A useful result in searches for good vertex-modified number-theoretic rules
type: Item
instance of: scholarly article
title: A useful result in searches for good vertex-modified number-theoretic rules
zbMATH Open document ID: 0861.65017
DOI: 10.1016/0377-0427(96)00007-6
author: Stephen Joe
published in: Journal of Computational and Applied Mathematics
publication date: 1996-01-01T00:00:00Z
review text: This paper is concerned with how to efficiently search for good parameters for certain types of lattice rules for the numerical computation of multiple integrals. The work is based on a theorem of Korobov that can be used to restrict the search domain for lattice rules. The original theorem appeared in a Russian book and had not been widely known. It was rediscovered by the author, who provides a short proof. The theorem is applied to searches for the vertex-modified lattice rules that are useful for the integration of non-periodic functions. Searches to minimize quadratic discrepancy and searches to minimize vertex variance are both considered. In each case, it is shown that the application of the theorem can reduce the search time by a factor of approximately two.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 932493
zbMATH Keywords: number-theoretic rules
zbMATH Keywords: computation of multiple integrals
zbMATH Keywords: vertex-modified lattice rules
zbMATH Keywords: quadratic discrepancy
zbMATH Keywords: vertex variance
reviewed by: A. Genz
MaRDI profile type: Publication
full work available at URL: 0377-0427(96)00007-6
OpenAlex ID: W2050141816
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description: scientific article; zbMATH DE number 932493