Heads up for a hot new root seeking algorithm!!

[emece67]

These are my findings so far.

Legend:

• Iter: number of iterations
• TNFE: total number of function evaluations
• COC: computational order of convergence
• EI: efficiency index
• Time: referenced to the fastest method
  

COC is rounded to the nearest integer, except for the \(x^6-1\) case.

Derivatives are always computed by means of the analytical expressions for them (not approximated with differences).

The Potra-Ptak method is a 3rd order method requiring two evaluations for f(x) and one for its derivative. The Kung-Traub method is the 8th order one.

Although I expected bigger differences between different methods, the Ostrowsky-Traub method seems a winner to me.

Regards.