求解加权线性最小二乘问题的一类预处理GAOR方法

doi:10.12286/jssx.2020.1.63

计算数学 ›› 2020, Vol. 42 ›› Issue (1): 63-79.DOI: 10.12286/jssx.2020.1.63

求解加权线性最小二乘问题的一类预处理GAOR方法

王丽¹, 罗玉花², 王广彬³

1. 西北师范大学数学与统计学院, 兰州 730070;
2. 兰州大学数学与统计学院, 兰州 730000;
3. 青岛农业大学数学系, 青岛 266109

收稿日期:2018-05-23 出版日期:2020-02-15 发布日期:2020-02-15
通讯作者: 王广彬,E-mail:wguangbin750828@sina.com
基金资助:
西北师范大学数学与统计学院大学生创新计划；山东高校科技计划（J16LI04）.

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王丽, 罗玉花, 王广彬. 求解加权线性最小二乘问题的一类预处理GAOR方法[J]. 计算数学, 2020, 42(1): 63-79.

Wang Li, Luo Yuhua, Wang Guangbin. A CLASS OF PRECONDITIONED GAOR METHODS FOR SOLVING WEIGHTED LINEAR LEAST-SQUARES PROBLEM[J]. Mathematica Numerica Sinica, 2020, 42(1): 63-79.

A CLASS OF PRECONDITIONED GAOR METHODS FOR SOLVING WEIGHTED LINEAR LEAST-SQUARES PROBLEM

Wang Li¹, Luo Yuhua², Wang Guangbin³

1. College of Mathematics and Statistics, Northwest Normal University, LanZhou 730070, China;
2. College of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China;
3. Department of Mathematics, Qingdao Agricultural University, Qingdao 266109, China

Received:2018-05-23 Online:2020-02-15 Published:2020-02-15

为了快速求解一类来自加权线性最小二乘问题的2×2块线性系统，本文提出一类新的预处理子用以加速GAOR方法，也就是新的预处理GAOR方法.得到了一些比较结果，这些结果表明当GAOR方法收敛时，新方法比原GAOR方法和之前的一些预处理GAOR方法有更好的收敛性.而且，数值算例也验证了新预处理子的有效性．

关键词： 加权线性最小二乘问题, 预处理子, GAOR方法, 比较定理

In this paper, a new type of preconditioners are proposed for accelerating the GAOR method, which are the preconditioned GAOR methods, for solving a class of block 2×2 linear systems arising from the weighted linear least-squares problem. Some comparison results are obtained, the comparison results show that the convergence rate of the proposed preconditioned GAOR methods are indeed better than those of the original GAOR method and the preconditioned GAOR methods, whenever the original GAOR method is convergent. Furthermore, effectiveness of the proposed methods is verified by numerical experiment.

Key words: weighted linear least-squares problem, preconditioner, GAOR method, comparison theorems

MR(2010)主题分类:

65F10
65F15

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摘要

求解加权线性最小二乘问题的一类预处理GAOR方法

A CLASS OF PRECONDITIONED GAOR METHODS FOR SOLVING WEIGHTED LINEAR LEAST-SQUARES PROBLEM

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