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