Constructive approximation to real function by wavelet neural networks

Original Article

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 + 1 distinct samples with zero error. Then, without training, we constructed a wavelet neural network Xa(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.

Keywords

Wavelet neural networks Interpolation Uniform approximation 

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Copyright information

© Springer-Verlag London Limited 2008

Authors and Affiliations

  1. 1.School of Information Science and EngineeringCentral South UniversityChangshaChina
  2. 2.School of Mathematical Sciences and Computing TechnologyCentral South UniversityChangshaChina
  3. 3.State Key Laboratory of Petroleum Resource and ProspectingChina University of PetroleumBeijingChina

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