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.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
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)
关键词
神经网络
插值
连续泛函
逼近
neural networks
interpolation
continuous functional
approximation