一般有界Sigmoidal函数神经网络的插值与逼近  

Interpolation and approximation for neural networks with a bounded general Sigmoidal function

作　　者：章莉[1] 谢林森[1] 陆文秀[1] 

机构地区：[1]浙江师范大学数理与信息工程学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2013年第3期270-276,共7页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(11171137);浙江省自然科学基金资助项目(Y6110676)

摘　　要：研究了一维欧氏空间中神经网络的插值问题.首先,对于一组插值样本和定义在R上的一般有界Sig-moidal激活函数,给出了精确插值的单隐层前向神经网络存在的条件;然后,构造了近似插值网络,给出了估计精确和近似插值网络之间的误差;最后,利用连续模作为度量,分别估计了两类网络对连续函数的逼近误差.The interpolation of neural networks in the set of interpolation sample, using a bounded general unidimensional Euclid space was discussed. First, for a Sigmoidal function defined on R as the activation func- tion, condition for existence of exact interpolation of feedforward neural networks with single hidden layer was given. Then the approximate interpolation of neural networks was constructed, the errors between the exact and approximate interpolation neural networks were estimated. Finally, by using the modulus of continuity of function as a metric, the errors for the interpolation neural networks approximating continuous function were also estimated.

关 键 词：一般有界Sigmoidal函数 神经网络 精确插值 近似插值 误差估计 

分 类 号：O174.41[理学—数学]