The construction of good extensible Korobov rules
type: Item
instance of: scholarly article
title: The construction of good extensible Korobov rules
zbMATH Open document ID: 1131.11051
author: Josef Dick
author: Friedrich Pillichshammer
author: Benjamin J. Waterhouse
published in: Computing
publication date: 2007-03-28T00:00:00Z
review text: Given the point set \(P_s=\{h\vec z/n +\Delta: h=1,\dots,n-1\} \subset [0,1)^s\), where \(z=(1,a,\dots,a^{s_i-1})\) for some \(a\in \{1,2,\ldots, n-1\}\) and \(\Delta \in [0,1)^s\) is chosen i.i.d. the authors want to find \(a\) such that the worst case error for QMC-integration is small. As the authors point out, for applications it is important to find lattice rules that give small QMC-integration errors simultaneously in several dimensions \(\mathcal S=\{s_1,\dots, s_d\}\). In this sense the algorithm given in the paper finds good \(a\)'s. In the last section the authors give also numerical examples to confirm their algorithm.
reviewed by: Volker Ziegler
Mathematics Subject Classification ID: 11K45
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 65D30
zbMATH DE Number: 5138269
zbMATH Keywords: quasi-Monte-Carlo methods
zbMATH Keywords: lattice rules
zbMATH Keywords: Korobov rules
MaRDI profile type: Publication
full work available at URL: s00607-006-0216-9
OpenAlex ID: W2091172010
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DOI: 10.1007/S00607-006-0216-9
description: scientific article; zbMATH DE number 5138269