三阶Runge-Kutta法在病态线性方程组中的应用  

Application of Runge-Kutta Method in Ill Conditioned Linear System of Equations

作　　者：唐小平 李靖云 余荣川 TANG Xiaoping;LI Jingyun;YU Rongchuan(School of Mathematics and Computer Science,Guangxi Science&Technology Normal University,Laibin,Guangxi 546199,China)

机构地区：[1]广西科技师范学院数学与计算机科学学院

出　　处：《广西科技师范学院学报》2019年第6期123-129,共7页Journal of Guangxi Science & Technology Normal University

基　　金：教育部产学协同育人项目(201701015022、201702043066、20170219033、201802111029);2018年度广西科技师范学院本科教学改革工程项目“新工科建设背景下物联网专业课程教学改革的研究与实践”(2018GKSYJGZ02)

摘　　要：为了提高病态线性方程组数值迭代求解的精度,本文将其转化为常微分方程组初值问题,引入三阶Runge-Kutta法进行求解。采用四个经典算例,探讨了该方法在病态线性方程组求解中的应用。结果表明,三阶Runge-Kutta法可提高病态线性方程组求解的精度。同时,采用两个经典算例,探讨了三阶Runge-Kutta法在高维病态线性方程组中的应用。结果表明,该方法也可实现高维病态线性方程组高精度的求解。In order to improve the accuracy of solving the ill conditioned linear system of equations(ICLSE),this paper transforms it into an initial value problem of ordinary differential equations,and introduces the three order Runge-Kutta method(RK3)to solve the problem.Four classical examples are used to discuss the application of RK3 on ICLSE.The results show that RK3 can improve the accuracy of solving ICLSE.Two classical examples are also used to discuss the performance of RK3 for solving the high dimensional ICLSE.The results show that RK3 can improve the accuracy of solving the high dimensional ICLSE.

关 键 词：RUNGE-KUTTA法 病态矩阵 线性方程组 

分 类 号：O242[理学—计算数学]