7 papers
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…
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…
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 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 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…
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 r…