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arXiv · 1311.1393

Metric entropy, n-widths, and sampling of functions on manifolds

Martin Ehler·Frank Filbir
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Abstract

We first investigate on the asymptotics of the Kolmogorov metric entropy and nonlinear n-widths of approximation spaces on some function classes on manifolds and quasi-metric measure spaces. Secondly, we develop constructive algorithms to represent those functions within a prescribed accuracy. The constructions can be based on either spectral information or scattered samples of the target function. Our algorithmic scheme is asymptotically optimal in the sense of nonlinear n-widths and asymptotically optimal up to a logarithmic factor with respect to the metric entropy.

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Martin Ehler, Frank Filbir. 2013-11-06. Metric entropy, n-widths, and sampling of functions on manifolds. https://doi.org/10.1016/j.jat.2017.09.001

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