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dc.contributor.authorGorban, Alexander N.-
dc.contributor.authorTyukin, Ivan Yu.-
dc.contributor.authorProkhorov, D. V.-
dc.contributor.authorSofeikov, Konstantin I.-
dc.identifier.citationarXiv:1506.04631 [cs.NA]en
dc.descriptionarXiv admin note: text overlap with arXiv:0905.0677 MSC classes: 41A45, 41A45, 90C59, 92B20, 68W20en
dc.description.abstractIn 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 $L_2$ norm of order $O(1/N)$, where $N$ is the number of elements. We show that both strategies are successful providing that additional information about the families of functions to be approximated is provided at the stages of learning and practical implementation. In 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.en
dc.subjectNumerical Analysis (cs.NA)en
dc.subjectDiscrete Mathematics (cs.DM)en
dc.subjectRandom basesen
dc.subjectmeasure concentrationen
dc.subjectneural networksen
dc.titleApproximation with Random Bases: Pro et Contraen
dc.typeJournal Articleen
pubs.organisational-group/Organisation/COLLEGE OF SCIENCE AND ENGINEERINGen
pubs.organisational-group/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematicsen
Appears in Collections:Published Articles, Dept. of Mathematics

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