Title :
On hermitian positive definite solutions of a type of nonlinear matrix equations
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 matrix equation X + A* X-q A = I are studied, where A is an n times n nonsingular matrix. We give some necessary and sufficient conditions for the existence of a Hermitian positive definite solution of this equation. And based on them, some properties and two equivalent equations of X + A* X-q A = I are presented when the matrix equation has a Hermitian positive definite solution.
Keywords :
Hermitian matrices; nonlinear equations; Hermitian positive definite solution; nonlinear matrix equation; nonsingular matrix; Communication system control; Control theory; Dynamic programming; Educational institutions; Iterative methods; Matrix decomposition; Nonlinear equations; Stochastic processes; Sufficient conditions; Technology management; Hermitian positive definite solutions; iterative method; matrix equation; necessary and sufficient condition;
Conference_Titel :
Computing, Communication, Control, and Management, 2009. CCCM 2009. ISECS International Colloquium on
Conference_Location :
Sanya
Print_ISBN :
978-1-4244-4247-8
DOI :
10.1109/CCCM.2009.5268068
