The bisection method is considered the simplest one-dimensional root-finding algorithm. The general interest is to find the value of a continuous function such that .

Suppose we know the two points of an interval and , where , and that and lie along the continuous function, taking the midpoint of this interval as , where , the bisection method then evaluates this value as f(c).

Let's illustrate the setup of points along a nonlinear function with the following graph:

Since the value of f(a) is negative and f(b) is positive, the bisection method assumes that the root lies somewhere between a and b and gives .

If or is very close to zero by some predetermined error tolerance value, then a root is declared as found. If , then we may conclude that a root exists along the interval and , or interval and otherwise.

On the next evaluation, is replaced as either or accordingly. With the new interval shortened, the bisection method repeats with the same evaluation to determine...