On the reflexive solutions of the matrix equation AXB + CYD = E

Bulletin of the Korean Mathematical Society

Volumn 46, Issue 3, 2009, Pages 511-519

  Dehghan, Mehdi ^a   Hajarian, Masoud ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Anti reflexive matrix; Generalized reflection matrix; Matrix equation; Reflexive inverse; Reflexive matrix

Indexed keywords

EID: 67649881615     PISSN: 10158634     EISSN: None     Source Type: Journal    
DOI: 10.4134/BKMS.2009.46.3.511     Document Type: Article

References (31)

1. J. K. Baksalary and R. Kala, The matrix equation AX -Y B = C, Linear Algebra Appl. 25 (1979),41-43.
2. J. K. Baksalary and R. Kala, The matrix equation AXB + CY D = 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. Cvetković-Ilić, The reflexive solutions of the matrix equation AXB = C, Comput. Math. Appl. 51 (2006), no. 6-7, 897-902.
8. D. S. Cvetković-Ilić, The solutions of some operator equations, J. Korean Math. Soc. 45 (2008), no. 5,1417-1425.
9. D. S. Cvetković-Ilić, 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. 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 - YB = 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 + CY D = F, Linear Algebra Appl. 279 (1998), no. 1-3, 93-109.
30. B. Zhou and G. R. Duan, Solutions to generalized Sylvester matrix equation by Schur decomposition, Internat. J. Systems Sci. 38 (2007), no. 5, 369-375.
31. B. Zhou and G. R. Duan, On the generalized Sylvester mapping and matrix equations, Systems Control Lett. 57 (2008), no. 3, 200-208.