This diagram describes the operation of the bisection root finding algorithm. This method is similar to the binary search algorithm in its searching method and assumptions. The general idea of this algorithm is simple, however in order for it too work the following assumption must be true: The function must either be in increasing or decreasing order. Here is the general algorithm is listed order.

1. First, choose a midpoint value of the list and evaluate this value for a possible match for the root of the function.
2. If the function given the midpoint value evaluates to a value greater than zero, it means that the midpoint value is too high. In this case, we choose another midpoint value by averaging the current midpoint value with the lower bound value of the function. (If the function is in decreasing order than then we average the current midpoint with the upper bound value instead)
3. If the function given the midpoint value evaluates to a value less than zero, it means that the midpoint value is too low. In this case, we choose another midpoint value by averaging the current midpoint value with the upper bound value of the function. (If the function is in decreasing order than then we average the current midpoint with the lower bound value instead)
4. Repeat step 1 to evaluate the new midpoint value and step 2 and 3 as necessary until a matching value for the root of the function is found.