矩阵方程X+A*X-1A+B*X-2B=I正定解的一种求解方法

doi:10.16039/j.cnki.cn22-1249.2019.09.017

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摘要

主要给出了矩阵方程X+A*X^-1A+B*X^-2B=I的正定解的一种求解方法，即Hermite正定解. 首先给出一个矩阵迭代序列；然后根据不动点理论给出了方程正定解存在的一个充分条件；最后通过给出一个具体的数值算例来说明本文方法的可行性。

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	刘丽波
	崔晓梅

关键词: 矩阵方程迭代序列正定解正定矩阵半正定矩阵

Abstract:

In this paper, we study the positive definite solution of a class matrix equations, that is the Hermite positive definite solution of the equation. First ,we show a matrix iterative sequence,then, according to the fixed point theory, a sufficient condition for the existence of positive definite solutions is given. Finally, numerical examples show the feasibility of the proposed method.

Key words: matrix equation iterative sequence positive definite solution positive definite matrix positive semi-definite matrix

出版日期: 2019-09-25 发布日期: 2019-09-25 整期出版日期: 2019-09-25

0151.21

引用本文:

刘丽波, 崔晓梅. 矩阵方程X+A*X^-1A+B*X^-2B=I正定解的一种求解方法[J]. 吉林化工学院学报, 2019, 36(9): 73-75.
LIU Libo, CUI Xiaomei. A Solving Method of Positive Definite Solution About the equation . Journal of Jilin Institute of Chemical Technology, 2019, 36(9): 73-75.

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https://xuebao.jlict.edu.cn/CN/10.16039/j.cnki.cn22-1249.2019.09.017 或 https://xuebao.jlict.edu.cn/CN/Y2019/V36/I9/73

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