单变量Sigmoidal型神经网络的逼近  

On Approximation by Univariate Sigmoidal Neural Networks

作　　者：马国春[1] 虞旦盛[1] 周平 

机构地区：[1]杭州师范大学数学系,杭州310036 [2]Department of Mathematics,Statistics and Computer Science,St.Francis Xavier University

出　　处：《数学学报（中文版）》2014年第1期89-100,共12页Acta Mathematica Sinica：Chinese Series

基　　金：虞旦盛受国家自然科学基金(10901044);杭州师范大学优秀中青年教师支持计划项目资助;周平受加拿大NSERC资助

摘　　要：引入了一种新的sigmoidal型神经网络,给出了其对连续函数逼近的点态和整体估计.结果表明这种新的神经网络算子具有多项式逼近所不能达到的很好的逼近速度.为了改进对光滑函数的逼近速度,我们进一步引入了一种新的神经网络的线性组合,并给出了这种组合逼近的点态估计和整体估计.最后给出了一个数值例子.We first introduce a new type of neural network operators with sigmoidal functions, and give the pointwise and global estimates of the approximation by the networks. The new neural network operators can approximate the functions with a very good rate which can not be obtained by polynomial approximation. To further improve the approximation rate for functions of smoothness, we also introduce a new type of combinations of neural network operators, the approximation by the combinations. A our new method. and give pointwise and global estimates of numerical example is given to demonstrate

关 键 词：前向神经网络 sigmoidal函数 逼近速度 

分 类 号：O174.41[理学—数学]