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TW 277

R. Cools, E. Novak and K. Ritter
Smolyak's construction of cubature formulas of arbitrary trigonometric degree

Abstract

We study cubature formulas for d-dimensional integrals with a high trigonometric degree. To obtain a trigonometric degree l in dimension d, we need about d sup l/l function values if d is large. Only a small number of arithmetical operations is needed to construct the cubature formulas using Smolyak's technique. We also compare different methods to obtain formulas with high trigonometric degree.