基于神经网络的数值积分改进算法  

Improved numerical integration algorithm based on neural network

作　　者：闫丽娜[1] 王珂[1] 王世恒 

机构地区：[1]上海大学理学院,上海200444 [2]南阳农业职业学院,河南南阳473000

出　　处：《应用数学与计算数学学报》2016年第4期520-525,共6页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11301330);上海市教委高校教师国外访学进修计划项目(B.60-A101-12-010);"上海高校一流学科(B类)"经费资助项目;上海市高原学科资助项目

摘　　要：讨论了一种求解数值积分的改进算法,其基本思想是:基于样条基函数的神经网络模型,应用权值直接确定法构造样条基函数,从而逼近被积函数.讨论了数值积分定理及其推论,给出了具体算例检验算法的可行性和优越性.数值结果表明,该算法具有较高的计算精度和较快的计算速度,而且不需要知道被积函数的解析表达式,只需知道被积函数的离散数据便可求得积分值,因此在工程领域中有较大的应用价值.An improved algorithm for the numerical integration is proposed. The main idea is to construct a neural network model based on spline basis functions, which approximates the integrand by directly determining neural network weights. The theorem of numerical integration and one corollary are presented and proved. The numerical examples show that the algorithm is effective and has the proper- ties of high precision, fast convergence rate, and using only discrete values of the integrand. Therefore, this numerical integration approach should be significantly useful in many engineering applications.

关 键 词：数值积分 样条基函数 神经网络算法 权值直接确定 

分 类 号：O241.4[理学—计算数学]