About Hermitian Positive Definite Solutions of a Type of Nonlinear Matrix Equations

Author

Tan, Chengbo

Author_Institution

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

fYear

2009

fDate

5-6 Dec. 2009

Firstpage

100

Lastpage

102

Abstract

Let A be an n Ã— n nonsingular matrix. In image processing, we must solve a system of linear equations [B. L. Buzbee, G. H. Golub, C. W. Nielson (1970)] Mx = f, however, 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 matrix equation X + A* X^-q A = I . We give an equivalent equation of X + A*X^-q A = I when the matrix equation has a Hermitian positive definite solution.

Keywords

Hermitian matrices; image processing; nonlinear equations; Hermitian positive definite solutions; image processing; linear equations; matrix equation; nonlinear matrix equations; nonsingular matrix; Communication system security; Computer security; Image processing; Image resolution; Image restoration; Image sequences; Iterative methods; Matrix decomposition; Nonlinear equations; Sufficient conditions; Hermitian positive definite solutions; iterative method; matrix equation; necessary and sufficient condition;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer and Communications Security, 2009. ICCCS '09. International Conference on

Conference_Location

Hong Kong

Print_ISBN

978-0-7695-3906-5

Electronic_ISBN

978-1-4244-5408-2

Type

conf

DOI

10.1109/ICCCS.2009.37

Filename

5380312