The iterative methods for solving nonlinear matrix equation X+A⋆X−1A+B⋆X−1B=Q

被引：0
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作者：
Sarah Vaezzadeh
Seyyed Mansour Vaezpour
Reza Saadati
Choonkil Park
机构：
[1] Amirkabir University of Technology,Department of Mathematics and Computer Science
[2] Iran University of Science and Technology,Department of Mathematics
[3] Hanyang University,Research Institute for Natural Sciences
来源：
Advances in Difference Equations | / 2013卷
关键词：
nonlinear matrix equation; positive definite solution; inversion-free variant iterative method; convergence rate;
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摘要：
In this paper, we study the matrix equation X+A⋆X−1A+B⋆X−1B=Q, where A and B are square matrices, and Q is a positive definite matrix, and propose the iterative methods for finding positive definite solutions of the matrix equation. Also, general convergence results for the basic fixed point iteration for these equations are given. Some numerical examples are presented to show the usefulness of the iterations.
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