José M. Gutiérrez, Víctor Galilea
Published 2020-11-26Version 1
The purpose of this work is to give a first approach to the dynamical behavior of Schr\"oder's method, a well known iterative process for solving nonlinear equations. In this context we consider equations defined in the complex plane. By using topological conjugations, we characterize the basins of attraction of Schr\"oder's method applied to polynomials with two roots and different multiplicities. Actually, we show that these basins are half-planes or circles, depending on the multiplicities of the roots. We finish our study with a graphical gallery that allow us to compare the basins of attraction of Newton's and Schr\"ooder's method applied to some given polynomials. Key: Schr\"oder's method; basin of attraction; nonlinear equation.
On Basins of Attraction of Polynomials and Their Conjugates
A characterization of $(μ,ν)$-dichotomies via admissibility
Methods for determination and approximation of the domain of attraction
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