Abstract
In this paper, we give new convergence results for the basic fixed point iteration and its two inversion-free variants for finding the maximal positive definite solution of the matrix equation \(X+A^{*}X^{-1}A+B^{*}X^{-1}B=Q\), proposed by Long et al. (Bull Braz Math Soc 39:371–386, 2008) and Vaezzadeh et al. (Adv Differ Equ 2013). The new results are illustrated by numerical examples.
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The authors are grateful to editor and the reviewers for their helpful comments and suggestions. This paper is supported by the Project BG051PO 00l-3.3.06-0003 “Building and steady development of PhD students, post-PhD and young scientists in the areas of the natural, technical and mathematical sciences”. The Project is realized by the financial support of the Operative Program “Development of the human resources” of the European social fund of the European Union.
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Communicated by Jinyun Yuan.
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Hasanov, V.I., Ali, A.A. On convergence of three iterative methods for solving of the matrix equation \(X+A^{*}X^{-1}A+B^{*}X^{-1}B=Q\) . Comp. Appl. Math. 36, 79–87 (2017). https://doi.org/10.1007/s40314-015-0215-6
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DOI: https://doi.org/10.1007/s40314-015-0215-6