Construction of fully symmetric cubature formulae of degree 4k-3 for fully symmetric planar regions
type: Item
instance of: scholarly article
title: Construction of fully symmetric cubature formulae of degree 4k-3 for fully symmetric planar regions
zbMATH Open document ID: 0626.65017
DOI: 10.1016/0377-0427(87)90045-8
author: Ronald Cools
author: Ann Haegemans
published in: Journal of Computational and Applied Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The paper first outlines the T-method attributed to \textit{C. R. Morrow} and \textit{T. N. L. Patterson} [SIAM J. Numer. Analysis 15, No.5, 953-976 (1978; Zbl 0402.65013)] and to \textit{H. J. Schmid} [Multivariate approximation theory, Proc. Conf. Math. Res. Inst., Oberwolfach 1979, ISNM Vol. 51, 359-377 (1979; Zbl 0456.41026)]. This uses the connection between knots of a cubature formula for product regions and ideal theory. From this the authors develop their S-method. Using the ALTRAN formula manipulation system, they obtain several specific cubature formulas for the square, circle and the entire plane \((E_ 2^{r^ 2},E^ r_ 2)\). The 36 positive weights and abscissas of some rules of degree 13 are listed. Only two rules in this sequence of degree 17 have been constructed, and each has some negative weights. These, together with rules of degrees 5 and 9, are listed in the authors' corresponding Technical report TW71 of K. U. Leuven (1985).
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 4018217
zbMATH Keywords: fully symmetric cubature formulae
zbMATH Keywords: symmetric planar regions
zbMATH Keywords: polynomial ideal
zbMATH Keywords: T-method
zbMATH Keywords: S-method
zbMATH Keywords: ALTRAN formula manipulation system
zbMATH Keywords: positive weights
Wikidata QID: Q57779029
reviewed by: James N. Lyness
describes a project that uses: ALTRAN
MaRDI profile type: Publication
full work available at URL: 0377-0427(87)90045-8
OpenAlex ID: W2008954600
cites work: Q5789115
cites work: Construction of Cubature Formulas of Degree Seven and Nine Symmetric Planar Regions, Using Orthogonal Polynomials
cites work: Kubaturformeln mit minimaler Knotenzahl
cites work: Construction of Algebraic Cubature Rules Using Polynomial Ideal Theory
cites work: Q3905893
cites work: Q4158394
description: scientific article; zbMATH DE number 4018217