基于LU分解的阻尼谱修正迭代法在病态线性方程组中的应用  

Iteration method by correcting characteristic value with damping factor based on LU decomposition for ill-conditioned system of linear equations

作　　者：莫春鹏[1] 覃柏英[1] MO Chunpeng;QIN Boying(College of Science,Guangxi University of Science and Technology,Liuzhou 545006,China)

机构地区：[1]广西科技大学理学院,广西柳州545006

出　　处：《广西科技大学学报》2021年第3期113-119,共7页Journal of Guangxi University of Science and Technology

基　　金：广西自然科学基金项目(2018GXNSFAA294122);广西高校中青年教师基础能力提升项目(2017KY0339)资助.

摘　　要：基于阻尼谱修正迭代法,结合矩阵LU分解和新数值迭代方式,提出了基于矩阵LU分解的阻尼谱修正迭代法,将其应用于病态线性方程组的求解.采用经典算例,探讨矩阵LU分解和新数值迭代方式对阻尼谱修正迭代法求解病态线性方程组的性能影响.结果表明,矩阵LU分解和新数值迭代方式都可提高阻尼谱修正迭代法求解病态线性方程组的精度,且提出的算法可提高高维病态线性方程组求解的精度.Based on the iteration method by correcting characteristic value with damping factor,combined with LU matrix decomposition and a new numerical iteration method,this paper proposes an improved iteration method by correcting characteristic value with damping factor based on LU matrix decomposition,which is applied to solve ill-conditioned system of linear equations.Some classical examples are used to investigate the influence of LU matrix decomposition and the new numerical iteration method on the performance of the algorithm for solving ill-conditioned system of linear equations.The results show that both the LU matrix decomposition and the new numerical iteration method can improve the accuracy of the algorithm for solving ill-conditioned system of linear equations,and the proposed algorithm can also improve the accuracy of solving high-dimensional ill-conditioned system of linear equations.

关 键 词：LU分解 谱修正迭代法 病态矩阵 线性方程组 

分 类 号：O151.2[理学—数学] O241.6[理学—基础数学]