Cubature formulae and polynomial ideals
type: Item
instance of: scholarly article
title: Cubature formulae and polynomial ideals
zbMATH Open document ID: 0954.65020
author: Yuan Xu
published in: Advances in Applied Mathematics
publication date: 2000-03-21T00:00:00Z
review text: The main purpose of this paper is to study the structure of cubature formulae using the notion of a polynomial ideal and its variety. The author proves that if \(I\) is a polynomial ideal generated by a proper set of \((2n-1)\) orthogonal polynomials and if the cardinality of the variety \(V(I)\) is equal to the codimension of \(I\), then there exists a cubature formula of degree \(2n-1\) based on the points in the variety. The result generalizes Gaussian cubature formulae. This result also offers a new method for constructing cubature formulae.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 1420092
zbMATH Keywords: cubature formulae
zbMATH Keywords: polynomial ideal
reviewed by: Dumitru Acu
MaRDI profile type: Publication
full work available at URL: aama.1999.0652
OpenAlex ID: W2071792624
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DOI: 10.1006/AAMA.1999.0652
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description: scientific article; zbMATH DE number 1420092