Convergence analysis of iterative compositions in nonlinear modeling: exploring semilocal and local convergence phenomena

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 c...

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Vydáno v:Journal of numerical analysis and approximation theory Ročník 54; číslo 1; s. 140 - 156
Hlavní autoři: Kumar, Sunil, Janak Raj Sharma, Ioannis K. Argyros
Médium: Journal Article
Jazyk:angličtina
Vydáno: Publishing House of the Romanian Academy 30.06.2025
Témata:
Banach Space
Convergence
Convergence Order
Newton-type method
Radius of convergence
ISSN:2457-6794, 2501-059X
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Shrnutí: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.
ISSN:2457-6794
2501-059X
DOI:10.33993/jnaat541-1397