DocumentCode
3060606
Title
A New Algorithm for Solving the Equation X + A*X-1A = I
Author
Li, Min ; Yang, Yueting ; Li, Qingchun
Author_Institution
Dept. of Math., Beihua Univ., Jilin, China
fYear
2012
fDate
23-26 June 2012
Firstpage
41
Lastpage
44
Abstract
In this paper, we investigate the existence of positive definite solutions for the matrix equation X+A*X-1 A=I. A new inversion free variant of the basic fixed point iteration method for obtaining the maximal positive definite solution is established. Moreover, some necessary conditions and sufficient conditions for the existence of positive definite solutions of the matrix equation are obtained. In the end, one numerical example is given to illustrate the effectiveness of our results.
Keywords
iterative methods; matrix algebra; basic fixed point iteration method; inversion free variant; matrix equation; maximal positive definite solution; Iterative methods; Linear algebra; Mathematical model; Riccati equations; Sufficient conditions; Inversion free variant of the basic fixed point iteration; Matrix equation; Positive definite solution;
fLanguage
English
Publisher
ieee
Conference_Titel
Computational Sciences and Optimization (CSO), 2012 Fifth International Joint Conference on
Conference_Location
Harbin
Print_ISBN
978-1-4673-1365-0
Type
conf
DOI
10.1109/CSO.2012.17
Filename
6274674
Link To Document