Local convergence of Newton's method using Kantorovich convex majorants

Journal of Numerical Analysis and Approximation Theory

Ioannis K. Argyros¹ 

[1] Cameron University;

关键词: Newton's method;    Banach space;    Kantorovich's majorants;    convex function;    local/semilocal convergence;    Fréchet-derivative;   

DOI  :  

来源: DOAJ

【 摘 要 】

We are concerned with the problem of approximating a solution of an operator equation using Newton's method. Recently in the elegant work by Ferreira and Svaiter [6] a semilocal convergence analysis was provided which makes clear the relationship of themajorant function with the operator involved. However these results cannot provide information about the local convergence of Newton's method in their present form. Here we have rectified this problem by using two flexible majorant functions. The radius of convergence is also found. Finally, under the same computational cost, we show that our radius of convergence is larger, and the error estimates on the distances involved is finer than the corresponding ones [1], [11]-[13].

【 授权许可】

Unknown