基于多分辨分析神经网络的函数逼近

基于小波分析的基本理论，提出了迭代求解Daubechies小波函数和尺度函数，并用多项式最小二乘曲线拟合离散数据点，得到小波函数和尺度函数的近似封闭解析式的方法。最后基于L^2的多分辨逼近思想，构造了基于尺度函数的多分辨分析网络，用迭代的梯度下降算法训练网络，并用此网络对有局部奇异性的函数进行学习，获得了很好的逼近效果。数值仿真结果表明：本文提出的方法是可行的，它避免了无封闭解析式的小波和尺度函数在实际应用中需要大量进行插值运算的繁琐和求导运 算的不便。

FUNCTION APPROXIMATION BASED ON MUITI-RESOLUTION NEURAL NETWORK

Based on the basic theory of wavelet analysis,a new method is presented to obtain Daubechies compactly orthogonal wavelet function and scaling function by iteration.These discrete data are fitted by polynomial Least Mean Square method,and then the Wavelet function and scaling function have an approximate closed analytic form.Finally based on L 2 multi-resolution analysis idea,a multi-resolution network is constructed by scaling function and trained by iterative gradient-descent algorithm.The network is used to learn the function of local singularity and better approximate result is obtained.Simulation results show that the proposed method of this paper is practicable and it can avoid complicatedness of numerous interpolation and inconvenience for derivation in practical application of wavelet function and scaling function without closed analytic form.