[1]张 燕,杨 洋,陆伟东.相容线性系统的行投影块迭代算法[J].南京师范大学学报(工程技术版),2006,06(01):047-51.
　ZHANG Yan~.Block-Iterative Algorithm with Row Projection for Consistent Linear System[J].Journal of Nanjing Normal University(Engineering and Technology),2006,06(01):047-51.
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相容线性系统的行投影块迭代算法
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南京师范大学学报（工程技术版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
06卷
期数:
2006年01期
页码:
047-51
栏目:
出版日期:
2006-03-30

文章信息/Info

Title:
Block-Iterative Algorithm with Row Projection for Consistent Linear System
作者:
张  燕1;  2;  杨 洋1;  陆伟东1
1. 南京审计学院应用数学系, 江苏南京210029; 2. 河海大学理学院, 江苏南京210098
Author(s):
ZHANG Yan~
1,2),YANG Yang~1,LU Weidong~1
关键词:
行投影块迭代算法;  列分解策略;  最远块
Keywords:
b lock- itera tive a lgor ithm w ith row pro jec tion;  column partition stra tegy;  the rem otest block
分类号:
O241.6
摘要:
探讨了一种行投影块迭代算法来求解大型相容线性系统.该算法基于Kaczmarz算法,主要思想是首先对系数矩阵A进行分块,然后通过选取离当前迭代点距离最远的块来进行投影,并将投影作为下一个迭代点.数值结果显示,行投影迭代算法对坏条件问题非常有效,所提出的算法与经典的C imm ino算法相比,收敛速度更快.另外还提出一种新的对系数矩阵A分块的列分解策略,该策略基于每块的列相关性估计而得出.
Abstract:
In th is paperw e d iscuss a b lock- itera tive algorithm w ith row projection for solv ing large consistent linear system. Th is a lgor ithm is based on theKaczm arz a lgor ithm. The key idea is tha t the coe ffic ient m atr ixA is firstly d-i v ided into b locks, then the current iterativ e po int is pro jec ted onto the remo test b lo ck measured by the distance between the ite rative po int and the b lo ck, and the pro jec tion is taken as the nex t iterative po int. Num er ica l simu la tions show that block- iterative a lgo rithm w ith row pro jection is very effic ient fo r so lv ing il-l conditioned problem s. Com pared w ith the c lassical C imm ino a lgo rithm, a lgo rithm acce le rates the converg ence greatly. In addition w e present a new co-l um n partition strategy, based on the estim ate o f co lumn-dependence o f each block, to d iv ide the coeffic ientm atrixA.

参考文献/References:

[ 1] SCOLNIK H, ECHEBEST N, GUARDARUCC IM T, et a.l A class o f optim ized row projection m e thods for so lv ing large nonsymme tr ic linear sy stem s[ J]. Appl Num erM a th , 2002, 41( 4): 499-513.
[ 2] CIMM INO G. Ca lco lo approssim ato pe r le so luzion i de i sistem i di equazion i linea ri[ J]. R icerca Sc i II, 1938, 9: 326-333.
[ 3] LIU CHANGWEN. An acce le ration schem e for row pro jection m ethods[ J] . Jour Comp ApplM ath, 1995, 57: 363-391.
[ 4] AHARONI R, CENSOR Y. B lo ck- iterative pro jection m ethods fo r paralle l com puta tion of so lutions to convex feasib ility problem s[ J]. Linear A lgebra App,l 1989, 120: 165-175.
[ 5] GUB IN L G, POLYAK B T, RA IK E V. The m ethod o f pro jections for finding the common point o f conv ex se ts[ J]. USSR Com putM a th Phy s, 1967, 7: 1-24.
[ 6] FLETCHER R. Practica lM ethods o fOptim ization[M ] . 2nd ed. New Yo rk: W iley, 1987: 199-202.
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备注/Memo

备注/Memo:
基金项目: 南京审计学院青年科研基金资助项目( NSK2005 /C08) .
作者简介: 张  燕( 1978-) , 女, 讲师, 主要从事应用数学方面的教学与研究. E-m a il:zhy8317@ nau. edu. cn
更新日期/Last Update: 2013-04-29