Sur les formules de quadrature numérique à nombre minimal de noeuds d'intégration
type: Item
instance of: scholarly article
title: Sur les formules de quadrature numérique à nombre minimal de noeuds d'intégration
zbMATH Open document ID: 0579.65022
DOI: 10.1007/BF01389541
author: B. George
published in: Numerische Mathematik
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133123
review text: We search, from the orthogonal polynomial theory, for conditions which allow to obtain cubature formulas on sets of \({\mathbb{R}}^ n\) with weight function which have a minimal number of knots and which are exact on the space \(Q_ k\) of all polynomials of degree \(\leq k\) respectively to each variable \(x_ i\), \(1\leq i\leq n\). These results, completed by original numerical examples in \({\mathbb{R}}^ 2\), adapt to the spaces \(Q_ k\) these proved by \textit{H. J. Schmid} [ibid. 31, 281-297 (1978; Zbl 0427.65014)] in the case of polynomial spaces \(P_ k\).
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 3928191
zbMATH Keywords: cubature formulas
zbMATH Keywords: minimal number of knots
zbMATH Keywords: numerical examples
zbMATH Keywords: polynomial spaces
MaRDI profile type: Publication
cites work: Q4162607
cites work: A Construction of Nonnegative Approximate Quadratures
cites work: Q4060253
cites work: Cubature and the Tchakaloff cone
cites work: Quadrature Formulas over Fully Symmetric Planar Regions
cites work: Q3847247
cites work: Cubature formulas of degree eleven for symmetric planar regions
cites work: Q5613046
cites work: On cubature formulae with a minimal number of knots
cites work: Q4158394
cites work: Q5535928
cites work: Q3243490
cites work: A General Algorithm for Nonnegative Quadrature Formulas
OpenAlex ID: W2601434634
description: scientific article; zbMATH DE number 3928191