陕西师范大学学报：自然科学版
陝西師範大學學報：自然科學版
협서사범대학학보：자연과학판
Journal of Shaanxi Normal University： Nat Sci Ed
2012年
6期
1-5
,共5页
小波神经网络%精确插值%近似插值%偏差估计
小波神經網絡%精確插值%近似插值%偏差估計
소파신경망락%정학삽치%근사삽치%편차고계
wavelet neural network%exact interpolation%appr error estimation obtained results for 1- neural networks are oximate interpolation
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．
研究瞭小波神經網絡插值問題．對于給定的一維插值樣本，使用一元連續小波函數作為激活函數，構造瞭一元單隱層前嚮神經網絡（稱為小波神經網絡）．在一定條件下，證明瞭一元精確插值小波神經網絡的存在性，構造瞭近似插值小波神經網絡，給齣瞭精確插值和近似插值小波神經網絡之間的偏差估計．對于多元情況，通過對插值節點作內積處理後，藉助一維空間中的方法，建立瞭多元精確插值與近似插值小波神經網絡，併給齣瞭兩者之間的偏差估計．
연구료소파신경망락삽치문제．대우급정적일유삽치양본，사용일원련속소파함수작위격활함수，구조료일원단은층전향신경망락（칭위소파신경망락）．재일정조건하，증명료일원정학삽치소파신경망락적존재성，구조료근사삽치소파신경망락，급출료정학삽치화근사삽치소파신경망락지간적편차고계．대우다원정황，통과대삽치절점작내적처리후，차조일유공간중적방법，건립료다원정학삽치여근사삽치소파신경망락，병급출료량자지간적편차고계．
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.
