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Order of Convergence: Iteration Scheme

  1. Feb 5, 2012 #1
    1. The problem statement, all variables and given/known data
    I have attached the actual problem as a picture (hope that is ok).

    Xn+1 = 12/(1+Xn), r=3

    For each of the following iteration schemes the sequence xn will converge to the given value of r provided the
    initial value x0 is sufficiently close to r. In each case determine the order of convergence.

    2. Relevant equations

    I have the equation:

    |en+1/enα| ≈ C

    en = r - xn
    en+1 = r - xn+1

    3. The attempt at a solution

    I have attempted to substitute xn+1 into the last equation and then divided terms, but I end up with a final result of 3/(1+xn). I cannot understand how to find the order of convergence from this. Any hints would be appreciated.

    Attached Files:

  2. jcsd
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