On a Moser-Steffensen type method for nonlinear systems of equations

TL;DR

This paper introduces a Moser-Steffensen iterative method for solving nonlinear systems that converges quadratically without derivatives, enhancing the applicability of existing methods like Newton and Steffensen.

Contribution

It develops a new derivative-free iterative scheme with proven quadratic convergence for nonlinear systems, expanding the tools available for such problems.

Findings

The method achieves quadratic convergence without derivatives.

It improves the applicability of Newton and Steffensen methods.

Numerical results confirm the theoretical convergence rate.

Abstract

This paper is devoted to the construction and analysis of a Moser-Steffensen iterative scheme. The method has quadratic convergence without evaluating any derivative nor inverse operator. We present a complete study of the order of convergence for systems of equations, hypotheses ensuring the local convergence and finally we focus our attention to its numerical behavior. The conclusion is that the method improves the applicability of both Newton and Steffensen methods having the same order of convergence.