Estimates of Approximation Rates by Gaussian Radial-Basis Functions

  • Paul C. Kainen
  • Věra Kůrková
  • Marcello Sanguineti
Conference paper

DOI: 10.1007/978-3-540-71629-7_2

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4432)
Cite this paper as:
Kainen P.C., Kůrková V., Sanguineti M. (2007) Estimates of Approximation Rates by Gaussian Radial-Basis Functions. In: Beliczynski B., Dzielinski A., Iwanowski M., Ribeiro B. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2007. Lecture Notes in Computer Science, vol 4432. Springer, Berlin, Heidelberg

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.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Paul C. Kainen
    • 1
  • Věra Kůrková
    • 2
  • Marcello Sanguineti
    • 3
  1. 1.Department of Mathematics, Georgetown University, Washington, D. C. 20057-1233USA
  2. 2.Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, Prague 8Czech Republic
  3. 3.Department of Communications, Computer, and System Sciences (DIST), University of Genoa, Via Opera Pia 13, 16145 GenovaItaly

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