Anomalies in the convergence of Traub‐type methods with memory

Abstract

The stability analysis of a new family of iterative methods with memory isintroduced. This family, designed from Traub's method, allows to add memorythrough the introduction of an accelerating parameter. Hence, the speed of con-vergence of the iterative method increases up to 3.30, with no new functionalevaluations. A dynamical study of the proposed family on quadratic polynomialsis presented obtaining interesting qualitative properties.