Sampling discretization error for function classes

Abstract

The new ingredient of this paper is that we consider infinitely dimensional classes of functions and instead of the relative error setting, which was used in previous papers on norm discretization, we consider the absolute error setting. We demonstrate how known results from two areas of research -- supervised learning theory and numerical integration -- can be used in sampling discretization of the square norm on different function classes.

Cited by in corpus (2)

• Marcinkiewicz-type discretization of $L^p$-norms under the Nikolskii-type inequality assumption
• Sampling discretization and related problems