PDF(475 KB)
PDF(475 KB)
PDF(475 KB)
由斜坡函数激发的神经网络算子逼近
Approximation by Neural Network Operators Activated by Smooth Ramp Functions
首先，引入一种由斜坡函数激发的神经网络算子，建立了其对连续函数逼近的正、逆定理，给出了其本质逼近阶.其次，引入这种神经网络算子的线性组合以提高逼近阶，并且研究了这种组合的同时逼近问题.最后，利用Steklov函数构造了一种新的神经网络算子，建立了其在Lp[a，b]空间逼近的正、逆定理.
Firstly, we introduce a kind of neural network operators by using a new smooth ramp function. We establish both the direct and converse results of approximation by the new operators, and thus give the essential approximation rate. Secondly, we use a linear combination of the new operators to improve the approximation rate for smooth functions. The uniform simultaneous approximation of the combination is also discussed. Finally, we introduce a new kind of neural network operators by using the Steklov functions, and establish both the direct and converse results of the approximation in Lp[a,b] spaces.
神经网络算子 / 插值 / 一致逼近 / 斜坡函数 / 同时逼近 {{custom_keyword}} /
neural netwrok operators / interpoltion / uniform approximation / ramp functions / simultaneous approximation {{custom_keyword}} /
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周平受加拿大自然科学及工程研究基金资助（NSERC）
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