Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Root-finding Algorithm Question

  1. Apr 7, 2012 #1
    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. jcsd
  3. Apr 7, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

  4. Apr 7, 2012 #3
    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.

    Here are a couple other links with information about it:


  5. Apr 7, 2012 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    The paper I linked to does have a fourth order convergence
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Root finding Algorithm Date
Finding the roots! Dec 12, 2012
Root-finding by iteration Jun 16, 2012
Linear Combinations of Trig Functions - Finding Roots Mar 11, 2010
Find the asymptotes of f(x)= x/square root(4x-1) May 19, 2005
Finding the roots Jan 1, 2005