Elsevier

Journal of Complexity

Volume 66, October 2021, 101569
Journal of Complexity

Function values are enough for L2-approximation: Part II

https://doi.org/10.1016/j.jco.2021.101569Get rights and content
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Abstract

In the first part we have shown that, for L2-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.

MSC

41A25
41A45
41A65
60B20
41A63

Keywords

L2-approximation
Information-based complexity
Least squares
Rate of convergence
Random matrices
Kadison-Singer

Cited by (0)

Communicated by E. Novak.