由斜坡函数激发的神经网络算子逼近

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L~pa,b]空间逼近的正、逆定理.

Approximation by Neural Network Operators Activated by Smooth Ramp Functions

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 L^pa,b] spaces.