## 留言板

 引用本文: 沈海龙, 邵新慧, 张铁. 求解加权线性最小二乘问题的预处理迭代方法[J]. 应用数学和力学, 2012, 33(3): 357-365.
SHEN Hai-long, SHAO Xin-hui, ZHANG Tie. Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems[J]. Applied Mathematics and Mechanics, 2012, 33(3): 357-365. doi: 10.3879/j.issn.1000-0887.2012.03.009
 Citation: SHEN Hai-long, SHAO Xin-hui, ZHANG Tie. Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems[J]. Applied Mathematics and Mechanics, 2012, 33(3): 357-365.

## 求解加权线性最小二乘问题的预处理迭代方法

##### doi: 10.3879/j.issn.1000-0887.2012.03.009

###### 通讯作者: 沈海龙(1971—),男,朝鲜族,吉林延吉人,讲师,博士生(E-mail: hailong-shen@126.com);邵新慧(1970—),女,山东青岛人,副教授,博士(联系人.Tel:+86-24-83684881; E-mail:xinhui1002@126.com).
• 中图分类号: O151.21;O241.6

## Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

• 摘要: 给出了求解一类加权线性最小二乘问题的预处理迭代方法，也就是预处理的广义加速超松弛方法（GAOR），得到了一些收敛和比较结果．比较结果表明当原来的迭代方法收敛时，预处理迭代方法会比原来的方法具有更好的收敛率．而且，通过数值算例也验证了新预处理迭代方法的有效性．
•  [1] YUAN Jin-yun, JIN Xiao-qing. Convergence of the generalized AOR method[J]. Appl Math Comput, 1999, 99(1) : 35-46. [2] ZHOU Xiao-xia , SONG Yong-zhong, WANG Li, LIU Qing-sheng. Preconditioned GAOR methods for solving weighted linear least squares problems[J]. J Comput Appl Math, 2009, 224(2): 242-249. [3] Hadjidimos A . Accelerated overrelaxation method[J]. Math Comput, 1978, 32(1):149-157. [4] Young D M. Iterative Solution of Large Linear Systems[M]. New York: Academic Press, 1971: 25-89. [5] SONG Yong-zhong. Extensions of Ostrowski-Reich theorem in AOR iteratives[J]. Math Numer Sinica, 1985, 7(3): 323-326. [6] SONG Yong-zhong. Convergence of the AOR iterative methods[J]. Math Numer Sinica, 1986, 8(3): 332- 337. [7] Darvishi M T, Hessari P. On convergence of the generalized AOR method for linear systems with diagonally dominant coefficient matrices[J]. Appl Math Comput, 2006, 176(1): 128-133. [8] Darvishi M T , Hessari P, YUAN Jin-yun. On convergence of the generalized accelerated overrelaxation method [J]. Appl Math Comput, 2006, 181(1): 468-477. [9] YUAN Jin-yun. Numerical methods for generalized least squares problems[J]. J Comput Appl Math, 1996, 66(5): 571-584. [10] YUAN Jin-yun, Iusem A N. SOR-type methods for generalized least squares problems[J] . Acta Math Appl Sinica, 2000, 16(1): 130-139. [11] Varge R S. Matrix Iterative Analysis. in: Springer Series in Computational Mathematics[M]. Berlin: Springer-Verlag, 2000: 35-51. [12] Berman A, Plemmons R J. Nonnegative Matrices in the Mathematics Sciences[M]. Philadelphia P A: SIAM, 1994: 23-36.

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##### 出版历程
• 收稿日期:  2011-10-10
• 修回日期:  2011-12-14
• 刊出日期:  2012-03-15

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