Heads up for a hot new root seeking algorithm!!

[JurgenRo]

(01-11-2017 08:05 PM)Namir Wrote:  

(01-10-2017 10:14 PM)Claudio L. Wrote:  ... but have you ever tested if it's actually worth it? Sometimes they just want to prove a theoretical point, but they are not really better than plain Newton.

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