Dynamical and numerical analysis of classical multiple roots finding methods applied for different multiplicities

Abstract

The aim of this paper is the study of the robustness of classical methods defined for finding multiple roots with single multiplicity m when they are used for approximating different roots of a function having different multiplicities. To do so, we first study the dynamical behaviour of such methods when they are applied for approximating multiple roots with different multiplicities of a polynomial. Secondly, based on the obtained dynamical results, we analyse numerically their behaviour and convergence when we carry out the approximation in the case of functions that combine polynomial, exponential and logarithmic functions.