Mario Ullrich

activity

20242026

collaborators

10 papers

math.FA2026

On bounds between all s-numbers and widths of convex sets

Mario Ullrich

We prove $a_{n} (S) \leq e (n + 1) s_{n} (S)$ for every s-number sequence $(s_{n})$ , every bounded linear operator $S$ between normed spaces, and every $n \in N_{0}$ , where $a_{n}$ ar…

math.NA2026

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…

math.NA2026

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…

math.NA2025

Noisy nonlinear information and entropy numbers

David Krieg, Erich Novak, Leszek Plaskota +1

It is impossible to recover a vector from $R^{m}$ with less than $m$ linear measurements, even if the measurements are chosen adaptively. Recently, it has been shown that on…

math.FA2025

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.

math.FA2025

Sampling projections in the uniform norm

David Krieg, Kateryna Pozharska, Mario Ullrich +1

We show that there are sampling projections on arbitrary $n$ -dimensional subspaces of $B (D)$ with at most $2 n$ samples and norm of order $n$ , where $B (D)$ is the space of co…