Title :
The Hermitian positive definite solution of matrix equations X + A* X− A = I
Author :
Wei, Peiyu ; Tan, Boxue ; Liu, Xueting
Author_Institution :
Sch. of Electr. & Electron. Eng., Shandong Univ. of Technol., Zibo, China
Abstract :
In this paper, we discuss the Hermitian positive definite solutions of the nonlinear matrix equation X + A* X-1 A = I. we give some necessary and sufficient conditions for the existence of a Hermitian positive definite solution of equation(1.1). Based on them, we also present some properties of the coefficient matrix A are presented and two equivalent equation of equation(1.1) when the matrix equation has a Hermitian positive definite solution. And construct an iterative methods for obtaining the Hermitian positive definite solutions of the equation are constructed.
Keywords :
Hermitian matrices; iterative methods; nonlinear equations; Hermitian positive definite solution; coefficient matrix; equivalent equation; iterative method; nonlinear matrix equation; Control theory; Dynamic programming; Filtering theory; Image processing; Iterative algorithms; Iterative methods; Matrix decomposition; Nonlinear equations; Stochastic processes; Sufficient conditions; Hermitian positive definite solutions; image processing; iterative method; matrix equation;
Conference_Titel :
Computer Science and Information Technology, 2009. ICCSIT 2009. 2nd IEEE International Conference on
Conference_Location :
Beijing
Print_ISBN :
978-1-4244-4519-6
Electronic_ISBN :
978-1-4244-4520-2
DOI :
10.1109/ICCSIT.2009.5234511
