The Hermitian Positive Definite Solution of Matrix Equations and Its Application

Author

Li, Hongkui ; Song, Daojin

Author_Institution

Coll. of Sci., Shandong Univ. of Technol., Zibo, China

Volume

2

fYear

2009

fDate

18-19 July 2009

Firstpage

340

Lastpage

343

Abstract

In image processing, we must solve a system of linear equations Mx = f . By, we know the solving of the System Mx = f can be transformed to the solving of the equations X + A* X^-q A = I. In this paper, we study the Hermitian positive definite solutions of the nonlinear matrix equation X + A* X^-q A = I . We discuss the relation between X and A by the eigenvalue and eigenvector of X and A respectively, and the property of numerical range of A , construct an iterative method for obtaining positive definite solutions of the equation at last.

Keywords

Hermitian matrices; eigenvalues and eigenfunctions; image processing; iterative methods; nonlinear equations; Hermitian positive definite solution; eigenvalue and eigenvector; image processing; iterative method; linear equation; nonlinear matrix equation; Control theory; Differential equations; Educational institutions; Eigenvalues and eigenfunctions; Image processing; Information processing; Iterative methods; Nonlinear equations; Partial differential equations; Sufficient conditions; Hermitian positive definite solutions; image processing; iterative method; matrix equation;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Processing, 2009. APCIP 2009. Asia-Pacific Conference on

Conference_Location

Shenzhen

Print_ISBN

978-0-7695-3699-6

Type

conf

DOI

10.1109/APCIP.2009.220

Filename

5197206