ON THE REFLEXIVE SOLUTIONS OF THE MATRIX EQUATION AXB + CYD

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 46, Issue 3, 2009, pp.511-519
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2009.46.3.511

Title & Authors

ON THE REFLEXIVE SOLUTIONS OF THE MATRIX EQUATION AXB + CYD

Dehghan, Mehdi; Hajarian, Masoud;

Dehghan, Mehdi; Hajarian, Masoud;

Abstract

A matrix is called a generalized reflection matrix if

Keywords

anti-reflexive matrix;generalized reflection matrix;matrix equation;reflexive inverse;reflexive matrix;

Language

English

Cited by

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References

1.

2.

J. K. Baksalary and R. Kala, The matrix equation AXB + CYD = E, Linear Algebra Appl. 30 (1980), 141–147

3.

H. C. Chen, Generalized reflexive matrices: special properties and applications, SIAM J. Matrix Anal. Appl. 19 (1998), no. 1, 140–153

4.

H. C. Chen, The SAS Domain Decomposition Method for Structural Analysis, CSRD Teach, report 754, Center for Supercomputing Research and Development, University of Illinois, Urbana, IL, 1988

5.

H. C. Chen and A. Sameh, Numerical linear algebra algorithms on the ceder system, in: A. K. Noor (Ed.), Parrallel computations and Their Impact on Mechanics, AMD-vol. 86, The American Society of Mechanical Engineers, 1987, 101–125

6.

K. E. Chu, Singular value and generalized singular value decompositions and the solution of linear matrix equations, Linear Algebra Appl. 88/89 (1987), 83–98

7.

D. S. Cvetkovic-Ilic, The reflexive solutions of the matrix equation AXB = C, Comput. Math. Appl. 51 (2006), no. 6-7, 897–902

8.

D. S. Cvetkovic-Ilic, The solutions of some operator equations, J. Korean Math. Soc. 45 (2008), no. 5, 1417–1425

9.

D. S. Cvetkovic-Ilic, Re-nnd solutions of the matrix equation AXB = C, J. Aust. Math. Soc. 84 (2008), no. 1, 63–72

10.

M. Dehghan and M. Hajarian, An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation, Appl. Math. Comput. 202 (2008), no. 2, 571–588

11.

M. Dehghan and M. Hajarian, An iterative algorithm for solving a pair of matrix equations AY B = E, CYD = F over generalized centro-symmetric matrices, Comput. Math. Appl. 56 (2008), no. 12, 3246–3260

12.

M. Dehghan and M. Hajarian, The reflexive and anti-reflexive solutions of a linear matrix equation and systems of matrix equations, Rocky Mountain J. Math. (in press)

13.

M. Dehghan and M. Hajarian, Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation $A_1X_1B_1 + A_2X_2B_2$ = C, Math. Comput. Model. 49 (2009), no. 9-10, 1937–1959

14.

F. Ding and T. Chen, Gradient based iterative algorithms for solving a class of matrix equations, IEEE Trans. Automat. Control 50 (2005), no. 8, 1216–1221

15.

F. Ding and T. Chen, Hierarchical gradient-based identification of multivariable discrete-time systems, Automatica J. IFAC 41 (2005), no. 2, 315–325

16.

F. Ding and T. Chen, Iterative least-squares solutions of coupled Sylvester matrix equations, Systems Control Lett. 54 (2005), no. 2, 95–107

17.

F. Ding and T. Chen, Hierarchical least squares identification methods for multivariable systems, IEEE Trans. Automat. Control 50 (2005), no. 3, 397–402

18.

F. Ding and T. Chen, On iterative solutions of general coupled matrix equations, SIAM J. Control Optim. 44 (2006), no. 6, 2269–2284

19.

F. Ding, P. X. Liu, and J. Ding, Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle, Appl. Math. Comput. 197 (2008), no. 1, 41–50

20.

H. Flanders and H. K. Wimmer, On the matrix equations AX−XB = C and AX−Y B = C, SIAM J. Appl. Math. 32 (1977), no. 4, 707–710

21.

Z. Y. Peng and X. Y. Hu, The reflexive and anti-reflexive solutions of the matrix equation AX = B, Linear Algebra Appl. 375 (2003), 147–155

22.

W. E. Roth, The equations AX−Y B = C and AX−XB = C in matrices, Proc. Amer. Math. Soc. 3 (1952), 392–396

23.

Q. W. Wang, A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity, Linear Algebra Appl. 384 (2004), 43–54

24.

Q. W. Wang, A system of four matrix equations over von Neumann regular rings and its applications, Acta Math. Sin. (Engl. Ser.) 21 (2005), no. 2, 323–334

25.

Q. W. Wang, Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations, Comput. Math. Appl. 49 (2005), no. 5-6, 641–650

26.

Q. W. Wang, H. X. Chang, and Q. Ning, The common solution to six quaternion matrix equations with applications, Appl. Math. Comput. 198 (2008), no. 1, 209–226

27.

Q. W. Wang and C. K. Li, Ranks and the least-norm of the general solution to a system of quaternion matrix equations, Linear Algebra Appl. (2008), (in press)

28.

Q. W.Wang and F. Zhang, The reflexive re-nonnegative definite solution to a quaternion matrix equation, Electron. J. Linear Algebra 17 (2008), 88–101

29.

G. Xu, M. Wei, and D. Zheng, On solutions of matrix equation AXB + CYD = F, Linear Algebra Appl. 279 (1998), no. 1-3, 93–109