解(1,1)块对称不定线性系统的广义修正SSOR迭代法  

Generalized modified ssor iterative method for solving which(1,1)block is symmetric indefinite linear systems

作　　者：程军[1] 李正彪 郑彭丹[3] 张莉君 CHENG Jun;LI Zhengbiao;ZHENG Pengdan;ZHANG Lijun(College of Teacher Education,Qujing Normal University,Qujing,Yunnan 655011,China;College of Mathematics and Statistic,Qujing Normal University,Qujing,Yunnan 655011,China;Swan College of Central South University of Forestry and Technology,ChangSha,Hunan 410211,China;Qujing Special education,Qujing,Yunnan 655000,China)

机构地区：[1]曲靖师范学院教师教育学院,云南曲靖655011 [2]曲靖师范学院数学与统计学院,云南曲靖655011 [3]中南林业科技大学涉外学院信息与工程学院,湖南长沙410211 [4]曲靖市特殊教育学校,云南曲靖655000

出　　处：《南昌大学学报（理科版）》2020年第3期222-224,共3页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(51463021);云南省教育厅科学研究基金资助项目(2019J0610,2018JS438);曲靖师范学院科学研究基金资助项目(2015QN018)。

摘　　要：在大规模稀疏线性系统中,对于2×2系统中(1,1)块矩阵为不定矩阵的鞍点问题,本文建立了求解(1,1)块为对称不定线性系统的GMSSOR方法。关于大型稀疏线性系统鞍点问题的对称和不确定条件,采用了强迫正定的方法,然后利用分裂方法构造了求解系数矩阵中1×1块是对称不定的鞍点问题的迭代方法,证明了这种新的迭代方法的收敛性。最后通过数值算例表明,具有适当参数的GMSSOR方法比具有最优参数的MSSOR方法具有更快的收敛速度。In a large scale sparse linear system,for the saddle point problem which(1,1)block is symmetric indefinite in 2×2 block linear systems.In this paper,we establish a GMSSOR method for solving linear systems which(1,1)block is symmetric indefinite.About symmetric and uncertain conditions of saddle point problem of large-scale sparse linear systems,using the Gill-Murray forced definite method,then the splitting method is used to construct an iterative method for solving the saddle point problem which 1×1 block is symmetric indefinite in the coefficient matrix,the convergence of this new iterative method is proved.Finally,numerical example is given to show that the GMSSOR method with appropriate parameters has a faster convergence rate than the MSSOR method with optimal parameters.

关 键 词：GMSSOR方法 对称不定 矩阵分裂 迭代方法 

分 类 号：O241.6[理学—计算数学]