矩阵方程X + A* X−A = I的厄米正定解

2009 2nd IEEE International Conference on Computer Science and Information Technology Pub Date : 2009-09-11 DOI:10.1109/ICCSIT.2009.5234511

Peiyu Wei, Boxue Tan, Xueting Liu

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摘要

本文讨论了非线性矩阵方程X + A* X−A = i的厄米正定解，给出了方程(1.1)的厄米正定解存在的充分必要条件。在此基础上，给出了系数矩阵A的一些性质，并给出了式(1.1)在矩阵方程有厄米正定解时的两个等价方程。并构造了求该方程厄密正定解的迭代方法。

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The Hermitian positive definite solution of matrix equations X + A* X− A = I

In this paper, we discuss the Hermitian positive definite solutions of the nonlinear matrix equation X + A* X− A = I. we give some necessary and sufficient conditions for the existence of a Hermitian positive definite solution of equation(1.1). Based on them, we also present some properties of the coefficient matrix A are presented and two equivalent equation of equation(1.1) when the matrix equation has a Hermitian positive definite solution. And construct an iterative methods for obtaining the Hermitian positive definite solutions of the equation are constructed.

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2009 2nd IEEE International Conference on Computer Science and Information Technology

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