On Newton's method using recurrent functions under hypotheses up to the second Fréchet derivative

Journal of Numerical Analysis and Approximation Theory

Ioannis K. Argyros¹  Saïd Hilout² 

[1] Cameron University;PoitiersUniversity;

关键词: Newton's method;    recurrent functions;    Banach space;    semilocal convergence;    Fréchet-derivative;    majorizing sequence;   

DOI  :  

来源: DOAJ

【 摘 要 】

We provide semilocal result for the convergence of Newton method to a locally unique solution of an equation in a Banach space setting using hypotheses up to the second Fréchet-derivatives and our new idea of recurrent functions. The advantages of such conditions over earlier ones in some cases are:finer bounds on the distances involved, and a better information on the location of the solution.

【 授权许可】

Unknown