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

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.