47 citations · 331 across the 35 of their papers we have counts for
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math.NA2013
On the randomized complexity of Banach space valued integration
Stefan Heinrich, Aicke Hinrichs
We study the complexity of Banach space valued integration in the randomized setting. We are concerned with -times continuously differentiable functions on the -dimensional u…
math.NA2013★ 21 cited
On Weak Tractability of the Clenshaw-Curtis Smolyak Algorithm
Aicke Hinrichs, Erich Novak, Mario Ullrich
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…
math.NA2013★ 47 cited
The Curse of Dimensionality for Numerical Integration of Smooth Functions II
Aicke Hinrichs, Erich Novak, Mario Ullrich +1
We prove the curse of dimensionality in the worst case setting for numerical integration for a number of classes of smooth -variate functions. Roughly speaking, we consider diff…