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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?
     
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  3. Apr 7, 2012 #2

    Office_Shredder

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  4. Apr 7, 2012 #3
    I think I found it, and here is an old thread in these forums about it:

    https://www.physicsforums.com/showthread.php?t=409453

    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:

    http://en.wikipedia.org/wiki/Halley's_method

    http://mathworld.wolfram.com/HalleysMethod.html
     
  5. Apr 7, 2012 #4

    Office_Shredder

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    The paper I linked to does have a fourth order convergence
     
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