基于矩阵分裂的预条件SOR迭代法收敛性  

Convergence discussion of SOR iterative method in precondition based on matrix splitting

作　　者：雷刚[1] 

机构地区：[1]宝鸡文理学院数学系,陕西宝鸡721013

出　　处：《河北大学学报（自然科学版）》2012年第1期12-16,共5页Journal of Hebei University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10071048);宝鸡文理学院重点基金资助项目(ZK1031)

摘　　要：对预条件方法解线性方程组,利用黄廷祝等在["modified SOR-type iterative method for z-matri-ces"]中提到的预条件能加速SOR迭代法的收敛性,结合矩阵分裂理论及比较定理,给出一种基于矩阵分裂的含参数预条件SOR迭代方法,说明这种方法不仅能加速SOR迭代法的收敛性,而且优于一般的预条件方法,找出参数的最优选取方法,最后通过数值例子加以说明.It studies the preconditioned iterative method for the solving the linear system.Ting-Zhu Huang gives the preconditioned to accelerate convergence of SOR iterative method at＂modified SOR-type iterative method for z-matrices＂.by using matrix iterative analysis and comparison theorems to make an improved SOR iterative method to solve the large linear system in preconditioned based on matrix splitting,then prove the improved method not only to accelerate the SOR iterative method,but also to excel the general preconditioned SOR method.Last the numerical example is given.

关 键 词：预条件 收敛性 SOR迭代法 谱半径 矩阵分裂 

分 类 号：O241.6[理学—计算数学]