Some Geometric Constructions of Two Variants of Newton’s Method to Solving Nonlinear Equations with Multiple Roots

Abstract

In this paper we give some geometric constructions of variations of Newton’s method, based on ideas of Schroder, for the case ¨ that roots are multiple. A straight line and a polynomial are used to construct the iteration equation when the multiplicity of the root is known. In the case that the multiplicity is unknown another straight line and a rational function are used. Representative figures of an example are given.