For a class F of complex-valued functions on a set D, we denote by gn (F) its sampling
numbers, ie, the minimal worst-case error on F, measured in L 2, that can be achieved with a …

We provide a new upper bound for sampling numbers (gn) n∈ N associated with the
compact embedding of a separable reproducing kernel Hilbert space into the space of …

In the first part we have shown that, for L 2-approximation of functions from a separable
Hilbert space in the worst-case setting, linear algorithms based on function values are …

We study the L_2 L 2-approximation of functions from a Hilbert space and compare the
sampling numbers with the approximation numbers. The sampling number e_n en is the …

We construct a least squares approximation method for the recovery of complex-valued
functions from a reproducing kernel Hilbert space on D⊂ R d. The nodes are drawn at …

We study multivariate approximation of periodic functions in the worst case setting with the
error measured in the L∞ norm. We consider algorithms that use standard information Λ std …

We show that independent and uniformly distributed sampling points are asymptotically as
good as optimal sampling points for the approximation of functions from Sobolev spaces on …

We study the circumradius of the intersection of an $ m $-dimensional ellipsoid $\mathcal E
$ with semi-axes $\sigma _1\geq\dots\geq\sigma _m $ with random subspaces of …

A novel linear integration rule called $\textit {control neighbors} $ is proposed in which
nearest neighbor estimates act as control variates to speed up the convergence rate of the …

This survey is concerned with the power of random information for approximation in the
(deterministic) worst-case setting, with special emphasis on information that is obtained …