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The Essential Approximation Order for Neural Networks with Trigonometric Hidden Layer Units

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Advances in Neural Networks - ISNN 2006 (ISNN 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3971))

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Abstract

There have been various studies on approximation ability of feedforward neural networks. The existing studies are, however, only concerned with the density or upper bound estimation on how a multivariate function can be approximated by the networks, and consequently, the essential approximation ability of networks cannot be revealed. In this paper, by establishing both upper and lower bound estimations on approximation order, the essential approximation ability of a class of feedforward neural networks with trigonometric hidden layer units is clarified in terms of the second order modulus of smoothness of approximated function.

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Author information

Authors and Affiliations

  1. Department of Information and Mathematics Sciences, College of Science, China Jiliang University, Hangzhou, Zhejiang, 310018, P.R. China

    Chunmei Ding & Feilong Cao

  2. Institute for Information and System Sciences, Faculty of Science, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, P.R. China

    Feilong Cao & Zongben Xu

Authors
  1. Chunmei Ding
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  2. Feilong Cao
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  3. Zongben Xu
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Editor information

Editors and Affiliations

  1. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China

    Jun Wang

  2. Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, 610054, Chengdu, P.R. China

    Zhang Yi

  3. Department of Electrical Engineering, University of Louisville, 40292, Louisville, KY, U.S.A

    Jacek M. Zurada

  4. Laboratory for Computational Biology, Shanghai Center for Systems Biomedicine, 800 Dong Chuan Rd., 200240, Shanghai, China

    Bao-Liang Lu

  5. School of Electrical and Electronic Engineering, University of Manchester, UK

    Hujun Yin

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© 2006 Springer-Verlag Berlin Heidelberg

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Ding, C., Cao, F., Xu, Z. (2006). The Essential Approximation Order for Neural Networks with Trigonometric Hidden Layer Units. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_11

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  • DOI: https://doi.org/10.1007/11759966_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34439-1

  • Online ISBN: 978-3-540-34440-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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