Starting points for Newton's method under a center Lipschitz condition for the second derivative

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:330

Article

Ezquerro, J. A.¹  Hernandez-Veron, M. A.¹  Magrenan, A. A.² 

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

[2] Univ Int La Rioja, Escuela Super Ingn & Tecnol, Ave Gran Via Rey Juan Carlos 1, Logrono 26002, Spain

关键词: Newton's method;    Semilocal convergence;    Majorizing sequence;    Error estimates;    Region of accessibility;    Integral equation;   

DOI  :  10.1016/j.cam.2016.12.013

来源: Elsevier

【 摘 要 】

We analyze the semilocal convergence of Newton's method under a center Lipschitz condition for the second derivative of the operator involved different from that used by other authors until now. In particular, we propose to center the Lipschitz condition for the second derivative in a different point from that where Newton's method starts. This allows us to obtain different starting points for Newton's method and modify the domain of starting points. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free