• 论文 • 上一篇    下一篇

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

缪树鑫   

  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

缪树鑫. 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[J]. 计算数学, 2022, 44(1): 89-96.

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
在"求解加权线性最小二乘问题的一类预处理GAOR方法"一文中,作者提出了求解加权线性最小二乘问题等价$2\times 2$块线性系统的一类预处理GAOR方法,并给出了几个比较定理来说明新提出预处理GAOR方法的优越性.本文我们将指出该文中几个比较定理的不完善之处和证明的错误之处,并给出正确的证明.
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.

MR(2010)主题分类: 

()
[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.
[1] 曹阳, 陈莹婷. 正则化HSS预处理鞍点矩阵的特征值估计[J]. 计算数学, 2020, 42(1): 51-62.
[2] 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.
[3] 戴平凡, 李继成, 白建超. 解线性互补问题的预处理加速模Gauss-Seidel迭代方法[J]. 计算数学, 2019, 41(3): 308-319.
[4] 任志茹. 三阶线性常微分方程Sinc方程组的结构预处理方法[J]. 计算数学, 2013, 35(3): 305-322.
阅读次数
全文


摘要