About this Journal Submit a Manuscript Table of Contents
Advances in Numerical Analysis
Volume 2011 (2011), Article ID 184314, 15 pages
http://dx.doi.org/10.1155/2011/184314
Research Article

Refinement Methods for State Estimation via Sylvester-Observer Equation

Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran

Received 6 December 2010; Revised 26 April 2011; Accepted 14 June 2011

Academic Editor: William J. Layton

Copyright © 2011 H. Saberi Najafi and A. H. Refahi Sheikhani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. N. Datta, Numerical Methods for Linear Control Systems: Design and Analysis, Elsevier Academic Press, San Diego, Calif, USA, 2004.
  2. A. C. Antoulas, Approximation of Large-Scale Dynamical Systems, vol. 6 of Advances in Design and Control, SIAM, Philadelphia, Pa, USA, 2005.
  3. U. Baur and P. Benner, “Cross-Gramian based model reduction for data-sparse systems,” Electronic Transactions on Numerical Analysis, vol. 31, pp. 256–270, 2008.
  4. D. C. Sorensen and A. C. Antoulas, “The Sylvester equation and approximate balanced reduction,” Linear Algebra and Its Applications, vol. 351/352, pp. 671–700, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  5. W. H. Enright, “Improving the efficiency of matrix operations in the numerical solution of stiff ordinary differential equations,” ACM Transactions on Mathematical Software, vol. 4, no. 2, pp. 127–136, 1978.
  6. D. Calvetti and L. Reichel, “Application of ADI iterative methods to the restoration of noisy images,” SIAM Journal on Matrix Analysis and Applications, vol. 17, no. 1, pp. 165–186, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  7. J. Z. Hearon, “Nonsingular solutions of TABT=C,” vol. 16, no. 1, pp. 57–63, 1977.
  8. E. de Souza and S. P. Bhattacharyya, “Controllability, observability and the solution of AXXB=C,” Linear Algebra and its Applications, vol. 39, pp. 167–188, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. G. H. Golub, S. Nash, and C. Van Loan, “A Hessenberg-Schur method for the problem AX + XB = C,” IEEE Transactions on Automatic Control, vol. 24, no. 6, pp. 909–913, 1979. View at Publisher · View at Google Scholar
  10. G. H. Golub and C. F. Van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, Md, USA, 3rd edition, 1996.
  11. A. El Guennouni, K. Jbilou, and A. J. Riquet, “Block Krylov subspace methods for solving large Sylvester equations,” Numerical Algorithms, vol. 29, no. 1–3, pp. 75–96, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  12. L. Bao, Y. Lin, and Y. Wei, “Krylov subspace methods for the generalized Sylvester equation,” Applied Mathematics and Computation, vol. 175, no. 1, pp. 557–573, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  13. L. Bao, Y. Lin, and Y. Wei, “A new projection method for solving large Sylvester equations,” Applied Numerical Mathematics, vol. 57, no. 5–7, pp. 521–532, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  14. D. Calvetti, B. Lewis, and L. Reichel, “On the solution of large Sylvester-observer equations,” Numerical Linear Algebra with Applications, vol. 8, no. 6-7, pp. 435–451, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  15. K. Jbilou, “ADI preconditioned Krylov methods for large Lyapunov matrix equations,” Linear Algebra and its Applications, vol. 432, no. 10, pp. 2473–2485, 2010. View at Publisher · View at Google Scholar
  16. M. Robbé and M. Sadkane, “A convergence analysis of GMRES and FOM methods for Sylvester equations,” Numerical Algorithms, vol. 30, no. 1, pp. 71–89, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  17. P. Benner, R.-C. Li, and N. Truhar, “On the ADI method for Sylvester equations,” Journal of Computational and Applied Mathematics, vol. 233, no. 4, pp. 1035–1045, 2009. View at Publisher · View at Google Scholar