activity
20142022
most citedMonte Carlo Methods for Uniform Approximation on Periodic Sobolev Spaces with Mixed Smoothness

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

collaborators

6 papers

math.NA2022

-Sampling recovery for non-compact subclasses of

Glenn Byrenheid, Serhii A. Stasyuk, Tino Ullrich

In this paper we study the sampling recovery problem for certain relevant multivariate function classes which are not compactly embedded into . Recent tools relating the…

math.NA2022

Rate-optimal sparse approximation of compact break-of-scale embeddings

Glenn Byrenheid, Janina Hübner, Markus Weimar

The paper is concerned with the sparse approximation of functions having hybrid regularity borrowed from the theory of solutions to electronic Schrödinger equations due to Yserenta…

math.NA2017★ 5 cited

Monte Carlo Methods for Uniform Approximation on Periodic Sobolev Spaces with Mixed Smoothness

Glenn Byrenheid, Robert J. Kunsch, Van Kien Nguyen

We consider the order of convergence for linear and nonlinear Monte Carlo approximation of compact embeddings from Sobolev spaces of dominating mixed smoothness defined on the toru…

math.NA2016

Optimal sampling recovery of mixed order Sobolev embeddings via discrete Littlewood-Paley type characterizations

Glenn Byrenheid, Tino Ullrich

In this paper we consider the -approximation of multivariate periodic functions with -bounded mixed derivative (difference). The (possibly non-linear) reconstruction…

math.NA2015

Tight error bounds for rank-1 lattice sampling in spaces of hybrid mixed smoothness

Glenn Byrenheid, Lutz Kämmerer, Tino Ullrich +1

We consider the approximate recovery of multivariate periodic functions from a discrete set of function values taken on a rank- integration lattice. The main result is the fact…

math.NA2014

Sampling on energy-norm based sparse grids for the optimal recovery of Sobolev type functions in

Glenn Byrenheid, Dinh Dũng, Winfried Sickel +1

We investigate the rate of convergence of linear sampling numbers of the embedding . Here governs the mixed smoothness…