• 论文 •

### 关于“求解加权线性最小二乘问题的一类预处理GAOR方法”一文的注记

1. 西北师范大学数学与统计学院, 兰州 730070
• 收稿日期:2020-07-06 出版日期:2022-02-14 发布日期:2022-02-14
• 基金资助:
国家自然科学基金（11861059）和西北师范大学科学计算团队（NWNU-LKQN-17-5）资助

Miao Shuxin. NOTE ON “A CLASS OF PRECONDITIONED GAOR METHODS FOR SOLVING WEIGHTED LINEAR LEAST-SQUARES PROBLEM”[J]. Mathematica Numerica Sinica, 2022, 44(1): 89-96.

### NOTE ON “A CLASS OF PRECONDITIONED GAOR METHODS FOR SOLVING WEIGHTED LINEAR LEAST-SQUARES PROBLEM”

Miao Shuxin

1. College of Mathematics and Statistics, Northwest Normal University, LanZhou 730070, China
• Received:2020-07-06 Online:2022-02-14 Published:2022-02-14

In the paper entitled "A class of preconditioned GAOR methods for solving weighted linear least-squares problem", authors proposed a class of preconditioned GAOR methods for solving the equivalent $2\times 2$ block linear system of the weighted linear least-squares problem, and presented some comparison theorems to illustrate the advantages of the new proposed method. In this note, we will point out the imperfections and errors in the proof of several comparison theorems, and give the correct proofs.

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 [1] Berman A, Plemmoms R J. Nonnegative Matrices in the Mathematical Sciences[M]. Academic Press, New York, 1979.[2] Varga R S. Matrix Iterative Analysis[M]. Springer, Berlin, 2000.[3] Wang G, Du Y, Tan F. Comparison results on preconditioned GAOR methods for weighted linear least squares problems[J]. J. Appl. Math., 2012, 9.[4] Yuan J Y. Numerical methods for generalized least squares problem[J]. J. Comput. Appl. Math., 1996, 66:571-584.[5] Huang Z G, Wang L G, Xu Z, Cui J J. Some new preconditioned generalized AOR methods for solving weighted linear least squares problems[J]. Comp. Appl. Math., 2018, 37:415-438.[6] 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, 42:63-79.
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