NEURAL NETWORKS AND THE BEST TRIGOMOMETRIC APPROXIMATION  

作　　者：Jianjun WANG ZongbenXU 

机构地区：[1]School of Mathematics & Statistics, Southwest University, Chongqing 400715, China [2]Institute for Information and System Science, Xi'an Jiaotong University, Xi'an 710049, China [3]Institute for Information and System Science, Xi'an Jiaotong University, Xi'an 710049, China.

出　　处：《Journal of Systems Science & Complexity》2011年第2期401-412,共12页系统科学与复杂性学报（英文版）

基　　金：This paper was supported by the National Basic Research Program of China （973 Program） under Grant No. 2007CB311000, the Natural Science Foundation of China under Grant Nos. 11001227, 60972155, 10701062, the Key Project of Chinese Ministry of Education under Grant No. 108176, Natural Science Foundation Project of CQ CSTC Nos. CSTC 2009BB2306, CSTC2009BB2305, the Fundamental Research Funds for the Central Universities under Grant No. XDJK2010B005, XDJK2010C023.

摘　　要：With the best trigonometric polynomial approximation as a metric, the rate of approxi- mation of the one-hidden-layer feedforward neural networks to approximate an integrable function is estimated by using a constructive approach in this paper. The obtained result shows that for any 2π-periodic integrable function, a neural networks with sigmoidal hidden neuron can be constructed to approximate the function, and that the rate of approximation do not exceed the double of the best trigonometric polynomial approximation of function.

关 键 词：APPROXIMATION best trigonometric approximation neural networks 

分 类 号：O174.41[理学—数学] TP18[理学—基础数学]