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