An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation

Applied Mathematics and Computation

Volumn 202, Issue 2, 2008, Pages 571-588

  Dehghan, Mehdi ^a   Hajarian, Masoud ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Generalized reflection matrix; Kronecker matrix product; Optimal approximation reflexive solution pair; Reflexive matrix; The generalized coupled Sylvester matrix equations

Indexed keywords

APPROXIMATION ALGORITHMS; BOOLEAN FUNCTIONS; CONTROL SYSTEMS; ITERATIVE METHODS; YTTRIUM ALLOYS;

CONTROL APPLICATIONS; ITERATIVE ALGORITHMS; MATRIX EQUATIONS; MATRIX PAIRS; MATRIX PENCIL (MP); OPTIMAL APPROXIMATION; REFLEXIVE MATRICES; SYLVESTER MATRIX EQUATIONS;

MATRIX ALGEBRA;

EID: 48149092968     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.02.035     Document Type: Article

References (33)

1. Axelsson O. Iterative Solution Methods (1996), Cambridge University Press
2. Bao L., Lin Y., and Wei Y. A new projection method for solving large Sylvester equations. Appl. Numer. Math. 57 (2007) 521-532
3. Chen H.C. Generalized reflexive matrices: special properties and applications. SIAM J. Matrix Anal. Appl. 19 (1998) 140-153
4. Chen H.C., and Sameh A. Numerical linear algebra algorithms on the ceder system. In: Noor A.K. (Ed). Parallel Computations and their Impact on Mechanics vol. 86 (1987), AMD, The American Society of Mechanical Engineers 101-125
5. 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.
6. Chu K.E. Symmetric solutions of linear matrix equations by matrix decompositions. Linear Algebra Appl. 119 (1989) 35-50
7. Cvetković-Iliíc D.S. The reflexive solutions of the matrix equations AXB = C. Comput. Math. Appl. 51 (2006) 879-902
8. Datta B.N. Numerical Linear Algebra and Applications (1995), Brooks/Cole Publishing Co., Pacific Grove, CA
9. Ding F., and Chen T. Gradient based iterative algorithms for solving a class of matrix equations. IEEE Trans. Autom. Control 50 (2005) 1216-1221
10. Ding F., and Chen T. Iterative least squares solutions of coupled Sylvester matrix equations. Syst. Control Lett. 54 (2005) 95-107
11. Ding F., and Chen T. Hierarchical gradient-based identification of multivariable discrete-time systems. Automatica 41 (2005) 315-325
12. Ding F., and Chen T. Hierarchical least squares identification methods for multivariable systems. IEEE Trans. Autom. Control 50 (2005) 397-402
13. Ding F., and Chen T. On iterative solutions of general coupled matrix equations. SIAM J. Control Optim. 44 (2006) 2269-2284
14. Ding F., Liu P.X., and Ding J. Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle. Appl. Math. Comput. 197 (2008) 41-50
15. Golub G.H., and Van Loan C.F. Matrix Computations. third ed. (1996), The Johns Hopkins University Press, Baltimore and London
16. Guennouni A.E., Jbilou K., and Riquet A.J. Block Krylov subspace methods for solving large Sylvester equations. Numer. Algor. 29 (2002) 75-96
17. Higham N.J. Computing a nearest symmetric positive semidefinite matrix. Linear Algebra Appl. 103 (1988) 103-118
18. Horn R.A., and Johnson C.R. Topics in Matrix Analysis (1991), Cambridge University Press
19. Huang G.-X., Yin F., and Guo K. An iterative method for the skew-symmetric solution and the optimal approximate solution of the matrix equation AXB = C. J. Comput. Appl. Math. 212 (2008) 231-244
20. T = C. Theoret. Comput. Sci. 259 (2001) 623-638
21. Kȧgström B., and Westin L. Generalized Schur methods with condition estimators for solving the generalized Sylvester equation. IEEE Trans. Autom. Control 34 (1989) 745-751
22. - 1 estimators. SIAM J. Matrix Anal. Appl. 13 (1992) 90-101
23. Kȧgström B., and Poromaa P. LAPACK-style algorithms and software for solving the generalized Sylvester equation and estimating the separation between regular matrix pairs. ACM Trans. Math. Software 22 (1996) 78-103
24. Lin Y. Minimal residual methods augmented with eigenvectors for solving Sylvester equations and generalized Sylvester equations. Appl. Math. Comput. 181 (2006) 487-499
25. 2 with applications. Comput. Math. Appl. 41 (2001) 929-935
26. Peng Z.Y., and Hu X.Y. The reflexive and antireflexive solutions of the matrix equation AX = C. Linear Algebra Appl. 375 (2003) 147-155
27. Peng Y.-X., Hu X.-Y., and Zhang L. An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB = C. Appl. Math. Comput. 160 (2005) 763-777
28. 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
29. 2. Appl. Math. Comput. 181 (2006) 988-999
30. Robbé M., and Sadkane M. Use of near-breakdowns in the block Arnoldi method for solving large Sylvester equations. Appl. Numer. Math. 58 (2008) 486-498
31. Xu G., Wei M., and Zheng D. On solutions of matrix equation AXB + CYD = F. Linear Algebra Appl. 279 (1998) 93-109
32. Wang Q.W. A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity. Linear Algebra Appl. 384 (2004) 43-54
33. Wang Q.W. A system of four matrix equations over von Neumann regular rings and Its applications. Acta Math. Sinica, English Ser. Apr. 21 (2005) 323-334