两步定常线性迭代法的收敛区域及最优参数选取  

ON CONVERGENCE REGIONS AND OPTIMAL PARAMETERS FOR LINEAR SECOND-DEGREE STATIONARY ITERATIVE METHODS

作　　者：张玉海[1] 朱本仁[1] 

机构地区：[1]山东大学数学与系统科学学院,济南250100

出　　处：《计算数学》2001年第2期239-245,共7页Mathematica Numerica Sinica

基　　金：山东大学青年科学基金资助项目

摘　　要：In this paper we concern the convergence regions and the optimal parameters for linear second-degree stationary iterative methods applied to complex linear system with the help of the generalized Louts-Hurwitz’s theorem. We show that the Chebyshev iteration is asymptotically equivalent to a linear second-degree stationary iteration. Finally some applications to CSOR and CMSOR are presented.In this paper we concern the convergence regions and the optimal parameters for linear second-degree stationary iterative methods applied to complex linear system with the help of the generalized Louts-Hurwitz's theorem. We show that the Chebyshev iteration is asymptotically equivalent to a linear second-degree stationary iteration. Finally some applications to CSOR and CMSOR are presented.

关 键 词：线性系统 迭代方法 收敛条件 收敛区域 最优参数 两步定常线性迭代法 

分 类 号：O241[理学—计算数学]