Positive Definite Solutions of the Matrix Equation Xr-∑i=1mAi∗X-δiAi=I
Author
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-07-12
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
We investigate the nonlinear matrix equation Xr-∑i=1mAi∗X-δiAi=I, where r is a positive integer and δi∈(0,1], for i=1,2,…,m.
We establish necessary and sufficient conditions for the existence of positive definite solutions of this equation.
A sufficient condition for the equation to have a unique positive definite solution is established.
An iterative algorithm is provided to compute the positive definite solutions for the equation and error estimate.
Finally, some numerical examples are given to show the effectiveness and convergence of this algorithm.
American Psychological Association (APA)
al-Dubiban, Asmaa M.. 2015. Positive Definite Solutions of the Matrix Equation Xr-∑i=1mAi∗X-δiAi=I. Abstract and Applied Analysis،Vol. 2015, no. 2015, pp.1-8.
https://search.emarefa.net/detail/BIM-1052054
Modern Language Association (MLA)
al-Dubiban, Asmaa M.. Positive Definite Solutions of the Matrix Equation Xr-∑i=1mAi∗X-δiAi=I. Abstract and Applied Analysis No. 2015 (2015), pp.1-8.
https://search.emarefa.net/detail/BIM-1052054
American Medical Association (AMA)
al-Dubiban, Asmaa M.. Positive Definite Solutions of the Matrix Equation Xr-∑i=1mAi∗X-δiAi=I. Abstract and Applied Analysis. 2015. Vol. 2015, no. 2015, pp.1-8.
https://search.emarefa.net/detail/BIM-1052054
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1052054