摘要
借助卷积逼近的工具研究前向神经网络对连续函数的逼近,构造了具有nd个神经元的一类神经网络,并证得用它逼近[0,1]d上的连续函数f(X)时,偏差是O{ω{f,n-d1+2}+n-d1+2‖f‖∞}.其中ω(f,δ)表示f(X)在[0,1]d上的连续模,‖f‖∞表示|f(X)|的极大值.
Discussed the approximation of continuous functions by the feed-forward artificial neural network with a tool of convolution approximation,which approximating the continuous function f(X) ind is the estimation error is O{ω{f,n-1d+2}+n-1d+2‖f‖∞}.Where ω(f,δ) is the continuity modulus of f(X) in d and ‖f‖∞ is the maximum of |f(X)|.
出处
《中国计量学院学报》
2011年第1期80-87,共8页
Journal of China Jiliang University
关键词
神经网络
卷积逼近
偏差估计
feed-forward artificial neural network
approximation by convolution
offset estimation
