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...

Full description

Saved in:

Bibliographic Details
Published in:	Journal of numerical analysis and approximation theory Vol. 54; no. 1; pp. 140 - 156
Main Authors:	Kumar, Sunil, Janak Raj Sharma, Ioannis K. Argyros
Format:	Journal Article
Language:	English
Published:	Publishing House of the Romanian Academy 30.06.2025
Subjects:	Banach Space Convergence Convergence Order Newton-type method Radius of convergence
ISSN:	2457-6794, 2501-059X
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	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