[1]谈雪媛.亏秩最小二乘问题的最优AOR方法(英文)[J].南京师大学报(自然科学版),2011,34(04):1-8.
　Tan Xueyuan.Optimal AOR for Rank Deficient Least Squares Problem[J].Journal of Nanjing Normal University(Natural Science Edition),2011,34(04):1-8.
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亏秩最小二乘问题的最优AOR方法(英文)()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第34卷
期数:
2011年04期
页码:
1-8
栏目:
数学
出版日期:
2011-12-20

文章信息/Info

Title:
Optimal AOR for Rank Deficient Least Squares Problem
作者:
谈雪媛
南京师范大学数学科学学院，江苏南京210046
Author(s):
Tan Xueyuan
School of Mathematical Sciences,Nanjing Normal University,Nanjing 210046,China
关键词:
AOR 方法; 最优参数; 2 -循环; 渐近半收敛因子; 亏秩线性最小二乘问题
Keywords:
AOR methods; optimal parameters; 2-cyclic; asymptotical semiconvergence factor; rank deficient linear least squares problem
分类号:
O241.6
摘要:
主要研究了求解亏秩线性最小二乘问题的AOR方法的最优参数、渐近半收敛因子及其明晰的表达形式.并给出了两个数值例子阐明结论.
Abstract:
This paper studied the optimal parameters and asymptotical semiconvergence factor of AOR methods for rank deficient linear least squares problem and presented the explicit expressions of these factors． Finally，two numerical examples are given to illustrate our results．

参考文献/References:

［1］ Chen Y T． Iterative methods for linear squares problems［D］． Ontario: University of Waterloo，1975．
［2］ Niethammer W，J de Pillis，Varga R S． Convergence of block iterative methods applied to sparse least squares problems［J］． Linear Algebra Appl，1984， 58: 327-324．
［3］ Markham T L，Neumann M，Plemmons R J． Convergence of a direct-iterative method for large-scale least squares problems ［J］． Linear Algebra Appl，1985， 69: 155-167．
［4］ Saridakis Y G． An algorithmic approach for the analysis of extrapolated iterative schemes applied to least-squares problems ［J］． J Comput Appl Math，1988， 24: 209-225．
［5］ Miller V A，Neumann M． Successive overrelaxation methods for solving the rank deficient least squares problem［J］． Linear Algebra Appl， 1987， 88 /89: 533-557．
［6］ Tian Hongjun． Accelarated overrelaxation methods for rank deficient linear systems［J］． Appl Math Comput，2003， 140: 485- 499．
［7］ Tan Xueyuan，Song Yongzhong． Optimal parameters for 2-cyclic AOR［J］． Appl Math Comput，2010， 216: 1 428-1 442．
［8］ Varga R S． Matrix Iterative Analysis［M］． 2nd ed． Berlin: Springer-Verlag，2000．
［9］ Hadjidimos A． Successive overrelaxation and related methods［J］． J Comput Appl Math，2000， 123: 177-199．
［10］ Sisler M． Uber ein Zweiparametrigen Iterationsverfahrens［J］． Apl Mat， 1973( 18) : 325-332．

备注/Memo

备注/Memo:
Foundation item: Supported by the National Natural Science Foundation of China( 10971102) ，the Natural Science Foundation of Jiangsu Province of China( BK2009398) ，the Foundation for the Authors of the National Excellent Doctoral Thesis Award of China ( 200720) and Jiangsu Innovation Fund for Doctor of Science( CX07B － 027z) ． Corresponding author: Tan Xueyuan，Ph． D student， lecturer，majored in computational mathematics． E-mail: tanxueyuan@ njnu． edu． cn
更新日期/Last Update: 2013-03-21