- Journal Home
- Volume 39 - 2021
- Volume 38 - 2020
- Volume 37 - 2019
- Volume 36 - 2018
- Volume 35 - 2017
- Volume 34 - 2016
- Volume 33 - 2015
- Volume 32 - 2014
- Volume 31 - 2013
- Volume 30 - 2012
- Volume 29 - 2011
- Volume 28 - 2010
- Volume 27 - 2009
- Volume 26 - 2008
- Volume 25 - 2007
- Volume 24 - 2006
- Volume 23 - 2005
- Volume 22 - 2004
- Volume 21 - 2003
- Volume 20 - 2002
- Volume 19 - 2001
- Volume 18 - 2000
- Volume 17 - 1999
- Volume 16 - 1998
- Volume 15 - 1997
- Volume 14 - 1996
- Volume 13 - 1995
- Volume 12 - 1994
- Volume 11 - 1993
- Volume 10 - 1992
- Volume 9 - 1991
- Volume 8 - 1990
- Volume 7 - 1989
- Volume 6 - 1988
- Volume 5 - 1987
- Volume 4 - 1986
- Volume 3 - 1985
- Volume 2 - 1984
- Volume 1 - 1983
On Hermitian Positive Definite Solution of Nonlinear Matrix Equation X+A* X^{-2}A=Q
- BibTex
- RIS
- TXT
@Article{JCM-23-513,
author = {},
title = {On Hermitian Positive Definite Solution of Nonlinear Matrix Equation X+A* X^{-2}A=Q},
journal = {Journal of Computational Mathematics},
year = {2005},
volume = {23},
number = {5},
pages = {513--526},
abstract = { Based on the fixed-point theory, we study the existence and the uniqueness of the maximal Hermitian positive definite solution of the nonlinear matrix equation $X+A^*X^{-2}A=Q$, where $Q$ is a square Hermitian positive definite matrix and $A^*$ is the conjugate transpose of the matrix $A$. We also demonstrate some essential properties and analyze the sensitivity of this solution. In addition, we derive computable error bounds about the approximations to the maximal Hermitian positive definite solution of the nonlinear matrix equation $X+A^*X^{-2}A=Q$. At last, we further generalize these results to the nonlinear matrix equation $X+A^*X^{-n}A=Q$, where $n \ge 2$ is a given positive integer. },
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/8836.html}
}
TY - JOUR
T1 - On Hermitian Positive Definite Solution of Nonlinear Matrix Equation X+A* X^{-2}A=Q
JO - Journal of Computational Mathematics
VL - 5
SP - 513
EP - 526
PY - 2005
DA - 2005/10
SN - 23
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8836.html
KW - Nonlinear matrix equation
KW - Hermitian positive definite solution
KW - Sensitivity analysis
KW - Error bound
AB - Based on the fixed-point theory, we study the existence and the uniqueness of the maximal Hermitian positive definite solution of the nonlinear matrix equation $X+A^*X^{-2}A=Q$, where $Q$ is a square Hermitian positive definite matrix and $A^*$ is the conjugate transpose of the matrix $A$. We also demonstrate some essential properties and analyze the sensitivity of this solution. In addition, we derive computable error bounds about the approximations to the maximal Hermitian positive definite solution of the nonlinear matrix equation $X+A^*X^{-2}A=Q$. At last, we further generalize these results to the nonlinear matrix equation $X+A^*X^{-n}A=Q$, where $n \ge 2$ is a given positive integer.
Xiao-Xia Guo. (1970). On Hermitian Positive Definite Solution of Nonlinear Matrix Equation X+A* X^{-2}A=Q.
Journal of Computational Mathematics. 23 (5).
513-526.
doi:
Copy to clipboard