Extending the domain of starting points for Newton's method under conditions on the second derivative

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:340

Article

Argyros, I. K.¹  Ezquerro, J. A.²  Hernandez-Veron, M. A.²  Magrenan, A. A.³ 

[1] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA

[2] Univ La Rioja, Dept Math & Computat, Calle Luis de Ulloa S-N, Logrono 26004, Spain

[3] Univ Int La Rioja, Escuela Super Ingn & Tecnol, Ave La Paz 137, Logrono 26002, Spain

关键词: Newton's method;    Restricted domain;    Majorizing sequence;    Semilocal convergence;    Error estimates;    Integral equation;   

DOI  :  10.1016/j.cam.2018.01.024

来源: Elsevier

【 摘 要 】

In this paper, we propose a center Lipschitz condition for the second Frechet derivative together with the use of restricted domains in order to improve the domain of starting points for Newton's method. In addition, we compare the new result with an older one and see that the former improves the latter. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free