Numerical Analysis/Bisection Method Worked Example

X^3=20 ,f(X), X4=4, X1=1 take four iterations .

Example edit

Find an approximation of   correct to within 10-4 by using the bisection method on  . starting on [1, 2].

Analysis of the Problem edit

The number of iterations we will use, n, must satisfy the following formula:
Thus, we will use 14 iterations of the bisection method.

Iteration #1 edit

First, we find the midpoint of the interval [1, 2]:


Then we check if   is positive or negative:


The value of   is negative, which means that   is less than  .

We therefore use   as the left endpoint of our new interval and keep 2 as the right endpoint.


Iteration #2 edit

Repeat the process from Iteration #1 to do Iteration #2:

Iteration #3 - Iteration #14 edit

Complete Iteration #3 - Iteration #14:

the final answer is follow or describe below

Conclusion edit

Thus, we have found that

is an approximation of   correct to within 10-4.