, Volume 62, Issue 2, pp 147-162

Smolyak's Construction of Cubature Formulas of Arbitrary Trigonometric Degree

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Abstract.

We study cubature formulas for d-dimensional integrals with a high trigonometric degree. To obtain a trigonometric degree \(\ell\) in dimension d, we need about \(d^\ell/\ell !\) 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.

Received: April 8, 1998