  Many problems in applied mathematics require root finding algorithms.
Unfortunately, root finding methods have limitations. Firstly, regarding the
convergence, there is a trade-off between the size of it's domain and it's
rate. Secondly the numerous evaluations of the function and its derivatives
penalize the efficiency of high order methods. In this article, we present a
family of high order methods, that require few functional evaluations ( One for
each step plus one for each considered derivative at the start of the method),
thus increasing the efficiency of the methods.
