求解方程X + A*X- 1a = I的新算法

2012 Fifth International Joint Conference on Computational Sciences and Optimization Pub Date : 2012-06-23 DOI:10.1109/CSO.2012.17

Min Li, Yueting Yang, Qingchun Li

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引用次数: 0

摘要

本文研究了矩阵方程X+A*X-1 A=I正定解的存在性。建立了求最大正定解的基本不动点迭代法的一种新的无反转变体。此外，还得到了矩阵方程正定解存在的充分必要条件。最后，给出了一个数值算例，说明了所得结果的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A New Algorithm for Solving the Equation X + A*X-1A = I

In this paper, we investigate the existence of positive definite solutions for the matrix equation X+A*X-1 A=I. A new inversion free variant of the basic fixed point iteration method for obtaining the maximal positive definite solution is established. Moreover, some necessary conditions and sufficient conditions for the existence of positive definite solutions of the matrix equation are obtained. In the end, one numerical example is given to illustrate the effectiveness of our results.

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2012 Fifth International Joint Conference on Computational Sciences and Optimization

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