文章基本信息

标题：The iterative methods for solving nonlinear matrix equation X + A ⋆ X − 1 A + B ⋆ X − 1 B = Q
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作者：Sarah Vaezzadeh ; Seyyed Mansour Vaezpour ; Reza Saadati 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2013
卷号：2013
期号：1
页码：229
DOI：10.1186/1687-1847-2013-229
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we study the matrix equation X + A ⋆ X − 1 A + B ⋆ X − 1 B = 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. MSC:65F10, 65F30, 65H10, 15A24.
关键词：nonlinear matrix equation ; positive definite solution ; inversion-free variant iterative method ; convergence rate