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The rate of approximation of Gaussian radial basis neural networks in continuous function space

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Abstract

There have been many studies on the dense theorem of approximation by radial basis feedforword neural networks, and some approximation problems by Gaussian radial basis feedforward neural networks (GRBFNs) in some special function space have also been investigated. This paper considers the approximation by the GRBFNs in continuous function space. It is proved that the rate of approximation by GRNFNs with n d neurons to any continuous function f defined on a compact subset K ⊂ ℝd can be controlled by ω(f,n −1/2), where ω(f, t) is the modulus of continuity of the function f.

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Authors and Affiliations

  1. Institute of Metrology and Computational Science, China Jiliang University, Hangzhou, 310018, P. R. China

    Ting Fan Xie & Fei Long Cao

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  1. Ting Fan Xie
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  2. Fei Long Cao
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Correspondence to Fei Long Cao.

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Supported by National Natural Science Foundation of China (Grant Nos. 61101240 and 61272023) and the Zhejiang Provincial Natural Science Foundation of China (Grant No. Y6110117)

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Xie, T.F., Cao, F.L. The rate of approximation of Gaussian radial basis neural networks in continuous function space. Acta. Math. Sin.-English Ser. 29, 295–302 (2013). https://doi.org/10.1007/s10114-012-1369-4

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  • DOI: https://doi.org/10.1007/s10114-012-1369-4

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