插值小波神经网络的构造  

Constructions of interpolation wavelet neural networks

作　　者：银俊成[1] 曹怀信[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《陕西师范大学学报（自然科学版）》2012年第6期1-5,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11171197;61101240)

摘　　要：研究了小波神经网络插值问题.对于给定的一维插值样本,使用一元连续小波函数作为激活函数,构造了一元单隐层前向神经网络(称为小波神经网络).在一定条件下,证明了一元精确插值小波神经网络的存在性,构造了近似插值小波神经网络,给出了精确插值和近似插值小波神经网络之间的偏差估计.对于多元情况,通过对插值节点作内积处理后,借助一维空间中的方法,建立了多元精确插值与近似插值小波神经网络,并给出了两者之间的偏差估计.Interpolation problem by a wavelet neural network IS dlscussea, in l-almenslon case, for given 1-dimensional interpolated samples, a single hidden layer feed-forward neural network （called a wavelet neural network, WNN） is constructed by using a continuous wavelet function as the activation function. Under certain condition, the existence of the exact interpolation wavelet neural network （EIWNN） is proved first, and the approximate interpolation wavelet neural network （AIWNN） is constructed. Meanwhile, an estimation of the deviation between EIWNN and AIWNN is obtained. For given multi-dimensional interpolated samples, by considering the inner products of the interpolation nodes and some point and using the dimension case, the exact and approximate interpolation wavelet constructed, and an estimation of the deviation between them is proved.

关 键 词：小波神经网络 精确插值 近似插值 偏差估计 

分 类 号：O174.2[理学—数学] TP183[理学—基础数学]