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Journal of Applied Mathematics and Computing

Erschienen in:

01.11.2022 | Original Research

Fixed point iterative methods for solving the nonlinear matrix equation \(X-A^{*}X^{-n}A=I\)

verfasst von: Chang-Zhou Li

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 2/2023

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Abstract

The purpose of this study is to identify several sufficient conditions for the existence of the Hermitian positive definite (HPD) solutions of the nonlinear matrix equation (NME) \( X-A^{*}X^{-n}A=I \). In addition, the convergence order of the employed two fixed point iterations (FPIs) for solving this NME are derived, and the perturbation estimate for the NME is given. Finally, a comparison of three well-known current approaches with the two FPIs by some numerical examples demonstrates the FPIs’ universality and efficiency.

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Titel: Fixed point iterative methods for solving the nonlinear matrix equation
verfasst von: Chang-Zhou Li
Publikationsdatum: 01.11.2022
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 2/2023
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-022-01806-y

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