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Function approximation is one of the most important parts of the theory of functions which plays a very important role in the numerical computation. Using neural network to implement function approximation provides a new way to the development of function approximation.There are many advantages of using neural network to implement function approximation: First, it provides a standard approximation structure and approximation tool that can achieve arbitrary accuracy by changing the numbers of hidden layer; Second, there is a standard learning algorithm to determine the parameters of the approximation of functions, and the process is anthropopathic, namely a good simulation of the human learning process; Finally, it can deal with a wide range of data objects, such as a very large scale, highly non-linear, and incomplete data set.This paper takes several types of neural networks as the example(the BP neural network, the RBF neural network, the Orthogonal neural network and the Spline neural network).To study the methods of function approximation based on neural networks. The ability of function approximation is influenced by the numbers of neurons, learning rate, training objectives and so on. Therefore, to make a full use of the nonlinear approximation ability of neural networks in the process of the study, we should, first, make a study of structures and algorithms of the several neural networks, and then aiming at several kinds of conventional function curves, such as sine function, exponential function, logarithmic function, triangle waves and so on, compare experiment results of function approximation with typical neural network respectively to get the selection law of Neural Networks. All the conclusions are proved effective after the actual simulation test.The method studied by the article has significant reference for the research of function approximation.
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