On some cubature formulas on the sphere

Jürgen Prestin; Daniela Roşca

doi:10.1016/j.jat.2006.02.001

On some cubature formulas on the sphere

Jürgen Prestin^*, Daniela Roşca

^*Corresponding author for this work

Institute of Mathematics

Technical University of Cluj-Napoca

5 Citations (Scopus)

Abstract

We construct interpolatory cubature rules on the two-dimensional sphere, using the fundamental system of points obtained by Laín Fernández [Polynomial Bases on the Sphere, Logos-Verlag, Berlin, 2003; Localized polynomial bases on the sphere, Electron. Trans. Numer. Anal. 19 (2005) 84-93]. The weights of the cubature rules are calculated explicitly. We also discuss the cases when this cubature leads to positive weights. Finally, we study the possibility to construct spherical designs and the degree of exactness.

Original language	English
Journal	Journal of Approximation Theory
Volume	142
Issue number	1
Pages (from-to)	1-19
Number of pages	19
ISSN	0021-9045
DOIs	https://doi.org/10.1016/j.jat.2006.02.001
Publication status	Published - 01.09.2006

Funding

Research supported by the EU Research Training Network MINGLE, HPRN-CT-1999-00117. ∗Corresponding author. E-mail addresses: [email protected] (J. Prestin), [email protected] (D. Ros¸ca).

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10.1016/j.jat.2006.02.001

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On some cubature formulas on the sphere

Abstract

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