摘要
本文主要研究解对称正定矩阵的多级迭代法,并对其收敛性进行证明,最后用数值实验验证此方法的有效性.多级迭代法特别适用于并行计算,并且可以被理解为古典迭代法的扩展,或共轭梯度法的预处理子.
In this paper a multistage iterative method for solving the symmetric positive definite linear systems is established and the convergence of the method is proved. A numerical example is given to illustrate the effectiveness of our method. The method is especially suitable for parallel computation, and can be viewed as a extension of the classical iterative method or as a preconditioner for the conjugate gradient method.
出处
《数学理论与应用》
2013年第1期7-12,共6页
Mathematical Theory and Applications
基金
Supported by the National Natural Science Foundation of China under Grant No.10771022
Supported by FEDER Funds through"Programa Operacional Factores de Competitividade-COMPETE"
Supported by Portuguese Funds through"Fundao para a Ciência e aTecnologia"
within the Project PEst-C/MAT/UI0013/2011 and PTDC/MAT/112273/2009
Portugal
关键词
线性方程组
对称正定阵
多级分裂
迭代法
收敛性
Linear Systems Symmetric Positive Definite Matrix Multistage Splitting Iterative Method Convergence
