53 citations · 640 across the 36 of their papers we have counts for
4 papers · 1 filter
Complexity of Oscillatory Integration for Univariate Sobolev Spaces
Erich Novak, Mario Ullrich, Henryk Woźniakowski
We analyze univariate oscillatory integrals for the standard Sobolev spaces of periodic and non-periodic functions with an arbitrary integer . We find matching lower a…
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…
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…
Structure and eigenvalues of heat-bath Markov chains
Martin Dyer, Catherine Greenhill, Mario Ullrich
We prove that heat-bath chains (which we define in a general setting) have no negative eigenvalues. Two applications of this result are presented: one to single-site heat-bath chai…