In image processing, we must solve a system of linear equations[1] Mx = f , however, the solving of the System Mx = f can be transformed to the solving of the equations X + A^*X^-q A = I. In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X + A^*X^-q A = I are studied. We present some necessary and sufficient conditions for the existence of a Hermitian positive definite solution of this equation. And based on the necessary and sufficient conditions, some properties when the matrix equation has a Hermitian positive definite solution, and an iterative method for finding the maximal solution are given.

Date Published: 10 July 2009
PDF: 7 pages
Proc. SPIE 7490, PIAGENG 2009: Intelligent Information, Control, and Communication Technology for Agricultural Engineering, 74901B (10 July 2009); doi: 10.1117/12.836787

Published in SPIE Proceedings Vol. 7490:
PIAGENG 2009: Intelligent Information, Control, and Communication Technology for Agricultural Engineering
Honghua Tan; Qi Luo, Editor(s)