Generalized reflexive solutions of the matrix equation AXB = D and an associated optimal approximation problem

Computers and Mathematics with Applications

Volumn 56, Issue 6, 2008, Pages 1643-1649

  Yuan, Yongxin ^a   Dai, Hua ^b  

^a JIANGSU UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b NANJING UNIVERSITY OF AERONAUTICS AND ASTRONAUTICS   (China)

Author keywords

Generalized reflexive matrix; Generalized singular value decomposition (GSVD); Matrix equation; Optimal approximation; Unitary involution

Indexed keywords

MATRIX EQUATIONS; OPTIMAL APPROXIMATION;

EID: 46849117337     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2008.03.015     Document Type: Article

References (25)

1. Chen H.C. Generalized reflexive matrices: Special properties and applications. SIAM J. Matrix Anal. Appl. 19 (1998) 140-153
2. Weaver J.R. Centrosymmetric (cross-symmetric) matrices, their basic properties, eigenvalues, eigenvectors. Amer. Math. Monthly 92 (1985) 711-717
3. Datta L., and Morgera S. On the reducibility of centrosymmetric matrices - applications in engineering problems. Ciruits Systems Signal Process. 8 (1989) 71-96
4. Tao D., and Yasuda M. A spectral characterization of generalized real symmetric centrosymmetric and generalized real symmetric skew-centrosymmetric matrices. SIAM J. Matrix Anal. Appl. 23 (2002) 885-895
5. Delmas J. On adaptive EVD asymtotic distribution of centro-symmetric covariance matrices. IEEE Trans. Signal Process. 47 (1999) 1402-1406
6. Chen W., Wang X., and Zhong T. The structure of weighting coefficient matrices of harmonic differential quadrature and its application. Commun. Numer. Methods Eng. 12 (1996) 455-460
7. Good I.J. The inverse of a centrosymmetric matrix. Technometrics 12 (1970) 925-928
8. Andrew A.L. Solution of equations involving centrosymmetric matrices. Technometrics 15 (1973) 405-407
9. Andrew A.L. Eigenvectors of certain matrices. Linear Algebra Appl. 7 (1973) 151-162
10. Pye W.C., Boullino T.L., and Atchison T.A. The pseudoinverse of a centrosymmetric matrix. Linear Algebra Appl. 6 (1973) 201-204
11. Cantoni A., and Butler P. Eigenvalues and eigenvectors of symmetric centrosymmetric matrices. Linear Algebra Appl. 13 (1976) 275-288
12. Yasuda M. Spectral characterizations for Hermitian centrosymmetric K-matrices and Hermitian skew-centrosymmetric K-matrices. SIAM J. Matrix Anal. Appl. 24 (2003) 601-605
13. Penrose R. A generalized inverse for matrices. Proc. Cambridge Philos. Soc. 51 (1955) 406-413
14. Yuan Y.-X. On the symmetric solutions of a class of linear matrix equation. J. Eng. Math. 15 (1998) 25-29 (in Chinese)
15. Yuan Y.-X. Solvability for a class of matrix equation and its applications. Nanjing Univ. J. Math. Biquarterly 18 (2001) 221-227 (in Chinese)
16. Khatri C.G., and Matra S.K. Hermitian and nonnegative definite solutions of linear matrix equations. SIAM J. Appl. Math. 31 (1976) 579-585
17. Wang J.S., and Chang X.W. Symmetric solution of a linear matrix equation. Nanjing Univ. J. Math. Biquarterly 7 (1990) 125-129
18. Peng Z.-Y., and Hu X.-Y. The reflexive and anti-reflexive solutions of the matrix equation A X = B. Linear Algebra Appl. 375 (2003) 147-155
19. Cvetkovi{dotless}ć-Ili{dotless}íc D.S. The reflexive solutions of the matrix equation AXB = C. Comput. Math. Appl. 51 (2006) 897-902
20. Bai Z.-J., and Chan R.H. Inverse eigenproblem for centrosymmetric and centroskew matrices and their approximation. Theoret. Comput. Sci. 315 (2004) 309-318
21. Trench W.F. Minimization problems for (R, S)-symmetric and (R, S)-skew symmetric matrices. Linear Algebra Appl. 389 (2004) 23-31
22. Paige C.C., and Saunders M.A. Towards a generalized singular value decompostion. SIAM J. Numer. Anal. 18 (1981) 398-405
23. Stewart G.W. Computing the CS-decomposition of a partitioned orthogonal matrix. Numer. Math. 40 (1982) 297-306
24. Golub G.H., and Van Loan C.F. Matrix Computations (1983), The Johns Hopkins University Press, Baltimore
25. Aubin J.P. Applied Functional Analysis (1979), John Weiley, New York