摘要近来,Cybenko证明了下述 定理A 设δ(z)是一个连续的Sigmoidal函数,则下述形式 sum from j=1 to N (α_iδ(x·y_i+θ_i))的函数全体在C(I^n)中是稠密的,其中y_i∈R^n,x∈I^n,x·y是x与y的内积,α_i,θ_i分别为实数,I^n=[0,1]~n。
3Cybenko G. Approximation by superpositions of a single function[J]. Math Control, Signals & Systems, 1989, 2: 303-314.
4Chen Tianping, Chert Hong, Lin Ruewen. Approximation capability in C(R^n) by multilayer feedforward networks and related problems[J]. IEEE Trans Neural Networks, 1995, 6: 25-30.
5Xu Zongben, Cao Feilong. Simultaneous L^p-approximation order for neural networks[J]. Neural Networks, 2005, 18: 914-923.
6Huang G B, Babri H A. Feedforward neural networks with arbitrary bounded nonlinear activation functions[J]. IEEE Trans Neural Networks, 1998, 9(1): 224-229.
7Shrivatava Y, Dasgupta S. Neural networks for exact matching of functions on a discrete domain[A]. In: Proceedings of the 29th IEEE Conference on Decision and Control[C]. Honolulu, 1990, 1719-1724.
8Ito Y, Saito K. Superposition of linearly independent functions and finite mappings by neural networks[J]. Math Sci, 1996, 21: 27-33.
9Sontag E-D. Feedforward nets for interpolation and classification[J]. J Comput System Sei, 1992, 45: 20-48.
10Llanas B, Sainz F J. Constructive approximate interpolation by neural networks[J]. J Comput Appl Math, 2006, 188: 283-308.
