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

IF 0.4 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications Pub Date : 2023-12-07 DOI:10.1134/s1995423923040067

A. S. Popov

引用次数: 0

Abstract

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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寻找二十面体旋转群下球面不变的最佳立方公式

摘要描述了在球面上寻找在二十面体旋转组变换下不变的最佳（某种意义上）立方公式的过程。这种对称类型的最佳立方体公式的参数精确到第 30 级的 16 位有效数字。此外，还给出了一个表格，其中包含了迄今为止精确到第 79 阶的所有二十面体旋转组最佳立方体公式的主要特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Analysis and Applications MATHEMATICS, APPLIED-

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998. The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields. The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.