基于LS-SVM的第一类积分方程的近似解法  

Approximate Solutions to Integral Equations of the First Kind Based on LS-SVM

作　　者：曹秀梅[1] 朱明月 吴自库[1] CAO Xiumei;ZHU Mingyue;WU Ziku(School of Science and Information Science,Qingdao Agricultural University,Qingdao 266109,China)

机构地区：[1]青岛农业大学理学与信息科学学院,山东青岛266109

出　　处：《青岛农业大学学报（自然科学版）》2022年第3期222-225,共4页Journal of Qingdao Agricultural University(Natural Science)

基　　金：国家自然科学基金项目(41674037)。

摘　　要：提出一种基于最小二乘支持向量机逼近原理的第一类积分方程求解的数值算法,并利用该方法对第一类Volterra和第一类Fredholm积分方程进行数值求解。方法的核心是依据最小二乘支持向量机逼近原理构造解的逼近函数,并借助一种数值积分方法将参数估计问题转化为二次规划问题。数值结果表明该方法具有较高的精度和较好的稳定性,而且得到的是闭式解析解。A numerical algorithm for solving integral equations of the first kind based on least squares support vector machine is proposed,and the Volterra and Fredholm integral equations of the first kind are solved numerically by this method.The core of this method is to construct the approximation function of the solution according to least squares support vector machine,and transform the estimation parameter problem into a quadratic programming problem by using a numerical integration method.Numerical results show that the method has high accuracy and good stability.In addition,the closed-form analytical solutions are obtained.

关 键 词：数值积分 最小二乘支持向量机 第一类积分方程 二次规划 近似解 

分 类 号：O241.83[理学—计算数学]