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Iterative method

  1. Jan 25, 2012 #1
    1. The problem statement, all variables and given/known data

    The iterative method is used to find the approximate root of the equation x3 + x - 1000 = 0 in [9, 10]. What is the suitable iterative function?

    2. Relevant equations



    3. The attempt at a solution
    How to find the iterative function and is there any conditions for one?
    Thanks for helps.
     
  2. jcsd
  3. Jan 25, 2012 #2

    ehild

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    The iterative procedure is to calculate the next approximation of x from a function of the previous approximation: xi+1=f(xi). The iterative process can converge in a range of x where the derivative |df/dx |<1.

    You can try the ways: x=1000-x3 or x=(1000-x)^1/3.
    Which one works? And you can find other iterative functions for this equation.


    ehild
     
    Last edited: Jan 25, 2012
  4. Jan 25, 2012 #3
    The second one works ^^ Thank you very much. Your explanation is very clear:D
     
  5. Jan 25, 2012 #4

    ehild

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    Using cubic root in an iteration process is not too nice. You can find an other method without that. Hint: write x^3-1000 in the form (x-10)(x^2+10x+100), and isolate x from the x-10 factor.

    ehild
     
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