We construct Monte Carlo methods for the $L^2$-approximation in Hilbert spaces of multivariate functions sampling no more than $n$ function values of the target function. Their errors catch up with the rate of convergence and the preasymptotic behavior of the error of any algorithm sampling $n$ pieces of arbitrary linear information, including function values.
Tractability of the approximation of high-dimensional rank one tensors
Tractability of $\mathbb{L}_2$-approximation in hybrid function spaces
A unified analysis of elliptic problems with various boundary conditions and their approximation
![QR code for arXiv:1705.04567 [math.NA]](http://oss.arxitics.com/images/favicon.svg)