[1]农利伟,陈浦胤.求解主子阵约束下矩阵方程的算法[J].南京师大学报(自然科学版),2010,33(04):19-22.
　Nong Liwei,Chen Puyin.An Iterative Algorithm for Solving Matrix Equations With Submatrix Constraints[J].Journal of Nanjing Normal University(Natural Science Edition),2010,33(04):19-22.
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求解主子阵约束下矩阵方程的算法()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第33卷
期数:
2010年04期
页码:
19-22
栏目:
数学
出版日期:
2010-12-20

文章信息/Info

Title:
An Iterative Algorithm for Solving Matrix Equations With Submatrix Constraints
作者:
农利伟1;  陈浦胤2
1. 南宁地区教育学院数学系, 广西南宁530001 2. 上海交通大学数学系, 上海200240
Author(s):
Nong Liwei1; Chen Puyin2
1.Department of Mathematics,Nanning Prefecture’s Educational College,Nanning 530001,China 2. Departm ent ofM ethem at ics, Shanghai J iaotong Un ivers ity, Shanghai 200240, Ch in a
关键词:
矩阵方程;  迭代算法;  最小二乘解;  最佳逼近解
Keywords:
iterativ e algorithm s;  m atr ix equations;  least-squares so lutions;  the best approx im ation
分类号:
O151.21
摘要:
利用文中提出的求解一般有限维算子方程的抽象算法和理论,获得求解带主子阵约束下矩阵方程AXB=C反对称最小二乘解及最佳逼近解的一个迭代算法,进行了理论分析.并给出数值例子说明算法的计算效果.
Abstract:
By use of the abstract a lgor ithm and theoretica l analysis in [ 1] for so lv ing a finite-d imensional ope rato r equation, this pape r proposes an iterativ e a lgor ithm s for getting the skew- symm etr ic least-squares so lution and the best approx im ation solution of the ma tr ix equation AXB = C w ith a subm atrix constrain t. The convergence ana lys is of the algorithm is presented and several num er ica l examp les are reported to illustra te its compu tational pe rfo rm ance.

参考文献/References:

[ 1] H uang J, Nong L. An itera tive a lgor ithm for so lv ing a fin ite-dim ens iona l linear ope rato r equa tion T ( x ) = f w ith app lications [ J] . L inearA lgeb ra and Its Applica tions, 2010, 432( 5): 1 176-1 188.
[ 2] 龚丽莎, 胡锡炎, 张磊. 主子阵约束下矩阵方程AX = B 的对称最小二乘解[ J]. 数值计算与计算机应用, 2006, 27 ( 2): 154-160.
[ 3] 彭振赟, 胡锡炎, 张磊. 双对称矩阵的一类反问题[ J]. 计算数学, 2005, 27( 1): 11-18.
[ 4] 戴华. 对称正交对称矩阵反问题的最小二乘解[ J] . 计算数学, 2003, 25( 1): 59-66.
[ 5] Peng Z, Peng Y. An e fficient itera tivem e thod for so lv ing the m atr ix equation[ J]. Num er ica l L inea rA lgebraW ith App lications, 2006, 13( 6): 473-485.
[ 6] Peng Z. An itera tivem e thod for the least squares symm e tric so lution o f the linearm atrix equa tion[ J]. App liedM athem atics and Com putation, 2005, 170( 1) : 711-723.

相似文献/References:

[1]尤兴华,严涛,马圣容.矩阵方程AXB=C的反对称解问题[J].南京师大学报(自然科学版),2003,26(01):6.
　You Xinghua,Yan Tao,Ma Shengrong.Anti-symmetric Solution of Matrix Eqution AXB=C[J].Journal of Nanjing Normal University(Natural Science Edition),2003,26(04):6.
[2]顾 颖,葛志利,陈 新.求解一类模糊线性系统的全局FOM和GMRES方法[J].南京师大学报(自然科学版),2021,44(01):13.[doi:10.3969/j.issn.1001-4616.2021.01.003]
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备注/Memo

备注/Memo:
基金项目: 国家自然科学基金( 10771138) . 通讯联系人: 农利伟, 讲师, 研究方向: 数值代数. E-mail:nlw616@126. com
更新日期/Last Update: 2013-04-08