Sebastian Mayer

activity

20042019

most citedThe recovery of ridge functions on the hypercube suffers from the curse of dimensionality

5 citations · 7 across the 4 of their papers we have counts for

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4 papers · 1 filter

math.NA2019★ 5 cited

The recovery of ridge functions on the hypercube suffers from the curse of dimensionality

Benjamin Doerr, Sebastian Mayer

A multivariate ridge function is a function of the form $f (x) = g (a^{T} x)$ , where $g$ is univariate and $a \in R^{d}$ . We show that the recovery of an un…

math.NA2015

Counting via entropy: new preasymptotics for the approximation numbers of Sobolev embeddings

Thomas Kühn, Sebastian Mayer, Tino Ullrich

In this paper, we reveal a new connection between approximation numbers of periodic Sobolev type spaces, where the smoothness weights on the Fourier coefficients are induced by a (…

math.NA2015★ 1 cited

Entropy numbers of spheres in Banach and quasi-Banach spaces

Aicke Hinrichs, Sebastian Mayer

We prove sharp upper bounds on the entropy numbers $e_{k} (S_{p}^{d - 1}, ℓ_{q}^{d})$ of the $p$ -sphere in $ℓ_{q}^{d}$ in the case $k \geq d$ and $0 < p \leq q \leq \infty$ . In particular, we…

math.NA2013★ 1 cited

Entropy and sampling numbers of classes of ridge functions

Sebastian Mayer, Tino Ullrich, Jan Vybiral

We study properties of ridge functions $f (x) = g (a \cdot x)$ in high dimensions $d$ from the viewpoint of approximation theory. The considered function classes consist of ridge functi…