Local convergence of Newton's method using Kantorovich convex majorants

Ioannis K. Argyros

doi:10.33993/jnaat392-1029

Authors

Ioannis K. Argyros Cameron University, USA

DOI:

https://doi.org/10.33993/jnaat392-1029

Keywords:

Newton's method, Banach space, Kantorovich's majorants, convex function, local/semilocal convergence, Fréchet-derivative, radius of convergence

Abstract views: 246

Abstract

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 the majorant 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].

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References

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