Convergence of Bisection Method

  • Thread starter Adyssa
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Homework Statement



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

Homework 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

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?
 
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