Function values are enough for $L_2$-approximation: Part II

Abstract

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 almost as powerful as arbitrary linear algorithms if the approximation numbers are square-summable. That is, they achieve the same polynomial rate of convergence. In this sequel, we prove a similar result for separable Banach spaces and other classes of functions.

18 pages

References in corpus (2)

• On the worst-case error of least squares algorithms for $L_2$-approximation with high probability
• On optimal recovery in $L_2$

Cited by in corpus (2)

• A sharp upper bound for sampling numbers in $L_2$
• Sampling discretization and related problems