2005/09/05 by Hinrichs, Aicke, Novak, Erich · 1 citation
#65D32 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.math/0509101
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, 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.