Component-by-component construction of good lattice rules with a composite number of points
type: Item
instance of: scholarly article
title: Component-by-component construction of good lattice rules with a composite number of points
zbMATH Open document ID: 1022.65006
author: F. Y. Kuo
author: Stephen Joe
published in: Journal of Complexity
publication date: 2003-05-14T00:00:00Z
review text: Results and algorithms of \textit{I. H. Sloan}, \textit{F. Y. Kuo} and \textit{S. Joe} [Math. Comput. 71, No. 240, 1609-1640 (2002; Zbl 1011.65001)] and of \textit{I. H. Sloan} and \textit{A. V. Reztsov} [Math. Comput. 71, No. 237, 263-273 (2002; Zbl 0985.65018)] are extended to lattice rules with composite number of quadrature points. In both weighted Korobov and weighted Sobolev spaces strong tractability is achieved. Numerical results show that the quasi-Monte Carlo rules so constructed are almost as good as rules with prime number of points.
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 1910728
zbMATH Keywords: Monte Carlo methods
zbMATH Keywords: rare event simulation
zbMATH Keywords: hitting probabilities
zbMATH Keywords: large deviations
zbMATH Keywords: numerical results
zbMATH Keywords: lattice rules
reviewed by: Radu Theodorescu
MaRDI profile type: Publication
full work available at URL: jcom.2002.0650
OpenAlex ID: W1991368063
cites work: Theory of Reproducing Kernels
cites work: Error bounds for rank 1 lattice quadrature rules modulo composites
cites work: Integration and approximation in arbitrary dimensions
cites work: Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces
cites work: Q4889887
cites work: On the step-by-step construction of quasi--Monte Carlo integration rules that achieve strong tractability error bounds in weighted Sobolev spaces
cites work: Constructing Randomly Shifted Lattice Rules in Weighted Sobolev Spaces
cites work: Component-by-component construction of good lattice rules
cites work: Tractability of multivariate integration for weighted Korobov classes
DOI: 10.1006/JCOM.2002.0650
description: scientific article; zbMATH DE number 1910728