Title :
On Hermitian Positive Definite Solutions of a Type of Nonlinear Matrix Equations and Application
Author :
Li, Hongkui ; Liu, Xueting
Author_Institution :
Coll. of Sci., Shandong Univ. of Technol., Zibo, China
Abstract :
In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X+A*X-2 A=I are studied. We present some necessary and sufficient conditions for the existence of a Hermitian positive definite solution of this equation. And based on the necessary and sufficient conditions, some properties when the matrix equation has a Hermitian positive definite solution, and an iterative method for finding the maximal solution are given.
Keywords :
Hermitian matrices; iterative methods; nonlinear equations; Hermitian positive definite solutions; iterative method; nonlinear matrix equations; Application software; Educational institutions; Eigenvalues and eigenfunctions; Image restoration; Iterative methods; Mathematics; Nonlinear equations; Partial differential equations; Polynomials; Sufficient conditions; Hermitian positive definite solutions; image restoration; iterative method; matrix equation; necessary and sufficient condition;
Conference_Titel :
Future Computer and Communication, 2009. FCC '09. International Conference on
Conference_Location :
Wuhan
Print_ISBN :
978-0-7695-3676-7
DOI :
10.1109/FCC.2009.57
