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

collaborators

6 papers

math.FA2019

Entropy numbers of finite dimensional mixed-norm balls and function space embeddings with small mixed smoothness

Sebastian Mayer, Tino Ullrich

We study the embedding $id : ℓ_{p}^{b} (ℓ_{q}^{d}) \to ℓ_{r}^{b} (ℓ_{u}^{d})$ and prove matching bounds for the entropy numbers $e_{k} (id)$ provided that $0 < p < r \leq \infty$ an…

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…

math.DS2004

Immediate and Virtual Basins of Newton's Method for Entire Functions

Sebastian Mayer, Dierk Schleicher

We investigate the well known Newton method to find roots of entire holomorphic functions. Our main result is that the immediate basin of attraction for every root is simply connec…