An imbedded family of cubature formulae for \(n\)-dimensional product regions
type: Item
instance of: scholarly article
title: An imbedded family of cubature formulae for \(n\)-dimensional product regions
zbMATH Open document ID: 0821.65008
DOI: 10.1016/0377-0427(92)00007-V
author: Ronald Cools
author: Ann Haegemans
published in: Journal of Computational and Applied Mathematics
publication date: 1994-09-26T00:00:00Z
review text: An imbedded family of cubature formulae for \(n\)-dimensional fully symmetric product regions is developed in the manner of \textit{A. C. Genz} and \textit{A. A. Malik} [SIAM J. Numer. Anal. 20, 580-588 (1983; Zbl 0541.65012)]. A formula of degree \(2m + 1\) is based on \(m + 1\) generators obtained recursively. The \(n\)-dimensional cube and the whole of \(n\)- dimensional space with a Gaussian weight function are studied explicitly. Symbolic computation is used to obtain closed formulae for the (parameter-dependent) weights and points, enabling an investigation of the existence of formulae having positive weights and all points inside the region. Weights for the \(n\)-cube with degree \(\leq 7\), and for \(n\)- space with degree \(\leq 9\), are listed in tabular form.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 644311
zbMATH Keywords: imbedded sequence
zbMATH Keywords: symbolic computation
zbMATH Keywords: cubature formulae
zbMATH Keywords: fully symmetric product regions
zbMATH Keywords: Gaussian weight function
Wikidata QID: Q57779001
reviewed by: William E. Smith
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 644311