Local convergence of iterative methods for solving equations and system of equations using weight function techniques

Abstract This paper analyzes the local convergence of several iterative methods for approximating a locally unique solution of a nonlinear equation in a Banach space. It is shown that the local convergence of these methods depends of hypotheses requiring the first-order derivative and the Lipschitz condition. The new approach expands the applicability of previous methods and formulates their theoretical radius of convergence. Several numerical examples originated from real world problems illustrate the applicability of the technique in a wide range of nonlinear cases where previous methods can not be used.

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