Heads up for a hot new root seeking algorithm!!

[Namir]

Using Taylor series can easily explain the order of convergence for Newton, Halley, and Halston. But as the algorithms becomes more complication, generating one or more additional intermediate guesses per iteration, this get complicated.

I was asking in a previous message whether the number of iterations can be estimated using the efficiency index, if we know the number of iterations achieved by another algorithm with a known efficiency index--- for solving the root of the same function, using the same initial guess and tolerance value for the refined root.

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.

Namir