17 citations · 48 across the 5 of their papers we have counts for
5 papers
Exponential tractability of -approximation with function values
David Krieg, Pawel Siedlecki, Mario Ullrich +1
We study the complexity of high-dimensional approximation in the -norm when different classes of information are available; we compare the power of function evaluations with t…
Exponential tractability of linear weighted tensor product problems in the worst-case setting for arbitrary linear functionals
Peter Kritzer, Friedrich Pillichshammer, Henryk Woźniakowski
We study the approximation of compact linear operators defined over certain weighted tensor product Hilbert spaces. The information complexity is defined as the minimal number of a…
Reproducing Kernels of Sobolev Spaces on and Applications to Embedding Constants and Tractability
Erich Novak, Mario Ullrich, Henryk Woźniakowski +1
The standard Sobolev space , with arbitrary positive integers and for which , has the reproducing kernel $$ K_{d,s}(x,t)=\int_{\mathbb{R}^d}\fra…
The Curse of Dimensionality for Monotone and Convex Functions of Many Variables
Aicke Hinrichs, Erich Novak, Henryk Woźniakowski
We study the integration and approximation problems for monotone and convex bounded functions that depend on variables, where can be arbitrarily large. We consider the wors…
On the power of function values for the approximation problem in various settings
Erich Novak, Henryk Woźniakowski
This is an expository paper on approximating functions from general Hilbert or Banach spaces in the worst case, average case and randomized settings with error measured in the $L_p…