Heads up for a hot new root seeking algorithm!!

[Namir]

(01-10-2017 10:14 PM)Claudio L. Wrote:  Since it's on-topic:

What do you think about more advanced methods like this one:

http://ojs.excelingtech.co.uk/index.php/...ew/430/294


There's a lot of operations in each iteration, but smaller number of evaluations to find the root. Considering that newRPL has relatively slow CORDIC transcendental functions, evaluation is heavy and one of these could perhaps be beneficial, 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 looked at the article and my new method does not involve as much calculations per iterations! I think my new algorithm has the same order of convergence as Halley, which is third order.

Also the author of teh article is improving on Ostrowski (who improved on Newton). My new algorithms improves on Halley's method using Ostroskwi's approach.

Anyway, thanks for the articles. A few years ago I did a survey of recent algorithms that were inspired by Ostrowski. I found algorithms with three or more intermediate refinements for the root per iterations. While the number of iterations of these algorithms decreased (compared to Newton or Halley), the number of function calls went up! So I am conscious that the number of function calls, per iteration, should not get out of hand.

Namir