Function values are enough for L2-approximation: Part II

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 linear widths 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. (C) 2021 The Author(s). Published by Elsevier Inc.

Automated summary

In this paper, a similar result is proven for separable Banach spaces and other classes of functions in the worst-case setting for L-2 approximation. It shows that linear algorithms based on function values can achieve the same polynomial rate of convergence as arbitrary linear algorithms if the linear widths are square-summable.