Heads up for a hot new root seeking algorithm!!

[Namir]

(01-20-2017 08:59 AM)emece67 Wrote:  

(01-20-2017 01:24 AM)Namir Wrote:  My own perception is that the efficiency index is a qualitative indicator that gives you a general idea about the convergence rate. I doubt there exists a general formula for what I am asking above.

That's also my perception.

Regarding your question, seeing that algorithms can behave very differently (even with different orders of convergence) upon different functions and even around different roots of the same function, I also doubt that there's a way to ascertain the required number of iterations for a given algorithm to converge to a given root of a given function.

I think that what we can do is to build tables such that given here http://article.sapub.org/10.5923.j.ajcam...01.03.html in order to "have a feeling" about the behaviour of an algorithm compared to others.

Regards.

Regarding the link to the article you mentioned in your message. Can you check the new algorithm by the author Thukral. I implemented equation 7 in the article and got bizarre results! Perhaps I am doing something wrong? When I replaced the second subtraction in equation 7 with a multiplication, the algorithm worked but was painfully slow to converge!

I suspect typos om the article since the title has one " Nonlinear Equations of Type f(0)=0" instead of " Nonlinear Equations of Type f(x)=0".

Namir