On The Interpolation And Approximation For Feedforward Neural Networks With Single Hidden Layer

Artificial neural networks (ANNs) have wide applications in computational science, mathematics, engineering and so on. Many problems concerning the applications of neu-ral networks, such as pattern recognition and systems control, can be converted into the ones of approximating multi-variant functions by the ANNs. As a universal approxima-tor, ANNs, especially feedforward neural networks with single hidden layer(FNNs), have drown great attention. Interpolation is the one of important methods in approximation of function. In this paper, we focus on the exact interpolation for the FNNs, and study the density and complexity of FNNs in the different spaces. Some new results are obtained.The thesis is specified as followings:In Chapter1, the research background of the ANNs is introduced, and the motivation of studying FNNs is given. Some concepts used in this paper are also presented in this chapter.In Chapter2, for a set of interpolation sample, using a more general sigmoidal function, the condition of the existence of exact interpolation for FNNs is given. Then the approximate interpolation of neural network is constructed, and we estimate the errors between the exact and approximate interpolation neural networks.In Chapter3, based on the second chapter, with the Steklov mean function, the errors for the interpolation neural networks approximating Lebesgue integrable function are estimated by the modulus of smoothness in the Lp metric.