基于数学实验对线性变换收敛性的研究  

Research on the convergence of linear transformation based on mathematical experiments

作　　者：朴丽莎[1] PIAO Lisha(School of Technology,Dianchi College of Yunnan University,Kunming 650228,China)

机构地区：[1]云南大学滇池学院理工学院,云南昆明650228

出　　处：《高师理科学刊》2021年第9期73-76,共4页Journal of Science of Teachers＇College and University

基　　金：云南省教育厅科学研究基金项目(2019J0828);云南大学滇池学院骨干教师计划项目;云南大学滇池学院校级课程思政示范课程项目。

摘　　要：为研究迭代法的收敛性,将迭代法等价为线性变换,结合Matlab软件设计实验内容和算法.通过大量实验,分别得到迭代矩阵的谱半径在3种情况下迭代法的收敛性,即谱半径大于1,迭代法发散;谱半径小于1,迭代法收敛;谱半径等于1,无法判定.实验结果不仅与理论结果一致,而且更加直观地呈现了线性变换下迭代法收敛性的具体形态,这对实际问题开展研究具有指导意义.In order to further study the convergence of the iterative method,the iterative method was equated to a linear transformation,and then the experimental content and algorithm was designed with Matlab software.Through a large number of experiments,the convergence of the iterative method is obtained in three cases,when the spectral radius of the iterative matrix is greater than 1,the iterative method diverges.When the spectral radius is less than 1,the iterative method converges.When the spectral radius is equal to 1,which can not be determined.The experimental results are not only consistent with the theoretical results,but also more intuitively show the specific form of convergence of iterative method under linear transformation,which has guiding significance for the research of practical problems.

关 键 词：数学实验 线性变换 迭代法 谱半径 

分 类 号：O231.1[理学—运筹学与控制论] G642.0[理学—数学]