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Brauchart, Josef Dick","submitted_at":"2011-01-28T04:53:57Z","abstract_excerpt":"We study numerical integration on the unit sphere $\\mathbb{S}^2 \\subset \\mathbb{R}^3$ using equal weight quadrature rules, where the weights are such that constant functions are integrated exactly.\n  The quadrature points are constructed by lifting a $(0,m,2)$-net given in the unit square $[0,1]^2$ to the sphere $\\mathbb{S}^2$ by means of an area preserving map. A similar approach has previously been suggested by Cui and Freeden [SIAM J. Sci. Comput. 18 (1997), no. 2].\n  We prove three results. 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