Unformatted text preview: , we know that the root lies in or . In any case, our changeofsign interval is now half as large as before. Repeat this process with the new change of sign interval until the interval is sufficiently small and declare victory. We are guaranteed to converge. We can even compute the maximum number of steps this will take, because if the original changeofsign interval has length then after one bisection the current changeofsign interval is of length , etc . We know in advance how well we will approximate the root . These are very powerful facts, which make bisection a robust algorithmthat is, it is very hard to defeat it....
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 Continuous function, Rootfinding algorithm, Bisection Method

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