References
- W. N. Anderson, T. D. Morley and G. E. Trapp, Positive solutions to X=A−BX−1B*, Linear Algebra Appl. 134 (1990), pp. 53–62 doi: 10.1016/0024-3795(90)90005-W
- R. Bhatia, Matrix Analysis, Graduate Text in Mathematics, Spring, Berlin, 1997
- J. Cai and G. Chen, Some investigation on Hermitian positive definite solutions of the matrix equation Xs+A*X−t A=Q, Linear Algebra Appl. 430 (2009), pp. 2448–2456 doi: 10.1016/j.laa.2008.12.033
- J. Cai and G. Chen, On the Hermitian positive definite solutions of nonlinear matrix equation Xs+A*X−tA=Q, Appl. Math. Comput. 217 (2010), pp. 117–123 doi: 10.1016/j.amc.2010.05.023
- X. Duan and A. Liao, On the existence of Hermitian positive definite solutions of the matrix equation Xs+A*X−t A=Q, Linear Algebra Appl. 429 (2008), pp. 673–687 doi: 10.1016/j.laa.2008.03.019
- S. M. El-Sayed and M. El-Alem, Some properties for the existence of a positive definite solution of the matrix equation , Appl. Math. Comput. 128 (2002), pp. 99–108 doi: 10.1016/S0096-3003(01)00019-4
- S. M. El-Sayed and A. C.M. Ran, On an iterative methods of solving a class of nonlinear matrix equations, SIAM J. Matrix Anal. Appl. 23 (2001), pp. 632–645 doi: 10.1137/S0895479899345571
- J. C. Engwerda, On the existence of a positive definite solution of the matrix equation X+ATX−1A=I, Linear Algebra Appl. 194 (1993), pp. 91–108 doi: 10.1016/0024-3795(93)90115-5
- J. C. Engwerda, A. C.M. Ran and A. L. Rijkeboer, Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation X+A*X−1A=Q, Linear Algebra Appl. 186 (1993), pp. 255–275 doi: 10.1016/0024-3795(93)90295-Y
- I. G. Ivanov and S. M. El-Sayed, Properties of positive definite solutions of the equation X+A*X−2A=I, Linear Algebra Appl. 279 (1998), pp. 303–316 doi: 10.1016/S0024-3795(98)00023-8
- I. G. Ivanov and F. Uhlig, Improved methods and starting values to solve the matrix equations X±A*X−1A=I iteratively, Math. Comput. 74 (2004), pp. 263–278 doi: 10.1090/S0025-5718-04-01636-9
- I. G. Ivanov, V. I. Hasanov and B. V. Minchev, On matrix equations X±A*X−2A=I, Linear Algebra Appl. 326 (2001), pp. 27–44 doi: 10.1016/S0024-3795(00)00302-5
- X. Wang and Y. Li, Necessary and sufficient conditions for the existence of a positive definite solution of a nonlinear matrix equation, Int. J. Comput. Math. 87 (2010), pp. 2542–2551 doi: 10.1080/00207160802684442
- X. Yin, S. Liu and L. Fang, Solutions and perturbation estimates for the matrix equation Xs+A*X−tA=Q, Linear Algebra Appl. 431 (2009), pp. 1409–1421 doi: 10.1016/j.laa.2009.05.010
- X. Zhan and J. Xie, On the matrix equation X+ATX−1A=I, Linear Algebra Appl. 247 (1996), pp. 337–345 doi: 10.1016/0024-3795(95)00120-4
- Y. Zhang, On Hermitian positive solutions of the matrix equation X+A*X−2A=I, Linear Algebra Appl. 372 (2003), pp. 295–304 doi: 10.1016/S0024-3795(03)00530-5
- D. Zhou, G. Chen, G. Wu and X. Zhang, Some properties of the nonlinear matrix equation Xs+A*X−tA=Q, J. Math. Anal. Appl. 392 (2012), pp. 75–82 doi: 10.1016/j.jmaa.2012.02.046