On the existence of Hermitian positive definite solutions of the matrix equation Xs + A*X-tA = Q
On the existence of Hermitian positive definite solutions of the matrix equation Xs + A*X-tA = Q
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DOI：
10.1016/j.laa.2008.03.019
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发表时间：
2008-08
影响因子：
1.1
通讯作者：
X. Duan;A. Liao
中科院分区：
文献类型：
--
作者：
X. Duan;A. Liao
本文系统地、深入地研究了一般非线性矩阵方程Xs+A * X-tA=Q的厄米正定解的存在性。导出了厄米正定解的一个新估计。在不动点定理的基础上，得到了厄密正定解存在的一些新的充分条件和必要条件。最后，证明了一个厄密正定解存在的充分必要条件。
In this paper, the existence of Hermitian positive definite solutions of the general nonlinear matrix equation Xs+A∗X-tA=Q is studied systematically and deeply. A new estimate of Hermitian positive definite solutions is derived. Based on a fixed point theorem, some new sufficient conditions and new necessary conditions for the existence of Hermitian positive definite solutions are obtained. In the end, a necessary and sufficient condition for the existence of a Hermitian positive definite solution is proved.