摘要
证明了具有单一隐层的神经网络在L_w^q的逼近,获得了网络逼近的上界估计和下界估计.这一结果揭示了神经网络在加权逼近的意义下,网络的收敛阶与隐层单元个数之间的关系,为神经网络的应用提供了重要的理论基础.
This paper presents the approximation ability of a feedforward neural network with a single hidden layer in L^qω, including the estimation of its approximation upper and lower bounds. Under the principle of the weighted approximation, the work shows the rela- tionship between the approximation precision of an underlying feedforward neural network and the number of hidden nodes. The crucial point provides a theoretical foundation for the applications of feedforward neural networks.
出处
《数学年刊（A辑）》
CSCD
北大核心
2009年第6期741-750,共10页
Chinese Annals of Mathematics
基金
国家973计划(No2007CB311000)
国家自然科学基金(No10726040
No10701062
No10826081)
教育部科学技术重点项目(No108176)
中国博士后基金(No20080431237)
重庆市科委自然科学基金(NoCSTC2009BB2306)资助的项目
关键词
逼近估计
神经网络
JACOBI权
Approximation estimation, Neural networks, Jacobi weights
