Publication
Title
Near-minimal cubature formulae on the disk
Author
Abstract
The construction of (near-)minimal cubature formulae on the disk is still a complicated subject on which many results have been published. We restrict ourselves to the case of radial weight functions and make use of a recent connection between cubature and the concept of multivariate spherical orthogonal polynomials to derive a new system of equations defining the nodes and weights of (near-)minimal rules for general degree m=2n−1,n≥2 . The approach encompasses all previous derivations. The new system is small and may consist of only (n+1)2/4 equations when n is odd and n(n+2)/4 equations when n is even. It is valid for general n and has a Prony-like structure. It may admit a unique solution (such as for n=3 ) or an infinity of solutions (such as for n=7 ). In Section 2, the new approach is described, whereas the new system is derived in Sections 3 and 4. All well-known (near-)minimal cubature rules can be reobtained. Some typical illustrations of how this works are given in Section 5. We expect that this unifying theory will shed new light on the topic of cubature, in particular with respect to the discovery of new bounds on the number of nodes and their connection with the zeros of multivariate orthogonal polynomials.
Language
English
Source (journal)
IMA journal of numerical analysis. - London, 1981, currens
Publication
London : 2019
ISSN
0272-4979 [print]
1464-3642 [online]
DOI
10.1093/IMANUM/DRX069
Volume/pages
39 :1 (2019) , p. 297-314
ISI
000491255100010
Full text (Publisher's DOI)
Full text (open access)
Full text (publisher's version - intranet only)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identifier
Creation 28.02.2018
Last edited 09.10.2023
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