New Ostrowski-Halley root seeking algorithm
01-15-2017, 05:15 PM
Post: #1
 Namir Senior Member Posts: 810 Joined: Dec 2013
New Ostrowski-Halley root seeking algorithm
As I promised last week, here is my new algorithm that enhances Halley's method using an approach by Ostrowski (that he applied to Newton's method). To get the PDF file containing the report and the two Excel files containing the test functions click here and select the last item at the bottom to download the ZIP file associated with.

The pseudo code for the new algorithm 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)   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.

The report on my website actually shows and explains two flavors for the algorithm. The test functions are applied to both flavors.

Enjoy

Namir
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 Messages In This Thread New Ostrowski-Halley root seeking algorithm - Namir - 01-15-2017 05:15 PM RE: New Ostrowski-Halley root seeking algorithm - Namir - 01-16-2017, 09:12 PM

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