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Journal of Applied Mathematics
Volume 2012, Article ID 636078, 8 pages
http://dx.doi.org/10.1155/2012/636078
Research Article

Estimation of Approximating Rate for Neural Network in 𝐿𝑝𝑀 Spaces

1School of Mathematics & Statistics, Southwest University, Chongqing 400715, China
2Department of Mechanical Engineering, Taipei Chengshih University of Science and Technology, No.2 Xue-Yuan Rd., Beitou, Taipei 112, Taiwan

Received 13 February 2012; Accepted 27 March 2012

Academic Editor: Juan Manuel PeΓ±a

Copyright Β© 2012 Jian-Jun Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A class of Soblove type multivariate function is approximated by feedforward network with one hidden layer of sigmoidal units and a linear output. By adopting a set of orthogonal polynomial basis and under certain assumptions for the governing activation functions of the neural network, the upper bound on the degree of approximation can be obtained for the class of Soblove functions. The results obtained are helpful in understanding the approximation capability and topology construction of the sigmoidal neural networks.