Journal of Advances in Applied Mathematics

On the Hermite Positive Definite Solution of the Matrix Equation X + A∗ (I_m⊗ X-C)^-tA=Q

Download PDF (246 KB) PP. 63 - 70 Pub. Date: January 1, 2017

DOI: 10.22606/jaam.2017.21006

Author(s)

Yan Feng^*
School of Information Science and Technology, Qingdao University of Science and Technology, Qingdao, China
Luping Xu
School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, China
Minghui Wang
School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, China

Abstract

The nonlinear matrix equation X + A∗ (I_m⊗ X-C)^-tA=Q is considered in this paper. A sufficient and necessary condition for Hermite positive definite (HPD) solutions of this equation is presented by using properties of the Kronecker product. Two iterative methods for solving the equation are constructed by making use of the principle of the bounded sequence. The feasibility and effectiveness of the iterative methods are verified by numerical example.

Keywords

Nonlinear matrix equation; Hermite positive definite solution; fixed point iteration; inverse-free iteration.

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