Estimates of Approximation Rates by Gaussian Radial-Basis Functions
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- 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
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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