求解一类分块二阶线性方程组的QHSS迭代方法  

QHSS ITERATION METHOD FOR A CLASS OF BLOCK TWO-BY-TWO LINEAR SYSTEMS

作　　者：李天怡 陈芳[1] Li Tianyi;Chen Fang(School of Applied Science,Beijing Information Science and Technology University,Beijing 100192,China)

机构地区：[1]北京信息科技大学理学院,北京100192

出　　处：《计算数学》2021年第1期110-117,共8页Mathematica Numerica Sinica

基　　金：国家自然科学基金(No.11501038);北京市教育委员会科技计划项目(Nos.KM201911232010,KM201811232020)资助。

摘　　要：本文将QHSS迭代方法运用于求解一类分块二阶线性方程组.通过适当地放宽QHSS迭代方法的收敛性条件,我们给出了用QHSS迭代方法求解一类分块二阶线性方程组的具体迭代格式,并证明了当系数矩阵中的(1,1)块对称半正定时该QHSS迭代方法的收敛性.我们还用数值实验验证了QHSS迭代方法的可行性和有效性.We use the QHSS iteration method to solve a class of block two-by-two linear systems.By properly relaxing the convergence conditions of the QHSS iteration method,we give an alternative QHSS iteration scheme for solving the block two-by-two linear systems,and prove that when the(1,1)block of the coefficient matrix is symmetric and positive semidefinite,this QHSS iteration method is also convergent under certain conditions.We also use the numerical experiments to verify the feasibility and effectiveness of the QHSS iteration method.

关 键 词：分块二阶矩阵 迭代方法 收敛性 

分 类 号：O241.6[理学—计算数学]