Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A
Author
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-4, 4 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-08-29
Country of Publication
Egypt
No. of Pages
4
Main Subjects
Abstract EN
We consider the nonlinear matrix equation X=Q+A∗(X^−C)−1A, where Q is positive definite, C is positive semidefinite, and X^ is the block diagonal matrix defined by X^=diag(X,X,…,X).
We prove that the equation has a unique positive definite solution via variable replacement and fixed point theorem.
The basic fixed point iteration for the equation is given.
American Psychological Association (APA)
Gao, Dongjie. 2013. Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-4.
https://search.emarefa.net/detail/BIM-455264
Modern Language Association (MLA)
Gao, Dongjie. Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A. Abstract and Applied Analysis No. 2013 (2013), pp.1-4.
https://search.emarefa.net/detail/BIM-455264
American Medical Association (AMA)
Gao, Dongjie. Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-4.
https://search.emarefa.net/detail/BIM-455264
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-455264
