摘要
目的在预条件后运用SOR迭代法求解大型线性方程组Ax=b,以加快迭代法的收敛性。方法结合矩阵分裂理论及比较定理,引入参数α,给出预条件后一种改进的矩阵分裂形式,使矩阵分裂更加一般化。结果与结论说明这种方法不仅能加速SOR迭代法的收敛性,而且优于常见的SOR方法,并且给出参数的最优选取,为算法设计提供帮助。
Aim To accelerate the convergence with the preconditioned SOR iterative method for solving the large linear system Ax=b.Methods In combination with matrix splitting theory and comparison theorem,matrix splitting becomes more generalized by giving parameter α and an improved SOR iterative method for solving the large linear system after being preconditioned.Results and Conclusion The improved method can not only accelerate the convergence effect of the SOR iterative method,but also generaly SOR iterative,then give the method for optimal selection parameters,thus helping design algorithm.
出处
《宝鸡文理学院学报（自然科学版）》
CAS
2011年第3期13-17,21,共6页
Journal of Baoji University of Arts and Sciences(Natural Science Edition)
基金
国家自然科学基金资助项目(10071048)
宝鸡文理学院重点项目基金资助(zk1031)
关键词
预条件
收敛性
SOR迭代法
谱半径
precondition
convergence
the SOR iteration method
spectral radius
