New Ostrowski-Halley root seeking algorithm

[Namir]

I uploaded a new version of the algorithm that compromises between the two flavors of the algorithm I posted yesterday. You can upload the new ZIP file using the link in my first message.

The pseudo-code for the new version is:

Code:

Given the function f(x)=0, an initial guess, x, and a tolerance Toler for the guess:

Do
  h = 0.01 * (1 + |x|)
  F0 = f(x)
  Fp = f(x + h)
  Fm = f(x - h)
  Deriv1 = (Fp - Fm) / 2 / h
  Deriv2 = (Fp - 2 * F0 + Fm) / h / h
  Diff = F0 / Deriv1 / (1 - F0 * Deriv2 / Deriv1 / 2 / Deriv1)
  z = x - Diff
  Fz = f(z)
  If |x - z| < h Then h = x -z
  Deriv1b = (F0 - 2 * Fz) / (x - z)
  Deriv2b = (Fp - 2 * Fz + Fm) / h / h
  Diff2 = Fz / Deriv1b / (1 - Fz * Deriv2b / Deriv1b / 2 / Deriv1b)
  x = z – Diff2
Loop Until |Diff2| < Toler 
Return X as the refined guess for the root.