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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 461407, 15 pages
http://dx.doi.org/10.1155/2012/461407
Research Article

Iterative Algorithm for Solving a System of Nonlinear Matrix Equations

Faculty of Science and Arts, Qassim University, P.O. Box 1162, Buraydah 51431, Saudi Arabia

Received 15 August 2012; Accepted 7 November 2012

Academic Editor: Abdel-Maksoud A. Soliman

Copyright © 2012 Asmaa M. Al-Dubiban. 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. P. Lancaster and L. Rodman, Algebraic Riccati Equations, Oxford Science, 1995.
  2. B. Meini, “Matrix equations and structures: effcient solution of special discrete algebraic Riccati equations,” in Proceedings of the WLSSCOO, 2000.
  3. W. N. Anderson Jr., T. D. Morley, and G. E. Trapp, “Positive solutions to X=ABX1B*,” Linear Algebra and its Applications, vol. 134, pp. 53–62, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. A. M. Aldubiban, Iterative algorithms for computing the positive definite solutions for nonlinear matrix equations [Ph.D. thesis], Riyadh University for Girls, Riyadh, Saudi Arabia, 2008.
  5. O. L. V. Costa and R. P. Marques, “Maximal and stabilizing Hermitian solutions for discrete-time coupled algebraic Riccati equations,” Mathematics of Control, Signals, and Systems, vol. 12, no. 2, pp. 167–195, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. O. L. V. Costa and J. C. C. Aya, “Temporal difference methods for the maximal solution of discrete-time coupled algebraic Riccati equations,” Journal of Optimization Theory and Applications, vol. 109, no. 2, pp. 289–309, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. A. Czornik and A. Swierniak, “Lower bounds on the solution of coupled algebraic Riccati equation,” Automatica, vol. 37, no. 4, pp. 619–624, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. A. Czornik and A. Świerniak, “Upper bounds on the solution of coupled algebraic Riccati equation,” Journal of Inequalities and Applications, vol. 6, no. 4, pp. 373–385, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. R. Davies, P. Shi, and R. Wiltshire, “Upper solution bounds of the continuous and discrete coupled algebraic Riccati equations,” Automatica, vol. 44, no. 4, pp. 1088–1096, 2008. View at Publisher · View at Google Scholar
  10. I. G. Ivanov, “A method to solve the discrete-time coupled algebraic Riccati equations,” Applied Mathematics and Computation, vol. 206, no. 1, pp. 34–41, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. I. G. Ivanov, “Stein iterations for the coupled discrete-time Riccati equations,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 71, no. 12, pp. 6244–6253, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. H. Mukaidani, “Newton's method for solving cross-coupled sign-indefinite algebraic Riccati equations for weakly coupled large-scale systems,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 103–115, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. H. Mukaidani, S. Yamamoto, and T. Yamamoto, “A Numerical algorithm for finding solution of cross-coupled algebraic Riccati equations,” IEICE Transactions, vol. E91-A, pp. 682–685, 2008. View at Publisher · View at Google Scholar
  14. H. Mukaidani, “Numerical computation of cross-coupled algebraic Riccati equations related to H-constrained LQG control problem,” Applied Mathematics and Computation, vol. 199, no. 2, pp. 663–676, 2008. View at Publisher · View at Google Scholar