The number of lattice rules
type: Item
instance of: scholarly article
title: The number of lattice rules
zbMATH Open document ID: 0679.65010
DOI: 10.1007/BF02219238
author: Tor Sørevik
author: James N. Lyness
published in: BIT
publication date: 1989-01-01T00:00:00Z
review text: The authors determine the number \(\nu_ s(N)\) of distinct N-point S- dimensional lattice rules. First, it is established that \(\nu_ s(MN)\leq \nu_ s(M)\nu_ s(N)\) equality being attained if and only if M and N are mutually prime; then this is used to establish that, when L has prime factor expansion \(\prod_{j}p_ j^{t_ j}\), then \(\nu_ s(L)=\prod_{j}\nu_ s(p_ j^{t_ j})\) where \(\nu_ s=\prod^{S- 1}_{i=1}[(p^{i+t}-1)/(p^ i-1)];\quad S\geq 1,\quad t\geq 0.\)
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 4113839
zbMATH Keywords: multi-dimensional integration
zbMATH Keywords: quadrature
zbMATH Keywords: cubature
zbMATH Keywords: lattice rules
reviewed by: Prem Narain
MaRDI profile type: Publication
cites work: Q5831393
cites work: An Introduction to Lattice Rules and their Generator Matrices
cites work: Lattice methods for multiple integration
full work available at URL: https://doi.org/10.1007/bf02219238
OpenAlex ID: W1981640951
description: scientific article; zbMATH DE number 4113839