[1]尤兴华,马圣容.李亚普诺夫方程AX+XB=C的简洁解及其应用[J].南京师大学报(自然科学版),2011,34(03):44-49.
You Xinghua,Ma Shengrong.The Simple Formulae of Solutions to Liapunov Matrix Equation AX+XB=C and Its Application[J].Journal of Nanjing Normal University(Natural Science Edition),2011,34(03):44-49.
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李亚普诺夫方程AX+XB=C的简洁解及其应用(
)
《南京师大学报(自然科学版)》[ISSN:1001-4616/CN:32-1239/N]
- 卷:
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第34卷
- 期数:
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2011年03期
- 页码:
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44-49
- 栏目:
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数学
- 出版日期:
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2011-09-20
文章信息/Info
- Title:
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The Simple Formulae of Solutions to Liapunov Matrix Equation AX+XB=C and Its Application
- 作者:
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尤兴华1; 马圣容2
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( 1. 南京工程学院基础部,江苏南京211167) ( 2. 南京晓庄学院数学与信息技术学院,江苏南京211171)
- Author(s):
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You Xinghua1; Ma Shengrong2
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1.Department of Basic Course,Nanjing Institute of Technology,Nanjing 211167,China
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- 关键词:
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李亚普诺夫方程; 约当标准型; 最小二乘解; 极小范数最小二乘解
- Keywords:
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Liapunov matrix equation; Jordan canonical form; the least-squares solution; the minimum-norm leastsquares solution
- 分类号:
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O241.6
- 摘要:
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首先给出了4种情况下李亚普诺夫方程AX+XB=C解的简洁表达式,然后,通过前述结论得出了矩阵方程AX+YB=E的最小二乘解以及极小范数最小二乘解的解析式,并且,通过相应数值例子验证了相关结论.
- Abstract:
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At first,the simple expression of solutions to matrix equation AX + XB = C is given,the second an explicit formulae for the minimum-norm least-squares solutions of matrix equation AX + YB = E is obtained,finally,a numerical example is given.
参考文献/References:
[1] You Xinghua,Ma Shengrong,Yan Shijian. The explicit solution to equation AX + XB = C in matrices[J]. Chinese Quarterly Journal of Mathematics,2009, 24( 2) : 516-524.
[2] Zheng Bing,Zhong Chengkui. The existence and expressions for the generalized inverse A( 2) T,S of linear operator in Hilbert space[J]. Acta Mathematica Scientia,2007, 27( 2) : 288-295.
[3] Jiang Tongsong,Wei Musheng. On a solution of the quaternion matrix equation X - A珚XB = C and its application[J]. Acta Mathematica Sinica,2004, 20( 6) : 1-8.
[4] Chen Xiaoshan,Li Wen. On the matrix equation X + A* X - 1 A = P: Solution and perturbation analysis[J]. Mathematica Numerica Sinica,2005, 27( 3) : 303-310.
[5] Jameson A. Solution of the equation AX + XB = C by inversion of an M × M or N × N matrix[J]. SIAM J Appl Math,1968, 28( 16) : 1 020-1 023.
[6] Eurice de Souza,Bhattacharyya S P. Controllability,observability and the solution of AX - XB = C[J]. Linear Algebra Appl, 1981, 39: 167-188.
[7] John Jones J K,Lew C. Solutions of Liapunov matrix equation BX - XA = C[J]. IEEE Trans Automatic Control,1982,AC - 27: 464-466.
[8] 陈玉明,肖衡. 矩阵方程AX - XB = C 的显式解[J]. 应用数学和力学, 1995, 15( 12) : 1 051-1 059.
[9] 韩维信. 李雅普诺夫矩阵方程的求解公式[J]. 天津大学学报: 自然科学与工程技术版, 2001, 34( 3) : 408-409.
[10] 汤学炳. 李雅普诺夫矩阵方程的新解法[J]. 江汉石油学院学报, 1998, 20( 3) : 126-129.
[11] 殷保群,奚宏生,杨孝先. 矩阵方程AX - XB = C 非奇异解的存在性[J]. 中国科学技术大学学报,2000,30( 3) : 340-344.
[12] Ben-Isracl A,Greville T N E. Generalized Inverse: Theory and Applications[M]. New York: Wiley,1974.
[13] 陈永林. 广义逆矩阵的理论与方法[M]. 南京: 南京师范大学出版社,2005.
备注/Memo
- 备注/Memo:
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基金项目:江苏省高校自然科学基金( 07KJD110077) .通讯联系人:尤兴华,讲师,研究方向: 计算数学理论及应用. E-mail: xhyou@ njit. edu. Cn
更新日期/Last Update:
2011-09-15