6 papers
Nonlinear approximation with adaptive dictionaries
V. Temlyakov
It is well known that the study of the Kolmogorov widths of a function class, which is the image of the unit ball of the space of an integral operator with the kernel $…
A survey of sampling discretization of integral and uniform norms
F. Dai, E. Kosov, V. Temlyakov
This paper surveys recent developments in the sampling discretization of integral and uniform norms for functions in general finite-dimensional spaces. These results generalize the…
A survey on sampling recovery
F. Dai, V. Temlyakov
The reconstruction of unknown functions from a finite number of samples is a fundamental challenge in pure and applied mathematics. This survey provides a comprehensive overview of…
Sampling recovery on classes defined by integral operators and sparse approximation with adaptive dictionaries
V. Temlyakov
In this paper we continue to develop the following general approach. We study asymptotic behavior of the errors of sampling recovery not for an individual smoothness class, how it…
Entropy numbers of classes defined by integral operators
V. Temlyakov
In this paper we develop the following general approach. We study asymptotic behavior of the entropy numbers not for an individual smoothness class, how it is usually done, but for…
Some lower bounds for optimal sampling recovery of functions with mixed smoothness
A. Gasnikov, V. Temlyakov
Recently, there was a substantial progress in the problem of sampling recovery on function classes with mixed smoothness. Mostly, it has been done by proving new and sometimes opti…