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.
"Estimation of Approximating Rate for Neural Network in Spaces." J. Appl. Math. 2012 1 - 8, 2012. https://doi.org/10.1155/2012/636078