Über die isotrope Diskrepanz von Folgen. (On the isotropic discrepancy of sequences)
type: Item
instance of: scholarly article
title: Über die isotrope Diskrepanz von Folgen. (On the isotropic discrepancy of sequences)
zbMATH Open document ID: 0568.10029
DOI: 10.1007/BF01194190
author: Gerhard Larcher
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: The isotropic discrepancy of a finite sequence \(w:=x_ 1,x_ 2,...,x_ N\) in the s-dimensional unit cube \(I^ s\) is defined by \(\sup_{C}| (A_ N(C)/N)-\lambda (C)|\) where the supremum is taken over all convex subsets C of \(I^ s\), \(A_ N(C)\) denotes the number of \(x_ i\) with \(x_ i\in C\) and \(\lambda\) is the s-dimensional Lebesgue measure. A method for estimating the isotropic discrepancy of a sequence directly is given, and is used for improving the known estimates for some of the most important sequences, as for example: The Hammersley sequence, the s- dimensional Halton sequence, the rotation on the s-dimensional torus.
Mathematics Subject Classification ID: 11K06
zbMATH DE Number: 3906593
zbMATH Keywords: uniform distribution of sequences
zbMATH Keywords: isotropic discrepancy
zbMATH Keywords: Hammersley sequence
zbMATH Keywords: s-dimensional Halton sequence
zbMATH Keywords: rotation on the s-dimensional torus
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3906593