Use the bisection method to find the root of:

x = e^-x

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- Sep 27th 2009, 09:12 PMjzelltBisection method
Use the bisection method to find the root of:

x = e^-x - Sep 27th 2009, 09:30 PMpickslides
Read "The Method" from here.

Bisection method - Wikipedia, the free encyclopedia

Choose $\displaystyle a=-1 $ and $\displaystyle b=1$ as endpoints for the first iteration

Now find c the midpoint that bisects the interal. $\displaystyle c = \frac{b+a}{2} = \frac{1-1}{2} = 0$

find $\displaystyle f(a), f(b)$ and $\displaystyle f(c)$

You will find

$\displaystyle f(a) = f(-1)<0 $

$\displaystyle f(b) = f(1) >0 $

$\displaystyle f(c) = f(0) <0 $

So now as $\displaystyle f(c) < 0$ choose it and $\displaystyle f(b) > 0$ to be the new interval as they have opposite signs as so on. The interval will get smaller and converge on the solution.