Title :
The Hermitian positive definite solution of a type of nonlinear matrix equations X + A*X -1A = 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, the Hermitian positive definite solutions of the nonlinear matrix equation X + A*X-1 A = I are studied. Suppose X is a positive definite solution of this equation, 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 the Hermitian positive definite solutions of the equation are constructed.
Keywords :
Hermitian matrices; eigenvalues and eigenfunctions; iterative methods; Hermitian positive definite solution; eigenvalue and eigenvector; iterative method; nonlinear matrix equations; Control theory; Dynamic programming; Eigenvalues and eigenfunctions; Filtering theory; Image processing; Iterative methods; Nonlinear equations; Nonlinear filters; Partial differential equations; Stochastic systems; 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.2009.5234588
