149
Views
29
CrossRef citations to date
0
Altmetric
Original Articles

On the reflexive and anti-reflexive solutions of the generalised coupled Sylvester matrix equations

&
Pages 607-625 | Received 16 Jul 2008, Accepted 19 May 2009, Published online: 10 Mar 2010

References

  • Bao , L , Lin , Y and Wei , Y . 2007 . A New Projection Method for Solving Large Sylvester Equations . Applied Numerical Mathematics , 57 : 521 – 532 .
  • Borno , I . 1995 . Parallel Computation of the Solutions of Coupled Algebraic Lyapunov Equations . Automatica , 31 : 1345 – 1347 .
  • Chen , HC . 1998 . Generalized Reflexive Matrices: Special Properties and Applications . SIAM Journal on Matrix Analysis and Applications , 19 : 140 – 153 .
  • Chen , HC and Sameh , A . 1987 . “ Numerical Linear Algebra Algorithms on the Ceder System ” . In Parallel Computations and Their Impact on Mechanics (AMD-Vol. 86) , Edited by: Noor , AK . 101 – 125 . New York : The American Society of Mechanical Engineers .
  • Chu , KE . 1987 . The Solution of the Matrix AXB − CXD = E and (YA − DZ, YC − BZ) = (E, F) . Linear Algebra and its Applications , 93 : 93 – 105 .
  • Cvetković-Ilić , DS . 2006 . The Reflexive Solutions of the Matrix Equation AXB = C . Computers & Mathematics with Applications , 51 : 879 – 902 .
  • Dehghan, and Hajarian, M. (2008b), ‘An Iterative Algorithm for Solving a Pair of Matrix Equations AY B = E, CY D = F Over Generalized Centro-Symmetric Matrices’, Computers & Mathematics with Applications, 56, 3246–3260
  • Dehghan , M and Hajarian , M . (2009a), ‘Finite Iterative Algorithms for the Reflexive and Anti-reflexive Solutions of the Matrix Equation A 1 X 1 B 1 + A 2 X 2 B 2 = C ’, Mathematical and Computer Modelling, 49, 1937–1959
  • Dehghan , M and Hajarian , M . (2009b), ‘On the Reflexive Solutions of the Matrix Equation AX B + CY D = E ’, Bulletin of the Korean Mathematical Society, 46, 511–519
  • Dehghan , M and Hajarian , M . (in press-a), ‘The Reflexive and Anti-reflexive Solutions of a Linear Matrix Equation and Systems of Matrix Equations’, Rocky Mountain Journal of Mathematics (in press)
  • Dehghan , M and Hajarian , M . (in press-b), ‘An Efficient Iterative Method for Solving the Second-order Sylvester Matrix Equation EV F 2 − AV F − CV = BW ’, IET Control Theory & Applications (in press)
  • Dehghan , M and Hajarian , M . (in press-c), ‘An Iterative Method for Solving the Generalized Coupled Sylvester Matrix Equations Over Generalized Bisymmetric Matrices’, Applied Mathematical Modelling (in press)
  • Ding , F and Chen , T . 2005a . Gradient Based Iterative Algorithms for Solving a Class of Matrix Equations . IEEE Transactions on Automatic Control , 50 : 1216 – 1221 .
  • Ding , F and Chen , T . 2005b . Hierarchical Gradient-based Identification of Multivariable Discrete-time Systems . Automatica , 41 : 315 – 325 .
  • Ding , F and Chen , T . 2005c . Hierarchical Least Squares Identification Methods for Multivariable Systems . IEEE Transactions on Automatic Control , 50 : 397 – 402 .
  • Ding , F and Chen , T . (2005d), ‘Iterative Least Squares Solutions of Coupled Sylvester Matrix Equations’, Systems & Control Letters, 54, 95–107
  • Ding , F and Chen , T . (2006), ‘On Iterative Solutions of General Coupled Matrix Equations’, SIAM Journal on Control and Optimization, 44, 2269–2284
  • Ding , F . Liu, P.X., and Ding, J. (2008), ‘Iterative Solutions of the Generalized Sylvester Matrix Equations by Using the Hierarchical Identification Principle’, Applied Mathematics and Computations, 197, 41–50
