Example 4.  Use Brent's Method to find the three roots of the cubic polynomial  .  

Solution 4.

Enter the function.  

Graph the function  .

Root (i).  Use Brent's Method to find the root that lies in the interval    with an accuracy of  .  

Compare with the Regula Falsi Method which is slower and takes about 36 iterations to achieve an accuracy of  .  

Compare with the Bisection Method which is slower and takes about 50 iterations to achieve an accuracy of  .  

Root (ii).  Use Brent's Method to find the root that lies in the interval    with an accuracy of  .  

Compare with the Regula Falsi Method which is slower and takes about 8 iterations to achieve an accuracy of  .  

Compare with the Bisection Method which is slower and takes about 47 iterations to achieve an accuracy of  .  

Root (iii).  Use Brent's Method to find the root that lies in the interval    with an accuracy of  .  

Compare with the Regula Falsi Method which is slower and takes about 50 iterations to achieve an accuracy of  .  

Compare with the Bisection Method which is slower and takes about 50 iterations to achieve an accuracy of  .  

(c) John H. Mathews 2005