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

JOURNAL OF APPROXIMATION THEORY

卷:225

Article

Ehler, Martin¹  Filbir, Frank^2,3 

[1] Univ Vienna, Dept Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[2] Tech Univ Miinchen, Fac Math, Boltzmannstr 3, D-85748 Garching, Germany

[3] Helmholtz Zentrum Munchen, Ingolstadter Landstr 1, D-85764 Neuherberg, Germany

关键词: Diffusion measure space;    Diffusion polynomials;    Sampling;    Metric entropy;   

DOI  :  10.1016/j.jat.2017.09.001

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free