- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 461407, 15 pages
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.
- P. Lancaster and L. Rodman, Algebraic Riccati Equations, Oxford Science, 1995.
- B. Meini, “Matrix equations and structures: effcient solution of special discrete algebraic Riccati equations,” in Proceedings of the WLSSCOO, 2000.
- W. N. Anderson Jr., T. D. Morley, and G. E. Trapp, “Positive solutions to ,” Linear Algebra and its Applications, vol. 134, pp. 53–62, 1990.
- 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.
- 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.
- 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.
- A. Czornik and A. Swierniak, “Lower bounds on the solution of coupled algebraic Riccati equation,” Automatica, vol. 37, no. 4, pp. 619–624, 2001.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- H. Mukaidani, “Numerical computation of cross-coupled algebraic Riccati equations related to -constrained LQG control problem,” Applied Mathematics and Computation, vol. 199, no. 2, pp. 663–676, 2008.