On weak tractability of the Clenshaw�Curtis Smolyak algorithm

• Autores: Aicke Hinrichs, Erich Novak, Mario Ullrich
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 183, Nº 1, 2014, págs. 31-44
• Idioma: inglés
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• Resumen

  • We consider the problem of integration of d-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.