![](/images/graphics-bg.png)
On the Hermitian Positive Definite Solutions of Nonlinear Matrix Equation Xs+A∗X−t1A+B∗X−t2B=Q
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-10-05
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
Nonlinear matrix equation Xs+A∗X−t1A+B∗X−t2B=Q has many applications in engineering; control theory; dynamic programming; ladder networks; stochastic filtering; statistics and so forth.
In this paper, the Hermitian positive definite solutions of nonlinear matrix equation Xs+A∗X−t1A+B∗X−t2B=Q are considered, where Q is a Hermitian positive definite matrix, A, B are nonsingular complex matrices, s is a positive number, and 0 Necessary and sufficient conditions for the existence of Hermitian positive definite solutions are derived. A sufficient condition for the existence of a unique Hermitian positive definite solution is given. In addition, some necessary conditions and sufficient conditions for the existence of Hermitian positive definite solutions are presented. Finally, an iterative method is proposed to compute the maximal Hermitian positive definite solution, and numerical example is given to show the efficiency of the proposed iterative method.
American Psychological Association (APA)
Liu, Aijing& Chen, Guo-Liang. 2011. On the Hermitian Positive Definite Solutions of Nonlinear Matrix Equation Xs+A∗X−t1A+B∗X−t2B=Q. Mathematical Problems in Engineering،Vol. 2011, no. 2011, pp.1-18.
https://search.emarefa.net/detail/BIM-450929
Modern Language Association (MLA)
Liu, Aijing& Chen, Guo-Liang. On the Hermitian Positive Definite Solutions of Nonlinear Matrix Equation Xs+A∗X−t1A+B∗X−t2B=Q. Mathematical Problems in Engineering No. 2011 (2011), pp.1-18.
https://search.emarefa.net/detail/BIM-450929
American Medical Association (AMA)
Liu, Aijing& Chen, Guo-Liang. On the Hermitian Positive Definite Solutions of Nonlinear Matrix Equation Xs+A∗X−t1A+B∗X−t2B=Q. Mathematical Problems in Engineering. 2011. Vol. 2011, no. 2011, pp.1-18.
https://search.emarefa.net/detail/BIM-450929
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-450929