A Class of Steffensen-Type Iterative Methods for Nonlinear Systems

Abstract

A class of iterative methods without restriction on the computation of Fréchet derivatives including multisteps for solving systems of nonlinear equations is presented. By considering a frozen Jacobian, we provide a class of m-step methods with order of convergence $m+1$. A new method named as Steffensen-Schulz scheme is also contributed. Numerical tests and comparisons with the existing methods are included.