152
Views
2
CrossRef citations to date
0
Altmetric
Section B

Perturbation analysis of the generalized Sylvester equation and the generalized Lyapunov equation

, &
Pages 408-420 | Received 16 Dec 2008, Accepted 25 Oct 2009, Published online: 01 Dec 2010

References

  • Antoulas , A. 2005 . Approximation of Large-scale Dynamical Systems , Philadelphia : SIAM .
  • Bartels , R. H. and Stewart , G. W. 1972 . Algorithm 432: Solution of the matrix equation AX+XB=C . Commun. ACM. , 15 : 820 – 826 .
  • Benner , P. , Quintana-Ortá , E. S. and Quintana-Ortá , G. 2006 . Solving stable Sylvester equations via rational iterative schemes . J. Sci. Comput. , 28 : 51 – 83 .
  • Calvetti , D. and Reichel , L. 1996 . Application of ADI iterative methods to the restoration of noisy images . SIAM J. Matrix Anal. Appl. , 17 : 165 – 186 .
  • Choi , C. and Laub , A. 1990 . Efficient matrix-valued algorithms for solving stiff Riccati differential equations . IEEE Trans. Autom. Control , 35 : 770 – 776 .
  • Chu , K.-W. E. 1987 . The solution of the matrix equation AXB−CXD=E and . Linear Algebr. Appl. , 93 : 93 – 105 .
  • Cucker , F. , Diao , H. and Wei , Y. 2007 . On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems . Math. Comput. , 76 : 947 – 963 .
  • Dieci , L. , Osborne , M. and Russell , R. 1988 . A Riccati transformation method for solving linear BVPs. I: Theoretical aspects . SIAM J. Numer. Anal. , 25 : 1055 – 1073 .
  • Epton , M. 1980 . Methods for the solution of AXD−BXC=E and its application in the numerical solution of implicit ordinary differential equations . BIT , 20 : 341 – 345 .
  • Gardiner , J. , Laub , A. , Amato , J. and Moler , C. 1992 . Solution of the Sylvester matrix equation AXB+CXD=E . ACM Trans. Math. Softw. , 18 : 223 – 231 .
  • Gohberg , I. and Koltracht , I. 1993 . Mixed, componentwise and structured condition numbers . SIAM J. Matrix Anal. Appl. , 14 : 688 – 704 .
  • Golub , G. H. , Nash , S. and Van Loan , C. 1979 . A Hessenberg–Schur method for the problem AX+XB=C . IEEE Trans. Autom. Control , 24 : 909 – 913 .
  • Graham , A. 1981 . Kronecker Products and Matrix Calculus with Application , New York : Wiely .
  • Higham , N. J. 1993 . Perturbation theory and backward error for AX−XB=C . BIT , 33 : 124 – 136 .
  • Horn , R. A. and Johnson , C. 1991 . Topics in Matrix Analysis , Cambridge : Cambridge University Press .
  • M. Konstantinov, P. Petkov, D. Gu, and V. Mehrmann, Sensitivity of general Lyapunov equations, Tech. Rep. 98–15, Department of Engineering, Leicester University, Leicester, UK
  • Konstantinov , M. , Gu , D. , Mehrmann , V. and Petkov , P. 2003 . Perturbation Theory for Matrix Equations , Amsterdam : Elsevier .
  • Stykel , T. 2002 . Numerical solution and perturbation theory for generalized Lyapunov equations . Linear Algebr. Appl. , 349 : 155 – 185 .

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.