基于多项式基函数的泛函网络构造方法与逼近理论  

Functional Network Construction Method and Approximation Theory Based on Polynomial Basis Functions

作　　者：周永权[1] 刘晓冀[1] 张明[2] 

机构地区：[1]广西民族大学数学与计算机科学学院,南宁530006 [2]大连水产学院理学院,大连116023

出　　处：《计算机科学》2008年第8期119-121,164,共4页Computer Science

基　　金：国家自然科学基金(60461001);广西自然科学基金(0542048;0832082);国家民委科研项目(08GX01);广西民族大学重大科研项目资助课题

摘　　要：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泛函网络,以任意精度逼近该多项式,所构造的网络的中间神经元个数仅与多项式基函数的阶数r有关,并能用r表达。该文所得结果对于基于多项式基函数的泛函网络逼近任意函数类的网络具体构造和逼近具有理论指导意义。It is investigated in this paper that the polynomial basis functions are approximated by functional network with three-layer. It is shown that for a given polynomial function with r order a three-layer functional network can be constructed by a constructive method to approximate the polynomial to any degree of accuracy. The number of mid-unit of the constructed functional network only depends on the order of approximated basis functions. The obtained results are more important for constructing a three-layer functional network to approximate the class of polynomial basis functions and for realizing the approximation.

关 键 词：多项式基函数 泛函网络 构造方法 逼近理论 

分 类 号：O174.14[理学—数学] V431[理学—基础数学]