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Approximation Bounds by Neural Networks in L ω p [-4pt]

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Advances in Neural Networks – ISNN 2004 (ISNN 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3173))

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Abstract

We consider approximation of multidimensional functions by feedforward neural networks with one hidden layer of Sigmoidal units and a linear output. Under the Orthogonal polynomials basis and certain assumptions of activation functions in the neural network, the upper bounds on the degree of approximation are obtained in the class of functions considered in this paper. The order of approximation \(O(n^{-\frac{r}{d}}),\) d being dimension, n the number of hidden neurons, and r the natural number.

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Author information

Authors and Affiliations

  1. Institute for Information and System Science, Faculty of Science, Xi’an Jiaotong University, Xi’an, Shaan’xi, 710049, P.R. China

    Jianjun Wang & ZongBen Xu

  2. School of Management, Xi’an Jiaotong University, Xi’an, Shaan’xi, 710049, P.R. China

    Weijun Xu

Authors
  1. Jianjun Wang
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  2. ZongBen Xu
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  3. Weijun Xu
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Editor information

Editors and Affiliations

  1. School of Electronic and Information Engineering, Dalian University of Technology, 116023, Dalian, China

    Fu-Liang Yin

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

    Jun Wang

  3. School of Electronic and Information Engineering, Dalian University of Technology, 116023, Dalian, Liaoning, China

    Chengan Guo

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© 2004 Springer-Verlag Berlin Heidelberg

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Wang, J., Xu, Z., Xu, W. (2004). Approximation Bounds by Neural Networks in L ω p [-4pt]. In: Yin, FL., Wang, J., Guo, C. (eds) Advances in Neural Networks – ISNN 2004. ISNN 2004. Lecture Notes in Computer Science, vol 3173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28647-9_1

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  • DOI: https://doi.org/10.1007/978-3-540-28647-9_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22841-7

  • Online ISBN: 978-3-540-28647-9

  • eBook Packages: Springer Book Archive

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