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The estimation of simultaneous approximation order for neural networks

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  • Li, Fengjun
  • Xu, Zongben

Abstract

A three-layer feed forward artificial neural network with trigonometric hidden-layer units is constructed. The essential order of approximation for the network which can simultaneously approximate function and its derivatives is estimated and a theorem of saturation (the largest capacity of simultaneous approximation) is proved. These results can precisely characterize the approximation ability of the network and the relationship among the rate of simultaneous approximation, the topological structure of hidden-layer and the properties of approximated functions.

Suggested Citation

  • Li, Fengjun & Xu, Zongben, 2008. "The estimation of simultaneous approximation order for neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 572-580.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:3:p:572-580
    DOI: 10.1016/j.chaos.2007.01.020
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    References listed on IDEAS

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    1. Zhang, Chunrui & Zheng, Baodong, 2005. "Hopf bifurcation in numerical approximation of a n-dimension neural network model with multi-delays," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 129-146.
    2. Guerra, Fábio A. & Coelho, Leandro dos S., 2008. "Multi-step ahead nonlinear identification of Lorenz’s chaotic system using radial basis neural network with learning by clustering and particle swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 967-979.
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    Cited by:

    1. Qian, Yunyou & Yu, Dansheng, 2022. "Rates of approximation by neural network interpolation operators," Applied Mathematics and Computation, Elsevier, vol. 418(C).

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