%0 Journal Article
%T Lp Simultaneous Approximation by Neural Networks with One Hidden Layer<br>单隐层神经网络的Lp同时逼近
%A CAO Fei-Long
%A LI You-Mei
%A XU Zong-Ben
%A <br>曹飞龙
%A 李有梅
%A 徐宗本
%J 软件学报
%D 2003
%I 
%X It is shown in this paper by a constructive method that for any Lebesgue integrable functions defined on a compact set in a multidimensional Euclidian space, the function and its derivatives can be simultaneously approximated by a neural network with one hidden layer. This approach naturally yields the design of the hidden layer and the convergence rate. The obtained results describe the relationship between the rate of convergence of networks and the numbers of units of the hidden layer, and generalize some known density results in uniform measure.
%K neural network
%K simultaneous approximation
%K hidden layer design
%K rate of convergence
%K Lebesgue measure<br>神经网络
%K 同时逼近
%K 隐层设计
%K 收敛速度
%K 勒贝格尺度
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=5B3AB970F71A803DEACDC0559115BFCF0A068CD97DD29835&cid=8240383F08CE46C8B05036380D75B607&jid=7735F413D429542E610B3D6AC0D5EC59&aid=C7835C208333C3C5&yid=D43C4A19B2EE3C0A&vid=F3583C8E78166B9E&iid=708DD6B15D2464E8&sid=498CA27CD8E53B72&eid=11C933E0BC2B8917&journal_id=1000-9825&journal_name=软件学报&referenced_num=0&reference_num=14