TY - JOUR
T1 - Constructive approximate interpolation by neural networks in the metric space
AU - Cao, Feilong
AU - Lin, Shaobo
AU - Xu, Zongben
PY - 2010/11
Y1 - 2010/11
N2 - In this paper, we construct two types of feed-forward neural networks (FNNs) which can approximately interpolate, with arbitrary precision, any set of distinct data in the metric space. Firstly, for analytic activation function, an approximate interpolation FNN is constructed in the metric space, and the approximate error for this network is deduced by using Taylor formula. Secondly, for a bounded sigmoidal activation function, exact interpolation and approximate interpolation FNNs are constructed in the metric space. Also the error between the exact and approximate interpolation FNNs is given.
AB - In this paper, we construct two types of feed-forward neural networks (FNNs) which can approximately interpolate, with arbitrary precision, any set of distinct data in the metric space. Firstly, for analytic activation function, an approximate interpolation FNN is constructed in the metric space, and the approximate error for this network is deduced by using Taylor formula. Secondly, for a bounded sigmoidal activation function, exact interpolation and approximate interpolation FNNs are constructed in the metric space. Also the error between the exact and approximate interpolation FNNs is given.
KW - Approximate interpolation
KW - Exact interpolation
KW - Metric space
KW - Neural networks
UR - https://www.scopus.com/pages/publications/77956011925
U2 - 10.1016/j.mcm.2010.06.035
DO - 10.1016/j.mcm.2010.06.035
M3 - 文章
AN - SCOPUS:77956011925
SN - 0895-7177
VL - 52
SP - 1674
EP - 1681
JO - Mathematical and Computer Modelling
JF - Mathematical and Computer Modelling
IS - 9-10
ER -