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Convergence of Bisection Method

  1. Aug 7, 2011 #1
    1. The problem statement, all variables and given/known data

    Show that the Bisection Method converges linearly with K = 1/2

    2. Relevant equations

    Note that x(sub n) converges to the exact root r with an order of convergence p if:

    lim(n->oo) (|r - x(n + 1)|) / (|r - x(n)|^p) = lim(n->oo) (|e(n + 1)|) / (|e(n)|^p) = K

    3. The attempt at a solution

    EDIT: I can rearrange the equation above as follows (K = 1/2):

    |e(n+1)| = 1/2|e(n)|^p

    and I know that the bisection method is a linear operation, reducing the interval by 1/2 each time and converging on the real root, so p = 1, but I'm not sure how to show this?
     
    Last edited: Aug 8, 2011
  2. jcsd
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