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

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

东北大学理学院, 沈阳 110004;

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
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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

Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

¹College of Sciences, Northeastern University, Shenyang 110004, P.R.China;²College of Information Sciences and Engineering, Northeastern University, Shenyang 110004, P.R.China

摘要

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．
- 预处理因子 /
- GAOR方法 /
- 加权最小二乘问题 /
- 收敛
Abstract: The preconditioned iterative methods for solving linear systems based on a class of weighted linear least square problems were proposed, which were the preconditioned generalized accelerated overrelaxation (GAOR) methods. Some convergence and comparison results were obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is indeed better than the rate of the original methods, whenever the original methods are convergent. Furthermore, effectiveness of the new preconditioned methods is shown by numerical experiment.
- preconditioning /
- GAOR method /
- weighted linear least squares problems /
- convergence

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参考文献(12)

[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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文章访问数: 1509
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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).

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Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

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留言板

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).

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出版历程

Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

计量

出版历程

目录

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).