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Abstract and Applied Analysis

Volume 2013 (2013), Article ID 216035, 4 pages

http://dx.doi.org/10.1155/2013/216035

Research Article

## Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation

Department of Mathematics, Heze University, Heze, Shandong 274015, China

Received 15 May 2013; Revised 23 June 2013; Accepted 4 July 2013

Academic Editor: Vejdi I. Hasanov

Copyright © 2013 Dongjie Gao. 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

- A. C. M. Ran and M. C. B. Reurings, “A nonlinear matrix equation connected to interpolation theory,”
*Linear Algebra and Its Applications*, vol. 379, pp. 289–302, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - A. Ferrante and B. C. Levy, “Hermitian solutions of the equation $X=Q+N{X}^{-1}{N}^{\ast}$,”
*Linear Algebra and Its Applications*, vol. 247, pp. 359–373, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - V. I. Hasanov, “Notes on two perturbation estimates of the extreme solutions to the equations $X\pm {A}^{\ast}{X}^{-1}A=Q$,”
*Applied Mathematics and Computation*, vol. 216, no. 5, pp. 1355–1362, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - D. J. Gao and Y. H. Zhang, “Hermitian positive definite solutions of the matrix equation $X-{A}^{\ast}{X}^{q}A=Q(q>0)$,”
*Mathematica Numerica Sinica*, vol. 29, no. 1, pp. 73–80, 2007 (Chinese). View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - X. Y. Yin and S. Y. Liu, “Positive definite solutions of the matrix equations $X\pm {A}^{\ast}{X}^{-1}A=Q(q>0)$,”
*Computers & Mathematics with Applications*, vol. 59, no. 12, pp. 3727–3739, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - J. Cai and G. L. Chen, “On the Hermitian positive definite solutions of nonlinear matrix equation ${X}^{s}+{A}^{\ast}{X}^{-t}A=Q$,”
*Applied Mathematics and Computation*, vol. 217, no. 1, pp. 117–123, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - A. M. Sarhan, N. M. El-Shazly, and E. M. Shehata, “On the existence of extremal positive definite solutions of the nonlinear matrix equation $Xr+{\sum}_{i=1}^{m}$${A}_{i}^{\ast}{X}^{{\delta}_{i}}{A}_{i}=I$,”
*Mathematical and Computer Modelling*, vol. 51, no. 9-10, pp. 1107–1117, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - Y. Lim, “Solving the nonlinear matrix equation $X=Q+{\sum}_{i=1}^{m}$${M}_{i}{X}^{{\delta}_{i}}{M}_{i}^{\ast}$ via a contraction principle,”
*Linear Algebra and its Applications*, vol. 430, no. 4, pp. 1380–1383, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - X. F. Duan and A. P. Liao, “On Hermitian positive definite solution of the matrix equation $X-{\sum}_{i=1}^{m}{A}_{i}^{\ast}{X}^{r}{A}_{i}=Q$,”
*Journal of Computational and Applied Mathematics*, vol. 229, no. 1, pp. 27–36, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - J.-G. Sun, “Perturbation analysis of the matrix equation $X=Q+{A}^{H}{(\widehat{X}-C)}^{-1}A$,”
*Linear Algebra and Its Applications*, vol. 372, pp. 33–51, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet