Heads up for a hot new root seeking algorithm!!

[Namir]

(01-17-2017 09:13 PM)JurgenRo Wrote:  [quote='Namir' pid='66624' dateline='1484165132']

I think my new algorithm has the same order of convergence as Halley, which is third order.

But again Namir, as you wrote "you think it is of 3rd order", but do you know for sure by means of a strict mathematical proof? Mathematics can't go without that ;-) A modification of a 3rd order algorithm does not necessarily result in an algorithm of the same convergence behavior. Did you try to adopt the proves of Halley/Ostrowski to your new algorithm? This would indeed make your work complete!

Juergen
[/quote

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