Iterative methods for use with nonlinear discrete algebraic models

A family of multi-point iterative methods for solving nonlinear equations were described in Cordero and Torregrosa (2008) [4], and a general error analysis was given, always for a simple root. Here we study the order of convergence of such methods when we have multiple roots. We prove that the order of convergence goes down to 1 but, when the multiplicity n is known, it may be raised to 2 by using different types of correction. For n unknown, we show that some methods of this family converge faster than the classical Newton’s method. In addition, we provide various numerical tests which confirm or improve on theoretical results and allow us to compare some methods of the aforementioned family.