J. Vybíral

activity

20102023

most citedBig Data of Materials Science - Critical Role of the Descriptor

938 citations · 1.2k across the 21 of their papers we have counts for

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8 papers · 1 filter

math.NA2023★ 11 cited

New lower bounds for the integration of periodic functions

David Krieg, Jan Vybiral

We study the integration problem on Hilbert spaces of (multivariate) periodic functions. The standard technique to prove lower bounds for the error of quadrature rules uses bump fu…

math.NA2021

Lower bounds for integration and recovery in $L_{2}$

Aicke Hinrichs, David Krieg, Erich Novak +1

Function values are, in some sense, "almost as good" as general linear information for $L_{2}$ -approximation (optimal recovery, data assimilation) of functions from a reproducing ker…

math.NA2019

A variant of Schur's product theorem and its applications

Jan Vybíral

We show the following version of the Schur's product theorem. If $M = (M_{j, k})_{j, k = 1}^{n} \in R^{n \times n}$ is a positive semidefinite matrix with all entries on the diagona…

math.NA2018★ 4 cited

The minimal $k$ -dispersion of point sets in high-dimensions

Aicke Hinrichs, Joscha Prochno, Mario Ullrich +1

In this manuscript we introduce and study an extended version of the minimal dispersion of point sets, which has recently attracted considerable attention. Given a set $\mathscr P_…

math.NA2018

Learning general sparse additive models from point queries in high dimensions

Hemant Tyagi, Jan Vybiral

We consider the problem of learning a $d$ -variate function $f$ defined on the cube $[- 1, 1]^{d} \subset R^{d}$ , where the algorithm is assumed to have black box access to sampl…

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.NA2013

Weak and quasi-polynomial tractability of approximation of infinitely differentiable functions

Jan Vybiral

We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable function…

math.NA2010★ 5 cited

Learning Functions of Few Arbitrary Linear Parameters in High Dimensions

Massimo Fornasier, Karin Schnass, Jan Vybiral

Let us assume that $f$ is a continuous function defined on the unit ball of $R^{d}$ , of the form $f (x) = g (A x)$ , where $A$ is a $k \times d$ matrix and $g$ is a function of…