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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.
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    [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.
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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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