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Constructive approximation to real function by wavelet neural networks

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Abstract

We present a type of single-hidden layer feed-forward wavelet neural networks. First, we give a new and quantitative proof of the fact that a single-hidden layer wavelet neural network with n + 1 hidden neurons can interpolate n + 1 distinct samples with zero error. Then, without training, we constructed a wavelet neural network X a (x, A), which can approximately interpolate, with arbitrary precision, any set of distinct data in one or several dimensions. The given wavelet neural network can uniformly approximate any continuous function of one variable.

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Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha, 410083, China

    Hou Muzhou

  2. School of Mathematical Sciences and Computing Technology, Central South University, Changsha, 410083, China

    Hou Muzhou & Han Xuli

  3. State Key Laboratory of Petroleum Resource and Prospecting, China University of Petroleum, Beijing, China

    Gan Yixuan

Authors
  1. Hou Muzhou
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  2. Han Xuli
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  3. Gan Yixuan
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Correspondence to Hou Muzhou.

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Muzhou, H., Xuli, H. & Yixuan, G. Constructive approximation to real function by wavelet neural networks. Neural Comput & Applic 18, 883–889 (2009). https://doi.org/10.1007/s00521-008-0194-2

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  • DOI: https://doi.org/10.1007/s00521-008-0194-2

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