p 同时逼近 李有梅 2, 徐宗本.pdfVIP

1000-9825/2003/14(11)1869 ©2003 Journal of Software 软 件 学 报 Vol.14, No.11 ∗ 单隐层神经网络的 Lp 同时逼近 1,2+ 2,3 2 曹飞龙 , 李有梅 , 徐宗本 1(绍兴文理学院 数理信息学院,浙江 绍兴 312000) 2(西安交通大学 理学院信息与系统科学研究所,陕西 西安 710049) 3( 山西大学 计算机系, 山西 太原 030006) p L Simultaneous Approximation by Neural Networks with One Hidden Layer CAO Fei-Long1,2+, LI You-Mei2,3, XU Zong-Ben2 1(School of Mathematical and Physical Information, Shaoxing College of Arts and Sciences, Shaoxing 312000, China) 2(Institute for Information and System Sciences, Faculty Science, Xi’an Jiaotong University, Xi’an 710049, China) 3(Department of Computer, Shanxi University, Taiyuan 030006, China) + Corresponding author: E-mail: flcao@263.net Received 2002-06-19; Accepted 2003-03-04 Cao FL, Li YM, Xu ZB. Lp simultaneous approximation by neural networks with one hidden layer. Journal of Software, 2003,14(11):1869~1874. /1000-9825/14/1869.htm Abstract: 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. Key words: neural network; simultaneous approximation; hidden layer design; rate of convergence; Lebesgue measure 摘 要: 用构造性的方法证明对任何定义在多维欧氏空间紧集上的勒贝格可积函数以及它的导数 可以用一个单隐层的神经网络同时逼近.这个方法 自然地得到了网络的隐层设计和收敛速度的估 计