Heads up for a hot new root seeking algorithm!!

[JurgenRo]

(01-18-2017 05:47 AM)Ángel Martin Wrote:  

(01-17-2017 10:42 PM)Namir Wrote:  The new algorithm matches or slightly improve on Halley. Sicne Halley is third order, the new algorithm could not be second or fourth order. I am saying 3rd order by induction.

Namir

And how do you define "it matches"? what criteria is used? What parameters? In what cases? all possible expressions??
IMHO induction is not applicable here...

Cheers,
ÁM

I fully agree with Ángels rating. I do not see how Induction could do the work here. Also, the convergence rate might (and likely will) depend on the properties of the function to be "rooted" (smoothness for example). That is why a "demonstration" of convergence with a couple of functions is not reliable at all. Then again it would be legitimate to say, that you guess that the scheme is of 3rd order (for sufficient smooth?) functions but that a rigorous proof is still missing ...

Juergen