留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

求解加权线性最小二乘问题的预处理迭代方法

沈海龙 邵新慧 张铁

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

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
基金项目: 国家自然科学基金资助项目(11071033);中央高校基本业务费资助项目(090405013)
详细信息
    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.
  • 加载中
计量
  • 文章访问数:  1236
  • HTML全文浏览量:  45
  • PDF下载量:  842
  • 被引次数: 0
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

目录

    /

    返回文章
    返回