Search for the Best Cubature Formulas on the Sphere Invariant under the Icosahedral Rotation Group

A process of searching on the sphere for the best (in a sense) cubature formulas that are invariant under the transformations of the icosahedral rotation group is described. The parameters of the best cubature formulas of this symmetry type up to the 30th order of accuracy are given to 16 significan...

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Bibliographic Details
Published in:Numerical analysis and applications Vol. 16; no. 4; pp. 348 - 358
Main Author: Popov, A. S.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.12.2023
Springer Nature B.V
Subjects:
Algorithms
Invariants
Mathematics
Mathematics and Statistics
Numerical Analysis
Polynomials
Rotation
Symmetry
invariant cubature formulas
invariant polynomials
numerical integration
icosahedral rotation group
ISSN:1995-4239, 1995-4247
Online Access:Get full text
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Summary:A process of searching on the sphere for the best (in a sense) cubature formulas that are invariant under the transformations of the icosahedral rotation group is described. The parameters of the best cubature formulas of this symmetry type up to the 30th order of accuracy are given to 16 significant digits. A table which contains the main characteristics of all the best to date cubature formulas of the icosahedral rotation group up to the 79th order of accuracy is given.
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ISSN:1995-4239
1995-4247
DOI:10.1134/S1995423923040067