Convergence analysis of iterative compositions in nonlinear modeling: exploring semilocal and local convergence phenomena
DOI:
https://doi.org/10.33993/jnaat541-1397Keywords:
Newton-type method, Radius of convergence, Banach Space, Convergence, Convergence OrderAbstract
In this work, a comprehensive analysis of a multi-step iterative composition for nonlinear equation is performed, providing insights into both local and semilocal convergence properties. The analysis covers a wide range of applications, elucidating the parameters affecting both local and semilocal convergence and offering insightful information for optimizing iterative approaches in nonlinear model-solving tasks. Moreover, we assert the solution's uniqueness by supplying the necessary standards inside the designated field. Lastly, we apply our theoretical deductions to real-world problems and show the related test results to validate our findings.
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Copyright (c) 2025 Sunil Kumar, Janak Raj Sharma, Ioannis K. Argyros
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
