Different quality indexes for lattice rules
type: Item
instance of: scholarly article
title: Different quality indexes for lattice rules
zbMATH Open document ID: 0889.65015
author: Ronald Cools
author: A. V. Reztsov
published in: Journal of Complexity
publication date: 1998-06-02T00:00:00Z
review text: This paper is concerned with methods for comparing lattice rules for the numerical computation of multiple integrals. Lattice rules are exact for certain sets of trigonometric polynomials, and roughly speaking, the quality of a lattice rule depends on how efficient the rule is at exactly integrating classes of trigonometric monomials. The authors define hyperbolic, hexagonal, spherical and octahedral quality indices for lattice rules and prove extremal properties for these indices. The paper then focuses on two-dimensional rules. Some new rules are presented that form a minimal family of the octahedral index. The hyperbolic, hexagonal and spherical quality indices for the new rules are derived and compared with the spherical index for some rules whose generators depend on the convergents of a continued fraction.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 42A10
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 1069067
zbMATH Keywords: lattice rules
zbMATH Keywords: multiple integrals
zbMATH Keywords: trigonometric polynomials
zbMATH Keywords: octahedral index
zbMATH Keywords: spherical index
reviewed by: A. Genz
MaRDI profile type: Publication
Wikidata QID: Q57779033
full work available at URL: jcom.1997.0443
OpenAlex ID: W2041165402
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DOI: 10.1006/JCOM.1997.0443
DBLP publication ID: journals/jc/CoolsR97
description: scientific article; zbMATH DE number 1069067