Function values are enough for L_2-approximation: Part II

11/03/2020

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by   David Krieg, et al.

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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.