摘要
讨论了一种神经网络算子f_n(x)=sum from -n^2 to n^2 (f(k/n))/(n~α)b(n^(1-α)(x-k/n)),对f(x)的逼近误差|f_n(x)-f(x)|的上界在f(x)为连续和N阶连续可导两种情形下分别给出了该网络算子逼近的Jackson型估计.
A kind of neural network operator f_n(x)=sum from -n^2 to n^2 (f(k/n))/(n~α)b(n^(1-α)(x-k/n)), is considered and the upper bounds of approximation errors |f_n(x)-f(x)| are discussed.The Jackson- type estimates are obtained respectively when f(x) being continuous and continuously differentiable for N-times.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2008年第1期79-85,共7页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(60473034)
浙江省自然科学基金(Y604003)
关键词
神经网络算子
连续模
逼近阶
neural network operator
modulus of continuity
order of approximation
