[1]孙合明,祁正萍,杨家稳.求矩阵方程AXB+CYD=E自反最佳逼近解的迭代算法[J].江西师范大学学报(自然科学版),2012,(02):171-176.
 SUN He-ming,QI Zheng-ping,YANG Jia-wen.The Iterative Algorithm for the Reflexive Optimal Approximation Solutions of Matrix Equations AXB+CYD=E[J].,2012,(02):171-176.
点击复制

求矩阵方程AXB+CYD=E自反最佳逼近解的迭代算法()
分享到:

《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2012年02期
页码:
171-176
栏目:
出版日期:
2012-03-01

文章信息/Info

Title:
The Iterative Algorithm for the Reflexive Optimal Approximation Solutions of Matrix Equations AXB+CYD=E
作者:
孙合明;祁正萍;杨家稳
河海大学理学院,江苏南京,211100;滁州职业技术学院基础部,安徽滁州,239000
Author(s):
SUN He-ming;QI Zheng-ping;YANG Jia-wen
关键词:
Sylvester矩阵方程Kronecker积复合最速下降法最佳逼近自反矩阵
Keywords:
Sylvester matrix equations Kronecker product hybrid steepest descent method optimal approximation reflexive matrix
分类号:
O24
文献标志码:
A
摘要:
利用复合最速下降法的迭代算法对基于自反矩阵(或反自反矩阵)下广义Sylvester矩阵方程AXB+CYD=-E最佳逼近解进行了研究,证明了无论矩阵方程AXB+CYD=E是否相容,该算法都可以用于计算其最佳逼近解.最后,通过2个数值实验证明了该算法的可行性.
Abstract:
An iterative algorithm to calculate the optimal approximation solutions of the generalized Sylvester matrix equations AXB+CYD=E over reflexive (anti-reflexive) matrix is studied by making use of the hybrid steepest descent method (HSDM). The given algorithm can be used to compute the optimal approximation solutions whether matrix equations AXB+CYD=E are consistent or not. The effectiveness of the proposed algorithm is verified by two numerical examples.

参考文献/References:

[1] Yasuda K, Skelton R E. Assigning controllability and observability gramians in feedback control [J]. Journal Guidance Control and Dynamics, 1991, 14(5): 878-885.
[2] Fujioka H, Hara S. State covariance assignment problem with measurement noise: a unified approach based on a symmetric matrix equation [J]. Linear Algebra and its Applications, 1994, 203/204: 579-605.
[3] Xu Guiping, Wei Musheng, Zheng Daosheng. On solutions of matrix equation AXB+CYD=F [J]. Linear Algebra and its Applications, 1998, 279(1/2/3): 93-109.
[4] Baksalary J K, Kaka R. The matrix equation AXB+CYD=E [J]. Linear Algebra and its Applications, 1980, 30: 141-147.
[5] 袁永新. 矩阵方程的最小二乘解 [J]. 高等学校计算数学学报, 2001, 23(4): 324-329.
[6] Peng Zhenyun, Peng Yaxin. An efficient iterative method for solving the matrix equation AXB+CYD=E [J]. Numerical Linear Algebra with Applications, 2006, 13(6): 473-485.
[7] 刘大瑾, 周海林, 袁东锦. AXB+CYD=F的中心对称解及其最佳逼近解的迭代算法 [J]. 扬州大学学报: 自然科学版, 2008, 11(3): 9-13.
[8] Dehghan Mehdi, Hajarian Masoud. Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation [J]. Mathematical and Computer Modelling, 2009, 49(9/10): 1937-1959.
[9] 彭振赟. 矩阵方程AXC+BYD=E的解及其最佳逼近 [J]. 数学理论与应用, 2002, 22(2): 99-103.
[10] 袁仕 芳, 廖安平, 雷渊. 矩阵方程AXB+CYD=E的对称极小范数最小二乘解 [J]. 计算数学, 2007, 29(2): 203-216.
[11] 廖安平, 白中治. 矩阵方程 的对称与反对称最小范数最小二乘解 [J]. 计算数学, 2005, 27(1): 81-95.
[12] 袁永新, 戴华. 矩阵方程 的极小范数最小二乘解 [J]. 高等学校计算数学学报, 2005, 27(3): 232-238.
[13] 盛兴平, 苏友峰, 陈果良. 矩阵方程 的极小范数最小二乘解的迭代解法 [J]. 高等学校计算数学学报, 2008, 30(4): 352-362.
[14] Chen Hsin Chu. Generalized reflexive matrices: special properties and applications [J]. SIAM J Matrix Anal Appl, 1998, 19(1): 140-153.
[15] Chen Hsin Chu, Sameh A H. Numerical linear algebra algorithms on the cedar system [J]. Parallel Computations and Their Impact on Mechanics, 1987, 86(1): 101-125.
[16] Chen Hsin Chu. The SAS domain decomposition method for structural analysis: center for supercomputing research and development [R]. Urbana: University of Illinois, 1988.
[17] Peng Xiangyang, Hu Xiyan, Zhang Lei. The reflexive and anti-reflexive solutions of the matrix equation [J]. Journal of Computational and Applied Mathematics, 2007, 200(2): 749-760.
[18] Peng Zhenyun, Hu Xiyan. The reflexive and anti-reflexive solutions of the matrix equation [J]. Linear Algebra and its Applications, 2003, 375: 147-155.
[19] Peng Zhuohua, Hu Xiyan, Zhang Lei. An efficient algorithm for the least-squares reflexive solution of the matrix equation A1XB1=C1, A2XB2=C2 [J]. Applied Mathematics and Computation, 2006, 181(2): 988-999.
[20] Yamada I. The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings[J]. Stud Comput Math, 2001, 8: 473- 504.
[21] Konstantinos Slavakis, Yamada Isao , Sakaniwa Kohichi . Computation of symmetric positive definite Toeplitz matrices by the hybrid steepest descent method [J]. Signal Processing, 2003, 83(5): 1135-1140.
[22] Yamada I, Ogura N, Shirakawa N .A numerically robust hybrid steepest descent method for the convexly constrained generalized inverse problems [J]. Contemporary Mathematics, 2002, 313: 269-305.

备注/Memo

备注/Memo:
安徽省高校省级自然科学基金(KJ2011B119)
更新日期/Last Update: 1900-01-01