求解一类分块二阶线性方程组的QHSS迭代方法

doi:10.12286/jssx.j2020-0657

计算数学 ›› 2021, Vol. 43 ›› Issue (1): 110-117.DOI: 10.12286/jssx.j2020-0657

求解一类分块二阶线性方程组的QHSS迭代方法

李天怡, 陈芳

北京信息科技大学理学院, 北京 100192

收稿日期:2020-01-02 出版日期:2021-02-15 发布日期:2021-02-04
通讯作者: 陈芳, chenfreesky@126.com
基金资助:
国家自然科学基金（No.11501038）和北京市教育委员会科技计划项目（Nos.KM201911232010，KM201811232020）资助.

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李天怡, 陈芳. 求解一类分块二阶线性方程组的QHSS迭代方法[J]. 计算数学, 2021, 43(1): 110-117.

Li Tianyi, Chen Fang. QHSS ITERATION METHOD FOR A CLASS OF BLOCK TWO-BY-TWO LINEAR SYSTEMS[J]. Mathematica Numerica Sinica, 2021, 43(1): 110-117.

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

Li Tianyi, Chen Fang

School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China

Received:2020-01-02 Online:2021-02-15 Published:2021-02-04

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.

关键词： 分块二阶矩阵, 迭代方法, 收敛性

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.

Key words: block two-by-two matrices, iteration method, convergence

MR(2010)主题分类:

65F10

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摘要

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

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