多项式函数的神经网络逼近:网络的构造与逼近算法  

Approximation of Polynomial Functions by Neural Network: Construction of Network and Algorithm of Approximation

作　　者：曹飞龙[1] 徐宗本[2] 梁吉业[3] 

机构地区：[1]绍兴文理学院数学系,绍兴312000 [2]西安交通大学理学院信息与系统科学研究所,西安710049 [3]山西大学计算机系,太原030006

出　　处：《计算机学报》2003年第8期906-912,共7页Chinese Journal of Computers

基　　金：国家自然基金 (60 2 75 0 19);教育部科技重点项目基金 (0 3 14 2 );宁夏高校科研基金 (JY2 0 0 2 10 7)资助

摘　　要：该文作者先用构造性方法证明 :对于给定的r阶多项式函数 ,可以具体地构造出一个三层前向神经网络 ,以任意精度逼近该多项式 ,所构造的网络的隐层节点个数仅与多项式的阶数r和网络的输入个数s有关 ,并能准确地用r表达 ;然后 ,给出一个实现这一逼近的具体算法 ;最后 ,给出两个数值算例进一步验证所得的理论结果 .It is investigated that the polynomial functions are approximated by feedforward neural network with three-layer. Firstly, It is shown that for a given polynomial function with r order a feed-forward neural network with three-layer can be constructed by a constructive method to approximate the polynomial to any degree of accuracy. The number of hidden-layer nodes of the constructed network only depends on the order of approximated polynomial and the number of input of the network. It can also be expressed by the order of approximated polynomial accurately. Then, an algorithm to realize the approximation is given. Finally, two numerical examples are given for further illustrating the results. The obtained results are more important for constructing a feed-forward neural network with three-layer to approximate the class of polynomial functions and for realizing the approximation.

关 键 词：多项式函数 神经网络 函数逼近 逼近算法 人工神经网络 

分 类 号：O174.41[理学—数学] TP183[理学—基础数学]