20 citations · 51 across the 12 of their papers we have counts for
14 papers
On bounds between all s-numbers and widths of convex sets
Mario Ullrich
We prove for every s-number sequence , every bounded linear operator between normed spaces, and every , where ar…
Constructive discretization and approximation in reproducing kernel Hilbert spaces
Abdellah Chkifa, Matthieu Dolbeault, David Krieg +1
We generalize the sparsification algorithm of Batson, Spielman and Srivastava, making one part of the result dimension-independent. In particular, we recover discretization inequal…
Approximation of Functions: Optimal Sampling and Complexity
David Krieg, Mario Ullrich
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numer…
Noisy nonlinear information and entropy numbers
David Krieg, Erich Novak, Leszek Plaskota +1
It is impossible to recover a vector from with less than linear measurements, even if the measurements are chosen adaptively. Recently, it has been shown that on…
Sampling and entropy numbers in the uniform norm
Mario Ullrich
We prove a sharp bound between sampling numbers and entropy numbers in the uniform norm for bounded convex sets of bounded functions.
Sparse grids vs. random points for high-dimensional polynomial approximation
Jakob Eggl, Elias Mindlberger, Mario Ullrich
We study polynomial approximation on a -cube, where is large, and compare interpolation on sparse grids, aka Smolyak's algorithm (SA), with a simple least squares method bas…
Nonlocal techniques for the analysis of deep ReLU neural network approximations
Cornelia Schneider, Mario Ullrich, Jan Vybiral
Recently, Daubechies, DeVore, Foucart, Hanin, and Petrova introduced a system of piece-wise linear functions, which can be easily reproduced by artificial neural networks with the…
How many continuous measurements are needed to learn a vector?
David Krieg, Erich Novak, Mario Ullrich
One can recover vectors from with arbitrary precision, using only continuous measurements that are chosen adaptively. This surprising res…
On the power of adaption and randomization
David Krieg, Erich Novak, Mario Ullrich
We present bounds on the maximal gain of adaptive and randomized algorithms over non-adaptive, deterministic ones for approximating linear operators on convex sets. If the sets are…
Inequalities between s-numbers
Mario Ullrich
Singular numbers of operators between Hilbert spaces were generalized to Banach spaces by s-numbers (in the sense of Pietsch). This allows for different choices, including approxim…
Sampling projections in the uniform norm
David Krieg, Kateryna Pozharska, Mario Ullrich +1
We show that there are sampling projections on arbitrary -dimensional subspaces of with at most samples and norm of order , where is the space of co…
On the power of iid information for linear approximation
Mathias Sonnleitner, Mario Ullrich
This survey is concerned with the power of random information for approximation in the (deterministic) worst-case setting, with special emphasis on information consisting of functi…
Function values are enough for -approximation: Part II
David Krieg, Mario Ullrich
In the first part we have shown that, for -approximation of functions from a separable Hilbert space in the worst-case setting, linear algorithms based on function values are…
Rapid mixing of Swendsen-Wang dynamics in two dimensions
Mario Ullrich
We prove comparison results for the Swendsen-Wang (SW) dynamics, the heat-bath (HB) dynamics for the Potts model and the single-bond (SB) dynamics for the random-cluster model on a…