摘要
对于线性方程组Ax=b,讨论了在预条件预矩阵I+S+R下系数矩阵为非奇异Z-阵时AOR迭代法的收敛性以及系数矩阵为非奇异不可约Z-阵时AOR方法的敛散性,进而得到了2个比较定理,并得出了预条件矩阵可以加快AOR方法的敛散速度,最后借助Matlab实现并验证了结论.
On linear equations Ax=b,it is analysed the convergence of AOR iterative method under this pre-conditioned matrix I＋S＋R when coefficient matrix is nonsingular Z-matrix.At the same time,it is discussed the convergence and divergence of AOR iterative method when coefficient matrix is non-singular irreducible Z-matrix.Then two comparision theorems are obtained.The preconditioned matrix can accelerate the rate of convergence and divergence of AOR iterative method.Finally the conclusion is achieved and verified by using Matlab.
出处
《纺织高校基础科学学报》
CAS
2010年第4期396-400,438,共6页
Basic Sciences Journal of Textile Universities
基金
国家自然科学基金资助项目(60671063)
关键词
预条件矩阵
AOR迭代法
收敛性
Z-矩阵
比较定理
preconditioned matrix
AOR iterative method
convergence
z-matrix
comparison theorem
