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DOI:
Journal of Software:2003.14(11):1869-1874

单隐层神经网络的Lp同时逼近
曹飞龙,李有梅,徐宗本
(绍兴文理学院,数理信息学院,浙江,绍兴,312000;西安交通大学,理学院信息与系统科学研究所,陕西,西安,710049;西安交通大学,理学院信息与系统科学研究所,陕西,西安,710049;山西大学,计算机系,山西,太原,030006)
Lp Simultaneous Approximation by Neural Networks with One Hidden Layer
CAO Fei-Long,LI You-Mei,XU Zong-Ben
()
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Received:June 19, 2002    Revised:March 04, 2003
> 中文摘要: 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,所得到的结果描述了网络收敛速度与隐层神经元个数之间的关系,同时也推广了已有的关于一致度量下的稠密性结果.
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.
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基金项目:Supported by the National Natural Science Foundation of China under Grant No.69975016 (国家自然科学基金); the Foundation of Key Item of Science and Technology of the Ministry of Education of China under Grant No.03142 (国家教育部科学技术重点项目基金); the Foundation of Higher School of Ningxia Province of China under Grant No.JY2002107 (宁夏高校科研基金) Supported by the National Natural Science Foundation of China under Grant No.69975016 (国家自然科学基金); the Foundation of Key Item of Science and Technology of the Ministry of Education of China under Grant No.03142 (国家教育部科学技术重点项目基金); the Foundation of Higher School of Ningxia Province of China under Grant No.JY2002107 (宁夏高校科研基金)
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曹飞龙,李有梅,徐宗本.单隐层神经网络的Lp同时逼近.软件学报,2003,14(11):1869-1874

CAO Fei-Long,LI You-Mei,XU Zong-Ben.Lp Simultaneous Approximation by Neural Networks with One Hidden Layer.Journal of Software,2003,14(11):1869-1874