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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 676978, 6 pages
http://dx.doi.org/10.1155/2013/676978
Research Article

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.

Linked References

  1. A. C. M. Ran and M. C. B. Reurings, “On the nonlinear matrix equation X+A* (X)A=Q: solutions and perturbation theory,” Linear Algebra and Its Applications, vol. 346, pp. 15–26, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  2. I. G. Ivanov, “On positive definite solutions of the family of matrix equations X+AXnA=Q,” Journal of Computational and Applied Mathematics, vol. 193, no. 1, pp. 277–301, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  3. J. F. Wang, Y. H. Zhang, and B. R. Zhu, “The Hermitian positive definite solutions of the matrix equation X+AXqA=I(q>0),” Mathematica Numerica Sinica, vol. 26, no. 1, pp. 61–72, 2004 (Chinese). View at MathSciNet
  4. S. M. El-Sayed and A. M. Al-Dbiban, “On positive definite solutions of the nonlinear matrix equation X+AXnA=I,” Applied Mathematics and Computation, vol. 151, no. 2, pp. 533–541, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  5. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  6. S. M. El-Sayed and M. G. Petkov, “Iterative methods for nonlinear matrix equations X+AXαA=I(α>0),” Linear Algebra and Its Applications, vol. 403, pp. 45–52, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  7. V. I. Hasanov, “Positive definite solutions of the matrix equations X±AXqA=Q(0<q1),” Linear Algebra and Its Applications, vol. 404, pp. 166–182, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  8. X. F. Duan and A. P. Liao, “The Hermitian positive definite solution of the matrix equation X+AXqA=Q(q1) and its perturbation analysis,” Numerical Mathematics, vol. 30, no. 3, pp. 280–288, 2008 (Chinese). View at MathSciNet
  9. X.-G. Liu and H. Gao, “On the positive definite solutions of the matrix equations Xs±ATXtA=In,” Linear Algebra and Its Applications, vol. 368, pp. 83–97, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  10. Y. Yueting, “The iterative method for solving nonlinear matrix equation Xs+AXtA=Q,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 46–53, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  11. G. W. Stewart and J. G. Sun, Matrix Perturbation Theory, Computer Science and Scientific Computing, Academic Press, Boston, Mass, USA, 1990. View at MathSciNet
  12. R. Bhatia, Matrix Analysis, vol. 169 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1997. View at Publisher · View at Google Scholar · View at MathSciNet