Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4607100 | Journal of Approximation Theory | 2014 | 14 Pages |
Abstract
We consider the problem of integration of dd-variate analytic functions defined on the unit cube with directional derivatives of all orders bounded by 1. We prove that the Clenshaw–Curtis Smolyak algorithm leads to weak tractability of the problem. This seems to be the first positive tractability result for the Smolyak algorithm for a normalized and unweighted problem. The space of integrands is not a tensor product space and therefore we have to develop a different proof technique. We use the polynomial exactness of the algorithm as well as an explicit bound on the operator norm of the algorithm.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Aicke Hinrichs, Erich Novak, Mario Ullrich,