兰州大学机构库 >数学与统计学院
解线性系统的预条件方法
Alternative TitleThe preconditioned methods for linear systems
常岩磊
Thesis Advisor张国凤
2008-05-24
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword预条件矩阵 Gauss-Seidel 迭代方法 SOR 迭代方法 AOR 迭代方法 比较定理 谱半径 M-矩阵
Abstract对于求解大型线性方程组, 迭代方法已取代直接法成为最重要的一类方法.迭代方法好坏的标准通常通过收敛速度来刻画,因此迭代方法的收敛速度成为一个很重要的问题.我们希望找到一种收敛速度比较快的迭代方法, 这样才有应用价值.为了更快的求解线性方程组, 我们引进了非奇异预条件矩阵,通过预条件矩阵作用加速了迭代法的收敛速度. 本文在以往学者的基础上,提出了在应用上更具广泛性的预条件 AOR 迭代方法,本文得到的预条件比较定理较之前人的成果更有一般性.
Other AbstractFor solving large linear systems,iterative methods have become one of the most important methods. We usually describe the convergence rate of the iterative methods to see whether it is a good method. So the convergence rate becomes more and more important. Then it is valuable to find a method which has a faster convergence rate. We introduce the nonsingular preconditioning matrix in order to solve the linear system faster and accelerate the convergence rate. In this paper, we establish the preconditioned AOR method to solve the large linear systems and receive a general result.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225008
Collection数学与统计学院
Recommended Citation
GB/T 7714
常岩磊. 解线性系统的预条件方法[D]. 兰州. 兰州大学,2008.
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