Heads up for a hot new root seeking algorithm!!

[emece67]

(01-21-2017 02:35 PM)Namir Wrote:  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".

Such Thukral algorithm is more or less useless, as it only works for zero roots. It states in the abstract that it can be used solely when the root is zero. Thus, the title f(0) = 0 is correct, the algorithm only converges to a root (yeah, with order 3 and only one function evaluation per iteration) if such root is zero.

I posted it just for the tables, not for the algorithm.

I'm working now on some Python code to test different algorithms. Up to now I was able to check that the Newton algorithm has indeed a 2nd order of convergence (I checked it working with 16, 32, 64, 128, 256, 512 & 1024 decimal digits). I'll test it with more equations and also will check the Halley & Ostrowsky methods. If all goes right, I can check your algorithm.

Regards.