The most basic models in numerical analysis are those which help find the root of an equation. The root is the x-value for which the equation, or function f(x) equals zero, or graphically, the point where the curve of the equation intersects the x-axis.

Two methods for finding roots are the Bisection method and the Newton-Raphson method. Both methods use iteration. This means picking arbitrary initial x-values on the curve, then using these values to proceed through a series of calculations repetitively, until the equation evaluates to zero. The more iterations done, the closer one is to the root. Numerous iterations are easily accomplished by the use of computers.

As stated in the Introduction, numerical analysis is limited in its precision, in that it only produces an approximation of the result. When using these numerical methods, one must decide on the level of precision desired. You are limited by the fact that computers have a finite capablity of storing numbers.

Before you start doing numerical analysis, you will always have to decide on this level of precision. How close should this be? This is called Epsilon - an arbitrary number which you choose as a measure of sufficient accuracy. Epsilon is how many places past the decimal you want your answer.

How do you use Epsilon? When you are doing your iterations, you must reach two successive answers which are less than Epsilon. Then you know you have reached your final answer.

Here we will present some tutorials for the Bisection and Newton-Raphson methods. Both take you step-by-step through the different root finding techniques, and highlight the strengths and weaknesses of each. To learn about one of the methods, select it from the left frame below.