Estimates of Approximation Rates by Gaussian Radial-Basis Functions

Authors:
Paul C. Kainen;Věra Kůrková;Marcello Sanguineti
Affiliations:
Department of Mathematics, Georgetown University, Washington, D. C. 20057-1233, USA;Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, Prague 8, Czech Republic;Department of Communications, Computer, and System Sciences (DIST), University of Genoa, Via Opera Pia 13, 16145 Genova, Italy
Venue:
ICANNGA '07 Proceedings of the 8th international conference on Adaptive and Natural Computing Algorithms, Part II
Year:
2007

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Abstract

Rates of approximation by networks with Gaussian RBFs with varying widths are investigated. For certain smooth functions, upper bounds are derived in terms of a Sobolev-equivalent norm. Coefficients involved are exponentially decreasing in the dimension. The estimates are proven using Bessel potentials as auxiliary approximating functions.