Abstract:
An algorithm for finding the best cubature formulas (in a sense) on the sphere that are invariant under the transformations of the dihedral group of rotations D4 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.
Keywords:
numerical integration, invariant cubature formulas, invariant polynomials, dihedral group of rotations.
Citation:
A. S. Popov, “Cubature formulas on the sphere that are invariant under the transformations of the dihedral group of rotations D4”, Sib. Èlektron. Mat. Izv., 17 (2020), 964–970
\Bibitem{Pop20}
\by A.~S.~Popov
\paper Cubature formulas on~the~sphere that are invariant under~the~transformations of~the~dihedral group of~rotations~$D_4$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 964--970
\mathnet{http://mi.mathnet.ru/semr1265}
\crossref{https://doi.org/10.33048/semi.2020.17.071}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000551512900001}
Linking options:
https://www.mathnet.ru/eng/semr1265
https://www.mathnet.ru/eng/semr/v17/p964
This publication is cited in the following 2 articles:
A. S. Popov, “Poisk nailuchshikh kubaturnykh formul na sfere, invariantnykh otnositelno gruppy vraschenii ikosaedra”, Sib. zhurn. vychisl. matem., 26:4 (2023), 415–430
A. S. Popov, “Cubature Formulas on the Sphere That Are Invariant Under the Transformations of the Dihedral Groups of Rotations With Inversion”, Sib. Electron. Math. Rep., 18 (2021), 703–709
Citation in format AMSBIB
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