A Comparison Study of the Classical and Modern Results of Semi-Local Convergence of Newton-Kantorovich Iterations

Autor:	Samundra Regmi, Ioannis K. Argyros, Santhosh George, Christopher I. Argyros
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	iterative methods Banach space semi-local convergence Mathematics QA1-939
Zdroj:	Mathematics, Vol 10, Iss 8, p 1225 (2022)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math10081225
Popis:	There are a plethora of semi-local convergence results for Newton’s method (NM). These results rely on the Newton–Kantorovich criterion. However, this condition may not be satisfied even in the case of scalar equations. For this reason, we first present a comparative study of established classical and modern results. Moreover, using recurrent functions and at least as small constants or majorant functions, a finer convergence analysis for NM can be provided. The new constants and functions are specializations of earlier ones; hence, no new conditions are required to show convergence of NM. The technique is useful on other iterative methods as well. Numerical examples complement the theoretical results.
Databáze:	Directory of Open Access Journals
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