The hermitian positive definite solution of matrix equations and its application

Xueting Liu; Hongkui Li

doi:10.1117/12.836787

10 July 2009 The hermitian positive definite solution of matrix equations and its application

Xueting Liu, Hongkui Li

Proceedings Volume 7490, PIAGENG 2009: Intelligent Information, Control, and Communication Technology for Agricultural Engineering; 74901B (2009) https://doi.org/10.1117/12.836787
Event: International Conference on Photonics and Image in Agriculture Engineering (PIAGENG 2009), 2009, Zhangjiajie, China

Abstract

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.

Citation Download Citation

Xueting Liu and Hongkui Li "The hermitian positive definite solution of matrix equations and its application", Proc. SPIE 7490, PIAGENG 2009: Intelligent Information, Control, and Communication Technology for Agricultural Engineering, 74901B (10 July 2009); https://doi.org/10.1117/12.836787

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