The submatrix constraint problem of matrix equation AXB + CYD = E

Applied Mathematics and Computation

Volumn 215, Issue 7, 2009, Pages 2578-2590

  Li, Jiao fen ^a   Hu, Xi yan ^a   Zhang, Lei ^a  

^a HUNAN UNIVERSITY   (China)

Author keywords

Iterative method; Least square problem; Perturbation analysis; Principal submatrices constraint; Symmetric centrosymmetric matrices; Symmetric matrix

Indexed keywords

LEAST SQUARE PROBLEM; PERTURBATION ANALYSIS; PRINCIPAL SUBMATRICES CONSTRAINT; SYMMETRIC CENTROSYMMETRIC MATRICES; SYMMETRIC MATRIX;

ALGORITHMS;

ITERATIVE METHODS;

EID: 70350707588     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.08.051     Document Type: Article

References (25)

1. Cantoni A., and Butler P. Eigenvalues and eigenvectors of symmetric centrosymmetric matrices. Linear Algebra Appl. 13 (1976) 275-288
2. Cantoni A., and Butler P. Properties of the eigenvectors of persymmetric matrices with applications to communication theory. IEEE Trans. Commun. COM 24 8 (1976) 804-809
3. Melman A. Symmetric centrosymmetric matrix-vector multiplication. Linear Algebra Appl. 320 (2000) 193-198
4. Liao A.P., and Lei Y. Least-suares solutions of matrix inverse problem for bi-symmeric matrices with a submatrix constraint. Numer. Linear Algebra Appl. 14 (2007) 425-444
5. Peng Z.Y., Hu X.Y., and Zhang L. The inverse problem of bisymmetric matrices with a submatrix constraint. Numer. Linear Algebra Appl. 11 (2004) 59-73
6. Bai Z.J. The inverse eigenproblem of centrosymmetric matrices with a submatrix constraint and its approximation. SIAM J. Matrix Anal. Appl. 26 (2005) 1100-1114
7. Yin Q.X. Construction of real antisymmetric and bi-antisymmetric matrices with prescribed spectrum data. Linear Algebra Appl. 389 (2004) 95-106
8. Deift P., and Nanda T. On the determination of a tridiagonal matrix from its spectrum and a submatrix. Linear Algebra Appl. 60 (1984) 43-55
9. Peng Z.Y., and Hu X.Y. Constructing Jacobi matrix with prescribed ordered defective eigenpairs and a principal submatrix. J. Comput. Appl. Math. 175 (2005) 321-333
10. Zhao L.J., Hu X.Y., and Zhang L. Least squares solutions to AX = B for bisymmetric matrices under a central principal submatrix constraint and the optimal approximation. Linear Algebra Appl. 428 (2008) 871-880
11. Gong L.S., Hu X.Y., and Zhang L. The expansion problem of anti-symmetric matrix under a linear constraint and the optimal approximation. J. Comput. Appl. Math. 197 (2006) 44-52
12. Yuan Y.X., and Dai H. Inverse problems for symmetric matrices with a submatrix constraint. Appl. Numer. Math. 57 (2007) 646-656
13. Peng Z.Y., and Peng Y.X. An efficient iterative method for solving the matrix equation AXB + CYD = E. Numer. Linear Algebra Appl. 13 (2006) 473-485
14. Lei Y., and Liao A.P. A minimal residual algorithm for the inconsistent matrix equation AXB = C over symmetric matrices. Appl. Math. Comput. 188 (2007) 499-513
15. * = E. SIAM J. Matrix Anal. Appl. 3 (2003) 802-808
16. Xu G., Wei M., and Zheng D. On the solutions of matrix equation AXB + CYD = F. Linear Algebra Appl. 279 (1998) 93-109
17. Peng Z.Y. The solutions of matrix AXC + BYD = E and its optimal approximation. Math. Theory Appl. 22 2 (2002) 99-103
18. Liao A.P., Bai Z.Z., and Lei Y. Best approximation solution of matrix equation AXB + CYD = E. SIAM J. Matrix Anal. Appl. 22 (2005) 675-688
19. Wang R.S. Functional Analysis and Optimization Theory (2003), Beljing Unlv of Aeronautics Astronautics Press, Beijing
20. Gersho A. Adaptive equalization of highly dispersive channels for data transmission. BSTJ 48 (1969) 55-70
21. Weaver J. Centrosymmetric (cross-symmetric) matrices, their basic properties, eigenvalues, and eigenvectors. Am. Math. Monthly 92 (1985) 711-717
22. Datta L., and Morgera S. On the reducibility of centrosymmetric matrices-applications in engineering problems. Circuits Systems Signal Process 8 (1989) 71-96
23. E. Stiefel, Ausgleichung ohne Aufstellung der Gausschen Normalgleichungen, Wiss. Z. Tech. Hochsch. Dresden 2 (1952-1953) 441-442.
24. Beattie C.A., and Smith S.W. Optimal matrix approximats in structural identification. J. Optim. Theory. Appl. 74 1 (1992)
25. Kelley C.T. Iterative Methods for Linear and Nonlinear Equations (1995), SIAM, Philadelphia