Sampling discretization error for function classes
It provides a new theoretical framework for sampling discretization that extends prior work from relative to absolute error, benefiting researchers in approximation theory and numerical analysis.
This paper introduces an absolute error setting for sampling discretization of the square norm on infinite-dimensional function classes, leveraging results from supervised learning theory and numerical integration to derive new discretization bounds.
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.