  • Dullerud , GE and Paganini , F . 2000 . A Course in Robust Control Theory–A Convex Approach , New York : Springer-Verlag .
  • Golub , GH and Van Loan , CF . 1996 . Matrix Computations, , 3rd , Baltimore and London : The Johns Hopkins University Press .
  • Guennouni , AE , Jbilou , K and Riquet , AJ . 2002 . Block Krylov Subspace Methods for Solving Large Sylvester Equations . Numerical Algorithms , 29 : 75 – 96 .
  • Kȧgström , B and Poromaa , P . 1992 . Distributed and Shared Memory Block Algorithms for the Triangular Sylvester Equation with Sep−1 Estimators . SIAM Journal on Matrix Analysis and Applications , 13 : 90 – 101 .
  • Kirrinnis , P . 2001 . Fast Algorithms for the Sylvester Equation AX − XB T = C . Theoretical Computer Science , 259 : 623 – 638 .
  • Lin , Y . 2006 . Minimal Residual Methods Augmented with Eigenvectors for Solving Sylvester Equations and Generalized Sylvester Equations . Applied Mathematics and Computations , 181 : 487 – 499 .
  • Peng , YX , Hu , XY and Zhang , L . 2005 . An Iteration Method for the Symmetric Solutions and the Optimal Approximation Solution of the Matrix Equation AXB = C . Applied Mathematics and Computations , 160 : 763 – 777 .
  • Robbé , M and Sadkane , M . 2008 . Use of Near- breakdowns in the Block Arnoldi Method for Solving Large Sylvester Equations . Applied Numerical Mathematics , 58 : 486 – 498 .
  • Starke , G and Niethammer , W . 1991 . SOR for AX − XB = C . Linear Algebra and its Applications , 154 : 355 – 375 .
  • Varga , A . 1999 . Balancing Related Methods for Minimal Realization of Periodic Systems . Systems & Control Letters , 36 : 339 – 349 .
  • Zhou , FZ . 2006 . The Solvability Conditions for the Inverse Eigenvalue Problems of Reflexive Matrices . Journal of Computational and Applied Mathematics , 188 : 180 – 189 .
  • Zhou , B . and Duan, G.R. (2005), ‘An Explicit Solution to the Matrix Equation AX − XF − BY ’, Linear Algebra and its Applications, 402, 345–366
  • Zhou , B . and Duan, G.R. (2006), ‘A New Solution to the Generalized Sylvester Matrix Equation AV − EV F = BW’, Systems & Control Letters, 55, 193–198
  • Zhou , B . and Duan, G.R. (2007), ‘Solutions to Generalized Sylvester Matrix Equation by Schur Decomposition’, International Journal of Systems Science, 38, 369–375
  • Zhou , B and Duan , GR . 2008 . On the Generalised Sylvester Mapping and Matrix Equations . Systems & Control Letters , 57 : 200 – 208 .
  • Zhou , B . Duan, G.R., and Li, Z.Y. (2009), ‘Gradient Based Iterative Algorithm for Solving Coupled Matrix Equations’, Systems & Control Letters, 58, 327–333
  • Zhou , B . Lam, J., and Duan, G.R. (2009), ‘On Smith-type Iterative Algorithms for the Stein Matrix Equation’, Applied Mathematics Letters, 22, 1038–1044
  • Zhou , B , Li , ZY , Duan , GR and Wang , Y . 2009a . Weighted Least Squares Solutions to General Coupled Sylvester Matrix Equations . Journal of Computational and Applied Mathematics , 224 : 759 – 776 .
  • Zhou , B . Li, Z.Y., Duan, G.R., and Wang, Y. (2009b), ‘Solutions to a Family of Matrix Equations by using the Kronecker Matrix Polynomials’, Applied Mathematics and Computations, 212, 327–336
  • Zhou , B . and Yan, Z.B. (2008), ‘Solutions to Right Coprime Factorizations and Generalized Sylvester Matrix Equations’, Transactions of the Institute of Measurement and Control, 30, 397–426

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.