Root-finding Algorithm Question

1. Apr 7, 2012

DuncanM

Some time ago I saw a thread in which was mentioned a root-finding algorithm that converges twice as fast as the Newton-Raphson method. Newton-Raphson converges to a zero at a quadratic rate, and a poster pointed out that another algorithm converges to a zero at a quartic rate.

I have tried to find that thread, but cannot.

Anybody here know what algorithm I am talking about? It is for computing the roots of a function and converges to a solution at twice the rate of Newton-Raphson?

2. Apr 7, 2012

Office_Shredder

Staff Emeritus
3. Apr 7, 2012

DuncanM

I think I found it, and here is an old thread in these forums about it:

It is called Halley's Method.

I was mistaken; it actually offers cubic convergence, not quartic.
In any case, is still faster convergence than the Newton-Raphson Method.