53 citations · 640 across the 36 of their papers we have counts for
37 papers
Sampling recovery in and other norms
David Krieg, Kateryna Pozharska, Mario Ullrich +1
We study the recovery of functions in various norms, including with , based on function evaluations. We obtain worst case error bounds for general classes of…
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…
A sharp upper bound for sampling numbers in
Matthieu Dolbeault, David Krieg, Mario Ullrich
For a class of complex-valued functions on a set , we denote by its sampling numbers, i.e., the minimal worst-case error on , measured in , that can be achi…
On the worst-case error of least squares algorithms for -approximation with high probability
Mario Ullrich
It was recently shown in [4] that, for -approximation of functions from a Hilbert space, function values are almost as powerful as arbitrary linear information, if the approxi…
On the fixed volume discrepancy of the Fibonacci sets in the integral norms
Vladimir Temlyakov, Mario Ullrich
This paper is devoted to the study of a discrepancy-type characteristic -- the fixed volume discrepancy -- of the Fibonacci point set in the unit square. It was observed recently t…
Function values are enough for -approximation
David Krieg, Mario Ullrich
We study the -approximation of functions from a Hilbert space and compare the sampling numbers with the approximation numbers. The sampling number is the minimal worst c…