Cubature Formulas in Higher Dimensions
نویسندگان
چکیده
We study cubature formulas for d-dimensional integrals with an arbitrary symmetric weight function of tensor product form. We present a construction that yields a high polynomial exactness: for fixed degree l = 5 or l = 7 and large dimension d the number of knots is only slightly larger than the lower bound of Möller and much smaller compared to the known constructions. We also show, for any odd degree l = 2k+1, that the minimal number of points is almost independent of the weight function. This is also true for the integration over the (Euclidean) sphere. 2000 Mathematics Subject Classification: 65D32
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تاریخ انتشار 2008