Weighted spherical semidesigns and cubature formulae for calculating integrals on a sphere |
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Authors: | N. O. Kotelina A. B. Pevnyi |
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Affiliation: | 1. Syktyvkar State University, Oktyabr’skii pr. 55, Syktyvkar, 167001, Russia
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Abstract: | In this paper we study weighted spherical semidesigns, i.e., systems of points on a sphere of a specific type. We propose a new proof of the necessary and sufficient condition for a system of points on a sphere to be a weighted spherical semidesign. This criterion gives new approaches to the construction of cubature formulae for calculating integrals over a sphere with the degree of accuracy of 5 and 9. |
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