Sampling on energy-norm based sparse grids for the optimal recovery of Sobolev type functions in $H^{\gamma }$

Glenn Byrenheid, Dinh Dũng, Winfried Sickel +1

We investigate the rate of convergence of linear sampling numbers of the embedding $H^{\alpha ,\beta }({\mathbb{T}}^d)\hookrightarrow H^{\gamma }({\mathbb{T}}^d)$. Here $\alpha$ governs the mixed smoothness…