# Convergence of Bisection Method

## 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?

Last edited: