structural:summarization
The method

The method is applicable for numerically solving the equation f (x) = 0 for the real variable x, where f is a continuous function defined on an interval and where f (a) and f (b) have opposite signs. In this case a and b are said to bracket a root since, by the intermediate value theorem, the continuous function f must have at least one root in the interval (a, b).

At each step the method divides the interval in two parts/halves by computing the midpoint c = (a + b) / 2 of the interval and the value of the function f (c) at that point. If c itself is a root then the process has succeeded and stops. Otherwise, there are now only two possibilities: either f (a) and f (c) have opposite signs and bracket a root, or f (c) and f (b) have opposite signs and bracket a root. The method selects the subinterval that is guaranteed to be a bracket as the new interval to be used in the next step. In this way an interval that contains a zero of f is reduced in width by 50% at each step. The process is continued until the interval is sufficiently small.

Explicitly, if f (c)=0 then c may be taken as the solution and the process stops. Otherwise, if f (a) and f (c) have opposite signs, then the method sets c as the new value for b, and if f (b) and f (c) have opposite signs then the method sets c as the new a. In both cases, the new f (a) and f (b) have opposite signs, so the method is applicable to this smaller interval.