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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 676978, 6 pages
On the Positive Definite Solutions of a Nonlinear Matrix Equation
1School of Mathematics, Key Laboratory of Symbolic Computation and Knowledge Engineering (Ministry of Education), Jilin University, Changchun 130012, China
2Department of Mathematics, Beihua University, Jilin 132013, China
Received 28 November 2012; Revised 19 April 2013; Accepted 21 April 2013
Academic Editor: J. Biazar
Copyright © 2013 Panpan Liu et al. 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.
- A. C. M. Ran and M. C. B. Reurings, “On the nonlinear matrix equation : solutions and perturbation theory,” Linear Algebra and Its Applications, vol. 346, pp. 15–26, 2002.
- I. G. Ivanov, “On positive definite solutions of the family of matrix equations ,” Journal of Computational and Applied Mathematics, vol. 193, no. 1, pp. 277–301, 2006.
- J. F. Wang, Y. H. Zhang, and B. R. Zhu, “The Hermitian positive definite solutions of the matrix equation ,” Mathematica Numerica Sinica, vol. 26, no. 1, pp. 61–72, 2004 (Chinese).
- S. M. El-Sayed and A. M. Al-Dbiban, “On positive definite solutions of the nonlinear matrix equation ,” Applied Mathematics and Computation, vol. 151, no. 2, pp. 533–541, 2004.
- S. M. El-Sayed and A. C. M. Ran, “On an iteration method for solving a class of nonlinear matrix equations,” SIAM Journal on Matrix Analysis and Applications, vol. 23, no. 3, pp. 632–645, 2001/02.
- S. M. El-Sayed and M. G. Petkov, “Iterative methods for nonlinear matrix equations ,” Linear Algebra and Its Applications, vol. 403, pp. 45–52, 2005.
- V. I. Hasanov, “Positive definite solutions of the matrix equations ,” Linear Algebra and Its Applications, vol. 404, pp. 166–182, 2005.
- X. F. Duan and A. P. Liao, “The Hermitian positive definite solution of the matrix equation and its perturbation analysis,” Numerical Mathematics, vol. 30, no. 3, pp. 280–288, 2008 (Chinese).
- X.-G. Liu and H. Gao, “On the positive definite solutions of the matrix equations ,” Linear Algebra and Its Applications, vol. 368, pp. 83–97, 2003.
- Y. Yueting, “The iterative method for solving nonlinear matrix equation ,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 46–53, 2007.
- G. W. Stewart and J. G. Sun, Matrix Perturbation Theory, Computer Science and Scientific Computing, Academic Press, Boston, Mass, USA, 1990.
- R. Bhatia, Matrix Analysis, vol. 169 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1997.