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

fYear

2009

fDate

6-7 June 2009

Firstpage

194

Lastpage

197

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;

fLanguage

English

Publisher

ieee

Conference_Titel

Future Computer and Communication, 2009. FCC '09. International Conference on

Conference_Location

Wuhan

Print_ISBN

978-0-7695-3676-7

Type

conf

DOI

10.1109/FCC.2009.57

Filename

5235670

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=3327681