Another step forward in searching for cubature formulae with a minimal number of knots for the square
type: Item
instance of: scholarly article
title: Another step forward in searching for cubature formulae with a minimal number of knots for the square
zbMATH Open document ID: 0628.65014
DOI: 10.1007/BF02247942
author: Ronald Cools
author: Ann Haegemans
published in: Computing
publication date: 1988-01-01T00:00:00Z
review text: The knots and weights of a cubature formula are determined by a system of nonlinear equations. The number of equations and unknowns can be reduced by imposing some structure on the formula. We are concerned with the construction of cubature formulae which are invariant under rotations. Using invariant theory, we obtain a smaller system of algebraically independent equations. This is used to construct cubature formulae for the square. One of the results is a 24-point formula of degree 11.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 4022464
zbMATH Keywords: cubature formula
zbMATH Keywords: invariant theory
zbMATH Keywords: 24-point formula of degree 11
zbMATH Keywords: rotation invariant
MaRDI profile type: Publication
Wikidata QID: Q57779022
cites work: The construction of three-dimensional invariant cubature formulae
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cites work: Construction of fully symmetric cubature formulae of degree 4k-3 for fully symmetric planar regions
cites work: Q3796619
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cites work: Kubaturformeln mit minimaler Knotenzahl
cites work: Perfectly Symmetric Two-Dimensional Integration Formulas with Minimal Numbers of Points
cites work: Error-Correcting Codes and Invariant Theory: New Applications of a Nineteenth-Century Technique
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DBLP publication ID: journals/computing/CoolsH88
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description: scientific article; zbMATH DE number 4022464