Title :
The Hermitian Positive Definite Solution of Some Matrix Equations
Author :
Liu, Xuetting ; Wei, Peiyu
Author_Institution :
Sch. of Electr. & Electron. Eng., Shandong Univ. of Technol., Zibo, China
Abstract :
In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X + A* X-2 A = I are studied. 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 . An iterative method for obtaining positive definite solutions of the equation is constructed.
Keywords :
Hermitian matrices; eigenvalues and eigenfunctions; nonlinear equations; Hermitian positive definite solution; eigenvalue; eigenvector; nonlinear matrix equation; Control theory; Eigenvalues and eigenfunctions; Image resolution; Image restoration; Image sequences; Information processing; Iterative methods; Nonlinear equations; Partial differential equations; Sufficient conditions; Hermitian positive definite solutions; iterative method; matrix equation;
Conference_Titel :
Information Processing, 2009. APCIP 2009. Asia-Pacific Conference on
Conference_Location :
Shenzhen
Print_ISBN :
978-0-7695-3699-6
DOI :
10.1109/APCIP.2009.197
