小波变换、神经网络和小波网络的函数逼近能力分析与比较

基于对小波变换和神经网络之间内在联系的分析，利用神经网络不同激励函数的线性组合构造出了相应的小波函数，得出小波函数作为神经网络的激励函数与普通神经网络的激励函数在本质上是一致的结论，并引入了小波网络。通过对小波变换，神经网络和小波网络函数逼近能力的理论分析与比较，认为小波网络在函数逼近方面具有明显的优势，并且分别利用这3种方式对一典型函数进行了仿真逼近的验证。

ANALYSIS AND COMPARISON OF FUNCTION APPROXIMATION ABILITY BASED ON WAVELET TRANSFORMATION, NEURAL NETWORK AND WAVELET NETWORK

Based on the analysis of inherent relations between wavelet transformation and neural network, the corresponding wavelet functions can be constructed by the linear combination of different neural network aviation functions. As neural network aviation functions, the wavelet functions are consistent with common neural network aviation functions. This paper introduces wavelet network and gives theoretical analysis and comparisons of function approximation ability of wavelet transformation, neural network and wavelet network. The wavelet network is considered as having distinct advantages. The function approximation simulations for a typical function with these three means are done to support the conclusion.