正负定矩阵下GAOR迭代法的收敛性  

The convergence of GAOR iterative method on the basis of positive and negative definite matrices

作　　者：张改芹 畅大为[1] 李晓艳 ZHANG Gaiqin;CHANG Dawei;LI Xiaoyan(School of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710119,China)

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710119

出　　处：《纺织高校基础科学学报》2018年第1期74-80,共7页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(11226266;11401361)

摘　　要：为了研究GAOR迭代法在线性方程组系数矩阵分别为Hermite正定矩阵和负定矩阵两种情况下的收敛性,将Householder-John定理推广到负定情况下,并给出负定条件下GAOR迭代法收敛的充要条件.利用Householder-John定理,完善GAOR迭代法的收敛性结论.最后借助推广的Householder-John定理,分析GAOR迭代法在线性方程组系数矩阵为Hermite负定矩阵条件下的收敛性.In order to study the convergence of GAOR iterative method on the basis of Hermitian positive and negative definite matrices,firstly the Householder-John theorem is introduced and generalized to the case of negative definite matrices.Then a sufficient and necessary condition for the convergence of GAOR iterative method is given under the negative definite condition.By using the Housholder-John theorem,the convergent conclusion of GAOR iterative method is improved.Finally,the convergence of GAOR iterative method under the Hermitian negative definite condition is analyzed through the generalized Householder-John theorem.

关 键 词：收敛性 HERMITE矩阵 正定矩阵 负定矩阵 GAOR迭代法 

分 类 号：O241.6[理学—计算数学] TP301.1[理学—数学]