距离空间中的神经网络插值与逼近  

Interpolation and Approximation by Neural Networks in Distance Space

作　　者：曹飞龙[1] 张永全[1] 

机构地区：[1]中国计量学院信息与数学科学系,杭州310018

出　　处：《数学学报（中文版）》2008年第1期91-98,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(60473034);浙江省教育厅科研重点项目基金(20060543)

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.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.

关 键 词：神经网络 插值 连续泛函 逼近 

分 类 号：O174.41[理学—数学]