Heads up for a hot new root seeking algorithm!!

[Namir]

My study compared the number of iterations and functions for the method of Newton, Halley, Ostrowski, and my new algorithm. I used two dozen tes functions. The last three method generally had close number of iterations and function calls. Since Halley has been discussed on several books (and Wikipedia) to be third order, then Ostrowski and my new algorithm should have the same convergence rate. When you compare Newton's method with the other three, you can see that Newton's method is slower.

I am not sure that Ostrowski's method has an order 4 of convergence. Any reference that confirm this?

Namir