CUBATURE FORMULAS ON THE SPHERE THAT ARE INVARIANT UNDER THE TRANSFORMATIONS OF THE DIHEDRAL GROUPS OF ROTATIONS WITH INVERSION

被引：2

作者：

Popov, A. S. ^{[1
]}

机构：

[1] Inst Computat Math & Math Geophys SB RAS, 6 Akad Lavrenteva Ave, Novosibirsk 630090, Russia

来源：

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2021年 / 18卷

关键词：

numerical integration; invariant cubature formulas; invariant polynomials; dihedral group of rotations; RESPECT;

D O I：

10.33048/semi.2021.18.050

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An algorithm for finding the best cubature formulas (in a sense) on the sphere that are invariant under the transformations of the dihedral groups of rotations with inversion is described. This algorithm is applied for finding parameters of all the best cubature formulas of this symmetry type up to the 35th order of accuracy.

引用

页码：703 / 709

页数：7

共 29 条

[1] CUBATURE FORMULAS ON A SPHERE THAT ARE INVARIANT UNDER THE TRANSFORMATIONS OF THE DIHEDRAL GROUP OF ROTATIONS WITH INVERSION D3d
Popov, Anatolii Stepanovich
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2019, 16 : 1196 - 1204
[2] CUBATURE FORMULAS ON THE SPHERE THAT ARE INVARIANT UNDER THE TRANSFORMATIONS OF THE DIHEDRAL GROUP OF ROTATIONS D4
Popov, A. S.
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2020, 17 : 964 - 970
[3] Cubature Formulas on the Sphere that are Invariant under Dihedral Rotation Groups
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NUMERICAL ANALYSIS AND APPLICATIONS, 2025, 18 (01) : 78 - 85
[4] Cubature formulas on a sphere invariant under the dihedral group of rotations with inversion D-5d
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SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2018, 15 : 389 - 396
[5] CUBATURE FORMULAS ON A SPHERE INVARIANT UNDER THE DIHEDRAL GROUP OF ROTATIONS WITH INVERSION D4H
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SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2015, 12 : 457 - 464
[6] Cubature Formulas Invariant under the Icosahedral Group of Rotations with Inversion on a Sphere
Popov A.S.
Numerical Analysis and Applications, 2017, 10 (4) : 339 - 346
[7] On the construction of cubature formulas invariant under dihedral groups
É. A. Shamsiev
Ukrainian Mathematical Journal, 2008, 60 : 1153 - 1163
[8] ON THE CONSTRUCTION OF CUBATURE FORMULAS INVARIANT UNDER DIHEDRAL GROUPS
Shamsiev, E. A.
UKRAINIAN MATHEMATICAL JOURNAL, 2008, 60 (07) : 1153 - 1163
[9] CUBATURE FORMULAS ON A SPHERE INVARIANT UNDER THE TETRAHEDRAL GROUP WITH INVERSION
Popov, A. S.
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2014, 11 : 372 - 379
[10] CUBATURE FORMULAS FOR A SPHERE INVARIANT UNDER CYCLIC ROTATION GROUPS
POPOV, AS
RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING, 1994, 9 (06) : 535 - 546

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