Newton's method and regularly smooth operators

Journal of Numerical Analysis and Approximation Theory

卷:40

Ioannis K. Argyros¹ 

[1] Cameron University;

关键词: Newton's method;    Banach space;    majorizing sequence;    regularly smooth operators;    Fréchet-derivative;    semilocal convergence;   

DOI  :  

来源: DOAJ

【 摘 要 】

A semilocal convergence analysis for Newton's method in a Banach space setting is provided in this study. Using a combination of regularly smooth and center regularly smooth conditions on the operator involved, we obtain more precise majorizing sequences than in [7]. It then follows that under the same computational cost and the same or weaker hypotheses than in [7] the following benefits are obtained: larger convergence domain; finer estimates on the distances involved, and an at least as precise information on the location of the solution of the corresponding equation. Numerical examples are given to further validate the results obtained in this study.

【 授权许可】

Unknown