Analysis
The method is guaranteed to converge to a root of f if f is a continuous function on the interval and f(a) and f(b) have opposite signs. The absolute error is halved at each step so the method converges linearly, which is comparatively slow.
Specifically, if c1 = (a+b)/2 is the midpoint of the initial interval, and cn is the midpoint of the interval in the nth step, then the difference between cn and a solution c is bounded by
This formula can be used to determine in advance the number of iterations that the bisection method would need to converge to a root to within a certain tolerance.
Read more about this topic: Bisection Method
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