A numerical method for finding a root of an equation f(x) = 0. If values a and b are found such that f(a) and f(b) have opposite signs and f is continuous on the interval [a, b], then (by the intermediate value theorem) the equation has a root in (a, b). The method is to bisect the interval and replace it by either one half or the other, thereby closing in on the root.

Let $c=\frac{1}{2}(a+b)$. Calculate f(c). If f(c) has the same sign as f(a), then take c as a new value for a; if not (so that f(c) has the same sign as f(b)), take c as a new value for b. (If it should happen that f(c) = 0, then c is already a root.) Repeat this whole process until the length of the interval [a, b] is less than 2ε‎, where ε‎ is the desired accuracy, specified in advance. The midpoint of the interval can then be taken as an approximation to the root, and the error will be less than ε‎. Compare binary search algorithm.

http://archives.math.utk.edu/visual.calculus/1/bisection.3/index.html An interactive page which demonstrates the method for finding a root of a cubic equation.