H-矩阵方程组的预条件迭代法  

H-Matrix Equations of Preconditioned Iterative Method

作　　者：王炜[1] 禹跃[1] 

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《中北大学学报（自然科学版）》2012年第1期66-69,共4页Journal of North University of China(Natural Science Edition)

摘　　要：针对系数矩阵A为H-矩阵的线性方程组,引入了预条件矩阵I+Wβ.通过对系数矩阵施行初等行变换,提出了求解线性方程组的一种新的预条件Gauss-Seidel方法.给出了若A为H-矩阵,则(I+Wβ)A仍然为H-矩阵,并且得到了收敛性定理;从理论上证明了新的预条件Gauss-Seidel迭代法较经典的Gauss-Seidel迭代法收敛速度快;最后通过数值算例说明了新的预条件Gauss-Seidel迭代方法的有效性.For the coefficient matrix A being H-matrix of linear equations,the preconditioning matrix I＋Wβ was introduced.Through the elementary row transformation of the coefficient matrix,a new preconditioned Gauss-Seidel method was proposed to solve the linear equations.If A is an H-matrix,then（I＋Wβ）A is also an H-matrix.The convergence theorem was also obtained.It theoretically proved that the new preconditioned Gauss-Seidel iterative method converges faster than the classic Gauss-Seidel iteration method.Numerical example showed the validity of the new precondition Gauss-Seidel iteration method.

关 键 词：H-矩阵 预条件 GAUSS-SEIDEL迭代法 收敛性 

分 类 号：O151.21[理学—数学]