| 距离空间中的神经网络插值与逼近 |
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| 引用本文： | 曹飞龙,张永全.距离空间中的神经网络插值与逼近[J].数学学报,2008,51(1):91-98. |
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| 作者姓名： | 曹飞龙 张永全 |
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| 作者单位： | 中国计量学院信息与数学科学系,杭州310018 |
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| 基金项目： | 国家自然科学基金资助项目（60473034）;浙江省教育厅科研重点项目基金（20060543） |
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| 摘 要： | 已有的关于插值神经网络的研究大多是在欧氏空间中进行的,但实际应用中的许多问题往往需要用非欧氏尺度进行度量.本文研究一般距离空间中的神经网络插值与逼近问题,即先在距离空间中构造新的插值网络,然后在此基础上构造近似插值网络,最后研究近似插值网络对连续泛函的逼近.
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| 关 键 词： | 神经网络 插值 连续泛函 逼近 |
| 文章编号： | 0583-1431（2008）01-0091-08 |
| 收稿时间： | 2006-05-12 |
| 修稿时间： | 2007-07-06 |
Interpolation and Approximation by Neural Networks in Distance Space |
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| Fei Long CAO ,Yong Quan ZHANG.Interpolation and Approximation by Neural Networks in Distance Space[J].Acta Mathematica Sinica,2008,51(1):91-98. |
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| Authors: | Fei Long CAO Yong Quan ZHANG |
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| Institution: | Fei Long CAO Yong Quan ZHANG Department of Information and Mathematics Sciences,China Jiliang University,Hangzhou 310018,P.R.China |
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| Abstract: | There have been many studies on interpolation by neural networks in Euclidean spaces. However, there are plentiful concrete problems which must be measured by using non-Euclidean metrics. This paper deals with the interpolation and approximation of neural networks in general non-Euclidean spaces. That is, first construct interpolation networks in general spaces, and then construct approximate interpolation networks, finally, study the approximation of continuous functional with approximating network. |
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| Keywords: | neural networks interpolation continuous functional approximation |
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