椭圆方程五点格式的迭代法与快速算法的比较  

Comparison of Gauss-Seidel Iterative Method and Fast Poisson Algo⁃rithm in Five-Point Format for Elliptic Equations

作　　者：焦岑 孙唯唯 聂家升 JIAO Cen;SUN Weiwei;NIE JiaSheng(Applied Technology College,Suzhou University,Suzhou Zhejiang 215325,P.R.China)

机构地区：[1]苏州大学应用技术学院通识教育学院,江苏苏州215325

出　　处：《保山学院学报》2024年第2期56-65,共10页JOURNAL OF BAOSHAN UNIVERSITY

基　　金：2022年江苏省哲社一般项目“基于OBE-CDIO教育理念的新工科大学数学课程体系重构与教学内容改革研究”(项目编号:2022SJYB1538)。

摘　　要：主要讨论在椭圆方程五点格式的问题中,分别使用Gauss-Seidel迭代法与快速Poisson算法对其求解,并对二者求解该线性方程组的速度进行比较。在系数矩阵是稀疏的大型线性方程组中,迭代法是一个很好的求解该类型的算法,主要是因为给定一个初始向量,通过一定的迭代公式,可以求得之后任意一次迭代的结果,且运算简便,但是,对于迭代法所求得的近似解是否收敛于精确解,并且,在线性方程组有快速算法的情况下,迭代法是否还能在求解方程组中占优势,还需进一步比较。通过比较不同的系数、不同的步长[λ]以及不同的误差要求,来判断Gauss-Seidel迭代法与快速Poisson算法的优劣。This paper mainly discusses the solving of the five-point scheme of the elliptic equation by using the Gauss-Seidel iteration method and the fast Poisson algorithm,and compares the speeds of the two equations for solving the linear equations.We all know that in the large linear system of equations where the coefficient matrix is sparse,the iterative method is a good solution to this type of algorithm,mainly because given an initial vector,we can obtain a result of an arbitrary iteration,and the operation is simple,but whether the approximate solution obtained by the iterative method converges to the exact solution,and whether the iterative method can also solve the system of equations if the linear equations have a fast algorithm to take advantage,we must further compare.This paper mainly judges the advantages and disadvantages of Gauss-Seidel iterative method and fast Poisson algorithm by comparing different[λ],different step sizes and different error requirements.

关 键 词：椭圆方程五点格式 GAUSS-SEIDEL迭代法 快速Poisson算法 

分 类 号：O13[理学—数学]