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...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2025-06-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/1397 |
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| _version_ | 1849228792594169856 |
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| author | Sunil Kumar Janak Raj Sharma Ioannis K. Argyros |
| author_facet | Sunil Kumar Janak Raj Sharma Ioannis K. Argyros |
| author_sort | Sunil Kumar |
| collection | DOAJ |
| description |
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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| format | Article |
| id | doaj-art-52b8a137398e402db1a83008322895f2 |
| institution | Kabale University |
| issn | 2457-6794 2501-059X |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj-art-52b8a137398e402db1a83008322895f22025-08-22T15:39:22ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2025-06-0154110.33993/jnaat541-1397Convergence analysis of iterative compositions in nonlinear modeling: exploring semilocal and local convergence phenomenaSunil Kumar0Janak Raj Sharma1Ioannis K. Argyros2https://orcid.org/0000-0002-9189-9298Department of Mathematics, University Centre for Research and Development, Chandigarh University, IndiaDepartment of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, IndiaDepartment of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA 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. https://ictp.acad.ro/jnaat/journal/article/view/1397Newton-type methodRadius of convergenceBanach SpaceConvergenceConvergence Order |
| spellingShingle | Sunil Kumar Janak Raj Sharma Ioannis K. Argyros Convergence analysis of iterative compositions in nonlinear modeling: exploring semilocal and local convergence phenomena Journal of Numerical Analysis and Approximation Theory Newton-type method Radius of convergence Banach Space Convergence Convergence Order |
| title | Convergence analysis of iterative compositions in nonlinear modeling: exploring semilocal and local convergence phenomena |
| title_full | Convergence analysis of iterative compositions in nonlinear modeling: exploring semilocal and local convergence phenomena |
| title_fullStr | Convergence analysis of iterative compositions in nonlinear modeling: exploring semilocal and local convergence phenomena |
| title_full_unstemmed | Convergence analysis of iterative compositions in nonlinear modeling: exploring semilocal and local convergence phenomena |
| title_short | Convergence analysis of iterative compositions in nonlinear modeling: exploring semilocal and local convergence phenomena |
| title_sort | convergence analysis of iterative compositions in nonlinear modeling exploring semilocal and local convergence phenomena |
| topic | Newton-type method Radius of convergence Banach Space Convergence Convergence Order |
| url | https://ictp.acad.ro/jnaat/journal/article/view/1397 |
| work_keys_str_mv | AT sunilkumar convergenceanalysisofiterativecompositionsinnonlinearmodelingexploringsemilocalandlocalconvergencephenomena AT janakrajsharma convergenceanalysisofiterativecompositionsinnonlinearmodelingexploringsemilocalandlocalconvergencephenomena AT ioanniskargyros convergenceanalysisofiterativecompositionsinnonlinearmodelingexploringsemilocalandlocalconvergencephenomena |