - 2010/12

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AB - In this article we focus on two aspects of one-dimensional diaphony F(S σ b, N) of generalised van der Corput sequences in arbitrary bases. First we give a permutation with the best distribution behaviour concerning the diaphony known so far. We improve a result of Chaix and Faure from 1993 from a value of 1.31574... for a permutation in base 19 to 1.13794... for our permutation in base 57. Moreover for an infinite sequence X and its symmetric version X̃, we analyse the connection between the diaphony F(X, N) and the L 2-discrepancy L 2(X̃, N) using another result of Chaix and Faure. Therefore we state an idea how to get a lower bound for the diaphony of generalised van der Corput sequences in arbitrary base b.

KW - Diaphony

KW - Generalised van der Corput sequence

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DO - 10.1515/MCMA.2010.015

M3 - Article

AN - SCOPUS:84858398287

SN - 0929-9629

VL - 16

SP - 307

EP - 322

JO - Monte Carlo Methods and Applications

JF - Monte Carlo Methods and Applications

IS - 3-4

ER -

A good permutation for one-dimensional diaphony

Abstract

Keywords

ASJC Scopus subject areas

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