IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v36y2008i3p572-580.html
   My bibliography  Save this article

The estimation of simultaneous approximation order for neural networks

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007790700015X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.01.020?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kaslik, E. & Balint, St., 2009. "Bifurcation analysis for a discrete-time Hopfield neural network of two neurons with two delays and self-connections," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 83-91.
    2. Kaslik, E. & Balint, St., 2007. "Bifurcation analysis for a two-dimensional delayed discrete-time Hopfield neural network," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1245-1253.
    3. Yang, Yu & Ye, Jin, 2009. "Stability and bifurcation in a simplified five-neuron BAM neural network with delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2357-2363.
    4. Sangiorgio, Matteo & Dercole, Fabio, 2020. "Robustness of LSTM neural networks for multi-step forecasting of chaotic time series," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Wang, Hongbin & Jiang, Weihua, 2006. "Multiple stabilities analysis in a magnetic bearing system with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 789-799.
    6. Yang, Xiaofan & Yang, Maobin & Liu, Huaiyi & Liao, Xiaofeng, 2008. "Bautin bifurcation in a class of two-neuron networks with resonant bilinear terms," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 575-589.
    7. Zhang, Chunrui & Zheng, Baodong, 2007. "Stability and bifurcation of a two-dimension discrete neural network model with multi-delays," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1232-1242.
    8. Zheng, Baodong & Zhang, Yang & Zhang, Chunrui, 2008. "Stability and bifurcation of a discrete BAM neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 612-616.
    9. Zhang, Chunrui & Zu, Yuangang & Zheng, Baodong, 2006. "Stability and bifurcation of a discrete red blood cell survival model," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 386-394.
    10. Janmenjoy Nayak & Bighnaraj Naik, 2018. "A Novel Honey-Bees Mating Optimization Approach with Higher order Neural Network for Classification," Journal of Classification, Springer;The Classification Society, vol. 35(3), pages 511-548, October.
    11. Ait Maatallah, Othman & Achuthan, Ajit & Janoyan, Kerop & Marzocca, Pier, 2015. "Recursive wind speed forecasting based on Hammerstein Auto-Regressive model," Applied Energy, Elsevier, vol. 145(C), pages 191-197.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:36:y:2008:i:3:p:572-580. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.