Smolyak's Construction of Cubature Formulas of Arbitrary Trigonometric Degree
- Cite this article as:
- Cools, R., Novak, E. & Ritter, K. Computing (1999) 62: 147. doi:10.1007/s006070050018
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.