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Title: Approximation with Random Bases: Pro et Contra
Authors: Gorban, Alexander N.
Tyukin, Ivan Yu.
Prokhorov, D. V.
Sofeikov, Konstantin I.
First Published: 25-Sep-2015
Publisher: Elsevier
Citation: Information Sciences, 2016, 364–365, pp.129-145
Abstract: In this work we discuss the problem of selecting suitable approximators from families of parameterized elementary functions that are known to be dense in a Hilbert space of functions. We consider and analyze published procedures, both randomized and deterministic, for selecting elements from these families that have been shown to ensure the rate of convergence in L2 norm of order O(1/N), where N is the number of elements. We show that both randomized and deterministic procedures are successful if additional information about the families of functions to be approximated is provided. In the absence of such additional information one may observe exponential growth of the number of terms needed to approximate the function and/or extreme sensitivity of the outcome of the approximation to parameters. Implications of our analysis for applications of neural networks in modeling and control are illustrated with examples.
DOI Link: 10.1016/j.ins.2015.09.021
ISSN: 0020-0255
eISSN: 1872-6291
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2015 Elsevier Inc. All rights reserved. This manuscript version is made available after a 24-month embargo period from publication under the CC-BY-NC-ND 4.0 license
Description: arXiv admin note: text overlap with arXiv:0905.0677
Appears in Collections:Published Articles, Dept. of Mathematics

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