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Functional Iteration Problem

  1. Apr 30, 2007 #1
    1. The problem statement, all variables and given/known data
    Consider an iteration function of the form F(x) = x + f(x)g(x), where f(r) = 0 and f'(r) != 0. Find the precise conditions on the function g so that the method of functional iteration will converge cubically to r if started near r.

    2. Relevant equations
    I really don't know.



    3. The attempt at a solution
    I have no idea how to even begin!:grumpy:

    Thanks in advance!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 30, 2007 #2

    Hurkyl

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    Staff Emeritus
    Science Advisor
    Gold Member

    Try starting with definitions.
     
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