Journal of Applied Mathematics

Estimation of Approximating Rate for Neural Network in${L}_{w}^{p}$ Spaces

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 636078, 8 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.jam/1355495146

Digital Object Identifier
doi:10.1155/2012/636078

Mathematical Reviews number (MathSciNet)
MR2927253

Zentralblatt MATH identifier
1244.93155

Citation

Wang, Jian-Jun; Yang, Chan-Yun; Jing, Jia. Estimation of Approximating Rate for Neural Network in ${L}_{w}^{p}$ Spaces. J. Appl. Math. 2012 (2012), Article ID 636078, 8 pages. doi:10.1155/2012/636078. https://projecteuclid.org/euclid.jam/1355495146