Newton-Kantorovich-Vietoris method

TL;DR

This paper introduces a new iterative method combining Newton and Vietoris techniques for solving nonlinear equations in Banach spaces, analyzing its local convergence under broad noise conditions.

Contribution

It proposes a novel combined Newton-Vietoris method for nonlinear equations in Banach spaces and studies its local convergence properties.

Findings

Convergence established under general noise conditions

Method generalizes classical approaches

Potential for improved solution accuracy

Abstract

In this short work we consider nonlinear equation in Banach space $x = A(x)$. We combine classical Newton method with Vietoris method to propose new more general method. Under rather general conditions about the noise we investigate local convergence of the method.