Convergence and Dynamics of Schröder’s Method for Zeros of Analytic Functions with Unknown Multiplicity - Plamena I. Marcheva; Stoil I. Ivanov (Mathematics)
In this paper, we investigate the local convergence of Schröder’s method for finding zeros of analytic functions with unknown multiplicity. Thus, we obtain a convergence theorem that provides exact domains of initial points together with error estimates to ensure the Q-quadratic convergence of Schröder’s method right from the first step. A comparison with the famous Newton’s method, based on the convergence and dynamics when it is applied to some polynomial and non-polynomial equations, is also provided.