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Metric entropy, n-widths, and sampling of functions on manifolds.
J. Approx. Theory 225, 41-57 (2018)
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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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Publication type Article: Journal article
Document type Scientific Article
Keywords Diffusion Measure Space ; Diffusion Polynomials ; Metric Entropy ; Sampling; Nonlinear Dimensionality Reduction; Sobolev Spaces; Approximation; Frames
ISSN (print) / ISBN 0021-9045
Journal Journal of Approximation Theory
Quellenangaben Volume: 225, Pages: 41-57
Publishing Place San Diego
Institute(s) Institute of Computational Biology (ICB)