Simple cubature formulas with high polynomial exactness
The authors study cubature formulas for \(d\)-dimensional integrals with arbitrary weight function of tensor product form. They construct formulas that yield a high polynomial exactness. If the degree of accuracy is fixed then the number of knots depends on the dimension in an order-optimal way. They derived cubature formulae which are universal, that means that the order of convergence is almost optimal for two different scales of function spaces. The construction is simple because only a small number of arithmetical operations is needed to compute the knots and the weights of the formulae.
scientific article; zbMATH DE number 1398359