On the Newton-Kantorovich hypothesis for solving equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:169

Article

Argyros, LK

关键词: Newton's method;    Banach space;    majorant method;    semilocal-local convergence;    Newton-Kantorovich;    hypothesis;    Newton-Kantorovich theorem;    radius of convergence;    Frechet-derivative;    Lipschitz;    center-Lipschitz;    condition;   

DOI  :  10.1016/j.cam.2004.01.029

来源: Elsevier

【 摘 要 】

The famous Newton-Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton's method to a solution of an equation in connection with the Lipschitz continuity of the Frechet-derivative of the operator involved. Here using Lipschitz and center-Lipschitz conditions we show that the Newton-Kantorovich hypothesis can be weakened. The error bounds obtained under our semilocal convergence result are more precise than the corresponding ones given by the dominating Newton-Kantorovich theorem. (C) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

Free