On the Smolyak cubature error for analytic functions
The author examines the Smolyak cubature error for analytic functions in the Cartesian product of ellipses. Kronrod-Patterson quadrature formulae are proposed as the corresponding basic sequence and this choice is compared with Clenshaw-Curtis quadrature formulae. First, he calculates error bounds for the one-dimensional case, which lead by a recursion formula to error bounds for higher-dimensional integration. Finally, the author gives some numerical examples.
scientific article; zbMATH DE number 1419499