Using Majorizing Sequences for the Semi-local Convergence of a High-Order and Multipoint Iterative Method along with Stability Analysis

Mandana Moccari, Taher Lotfi

Abstract


This ‎paper‎ deals with the study of relaxed conditions for semi-local convergence for a general iterative method, k-step Newton's method, using ‎majorizing‎ sequences. Dynamical behavior of the mentioned method is also analyzed via Julia set and basins of attraction. Numerical examples of nonlinear systems of equations will be examined to clarify the given theory.

Keywords


Majorizing sequence; High order of convergence; Semi-local convergence; Julia set, Basin of attraction

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