| 单隐层神经网络与最佳多项式逼近 |
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| 引用本文： | 曹飞龙,张永全,张卫国.单隐层神经网络与最佳多项式逼近[J].数学学报,2007,50(2):385-392. |
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| 作者姓名： | 曹飞龙 张永全 张卫国 |
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| 作者单位： | 中国计量学院信息与数学科学系，中国计量学院信息与数学科学系，华南理工大学工商管理学院 杭州 310018 西安交通大学信息与系统科学研究所 西安 710049，杭州 310018，广州 510641 |
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| 基金项目： | 国家自然科学基金(60473034,70571024)，国家博士后科学基金(20040350225)，浙江省教育厅科研重点基金(20060543) |
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| 摘 要： | 研究单隐层神经网络逼近问题．以最佳多项式逼近为度量,用构造性方法估计单隐层神经网络逼近连续函数的速度．所获结果表明:对定义在紧集上的任何连续函数,均可以构造一个单隐层神经网络逼近该函数,并且其逼近速度不超过该函数的最佳多项式逼近的二倍．
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| 关 键 词： | 单隐层神经网络 逼近速度 最佳多项式逼近 |
| 文章编号： | 0583-1431（2007）02-0385-08 |
| 收稿时间： | 2005-12-9 |
| 修稿时间： | 2005-12-10 |
Neural Networks with Single Hidden Layer and the Best Polynomial Approximation |
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| Fei Long CAO,Yong Quun ZHANG,Wei Guo ZHANG.Neural Networks with Single Hidden Layer and the Best Polynomial Approximation[J].Acta Mathematica Sinica,2007,50(2):385-392. |
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| Authors: | Fei Long CAO Yong Quun ZHANG Wei Guo ZHANG |
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| Institution: | Fei Long CAO Department of Information and Mathematical Sciences,China Jiliang University,Hangzhou 310018,P.R.China Institute of Information and Systems Science,Xi'an Jiaotong University,Xi'an 710049,P.R.China Yong Quan ZHANG Department of Information and Mathematical Sciences,China Jiliang University,Hangzhou 310018,P.R.China Wei Guo ZHANG School of Business Administration,South China University of Technology,Guangzhou 510641,P.R.China |
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| Abstract: | The problem of approximation for neural networks with single hidden layer is studied in this paper.With the best polynomial approximation as a metric,the rate of approximation of the neural networks with single hidden layer to a continuous function is estimated by using a constructive approach.The result obtained shows that for any continuous function defined a compact set,a neural network with single networks can be constructed to approximate the function,and the rate of approximation do not exceed the double of the best polynomial approximation of the function. |
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| Keywords: | neural networks with single hidden layer rate of approximation best polynomial approximation |
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