Heads up for a hot new root seeking algorithm!!

[emece67]

The paper pointed by Claudio shows how the authors use a numerical computation to ascertain the order of convergence of the algorithm. I think that such approach can be used here to estimate the order of convergence of Namir's algorithm not needing a, perhaps cumbersome, rigorous demonstration. Provided, of course, you have a math software capable to work with high precision numbers (say Mathematica).

Knowing the order of convergence, the efficiency index can be calculated, perhaps a better metric to compare algorithms.

In any way, AFAIK, the basic (Newton based) Ostrowsky's algorithm has a convergence order of 4, not 3.