Extending the Newton-Kantorovich hypothesis for solving equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:234

Article

Argyros, Ioannis K.¹  Hilout, Said² 

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

[2] Univ Poitiers, Lab Math & Applicat, F-86962 Futuroscope, France

关键词: Newton's method;    Banach space;    Semilocal convergence;    Newton-Kantorovich hypothesis;    Chandrasekhar-type nonlinear integral equation;    Two boundary value problem with Green kernel;   

DOI  :  10.1016/j.cam.2010.04.014

来源: Elsevier

【 摘 要 】

The famous Newton-Kantorovich hypothesis (Kantorovich and Akilov, 1982 [3], Argyros, 2007 [2], Argyros and Hilout, 2009 [7]) 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, and our new idea of recurrent functions, we show that the Newton-Kantorovich hypothesis can be weakened, under the same information. Moreover, the error bounds are tighter than the corresponding ones given by the dominating Newton-Kantorovich theorem (Argyros, 1998 [1];[2,7]; Ezquerro and Hernandez, 2002[11]; [3]; Proinov 2009, 2010 [16,17]). Numerical examples including a nonlinear integral equation of Chandrasekhar-type (Chandrasekhar, 1960[9]), as well as a two boundary value problem with a Green's kernel (Argyros, 2007 [2]) are also provided in this study. Published by Elsevier B.V.

【 授权许可】

Free