神经网络的函数逼近理论

On Neural Networks Founction Approximation

分析了将函数逼近理论与方法引入神经网络研究的必要性；从经典函数逼近与统计分析两方面详细地讨论了多层前馈网（ＭＬＰ）逼近能力分析的基本方法及结论；分析了正则理论观点下的径向基函数网络（ＲＢＦ）的逼近能力；讨论了ＲＢＦ网与多层前馈网在最佳逼近特性上的差异。文末指出了神经网络函数逼近的发展方向。

In this paper,an analysis of the necessity to introduce classical function approximation theory and methods into the research of ANN is presented with a brief introduction of its contents.Then,the main results about the approximation capability of MLP network and the basic analysis methods are detailed from the two aspects of classical function appoximantion and statistical analysis.The approximation capability of RBF ntework is analyzed under the view of Regularity Theory,and the difference of the best approximation property between the RBF and MLP network is revealed.