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 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 …

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 …

For m, n∈ N, let X=(X ij) i≤ m, j≤ n be a random matrix, A=(a ij) i≤ m, j≤ na real
deterministic matrix, and XA=(a ij X ij) i≤ m, j≤ n the corresponding structured random …

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 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 study the complexity of high-dimensional approximation in the L 2-norm when different
classes of information are available; we compare the power of function evaluations with the …

Function values are, in some sense,“almost as good” as general linear information for L 2-
approximation (optimal recovery, data assimilation) of functions from a reproducing kernel …

We study $ L_q $-approximation and integration for functions from the Sobolev space $ W^
s_p (\Omega) $ and compare optimal randomized (Monte Carlo) algorithms with algorithms …

It was recently shown by D. Krieg and M. Ullrich that, for L 2-approximation of functions from
a reproducing kernel Hilbert space, function values are almost as powerful as arbitrary linear …