Lab for the Newton-Raphson Method

Newton-Raphson Iteration. Find a root of f(x) = 0 given an initial approximation using the iteration: .

Report to be handed in.
Computer Exercises.

Exercise 1. Use Newton's method to find the three roots of the cubic polynomial
.
Use the starting values . For each different starting value, explain what happened. Supply graphs and lists of iterations in your solution. Determine the Newton-Raphson formula
that is used. Show details of the computations starting with .

Starting with , type the following list of commands which perform Newton's method.

Now use the subroutine with the various starting values .

How many iterations did it take to converge starting with ?
What was the final approximation to the root ?
Adjust the number of iterations used so that unnecessary values are not printed.

How many iterations did it take to converge starting with ?
What was the final approximation to the root ?
Adjust the number of iterations used so that unnecessary values are not printed.

How many iterations did it take to converge starting with ?
What was the final approximation to the root ?
Adjust the number of iterations used so that unnecessary values are not printed.

How many iterations did it take to converge starting with ?
What was the final approximation to the root ?
Adjust the number of iterations used so that unnecessary values are not printed.

How many iterations did it take to converge starting with ?
What was the final approximation to the root ?
Adjust the number of iterations used so that unnecessary values are not printed.

How many iterations did it take to converge starting with ?
What was the final approximation to the root ?
Adjust the number of iterations used so that unnecessary values are not printed.

Exercise 2. Use Newton's method to find all the roots of the cubic polynomial
.
Supply graphs and lists of iterations in your solution.

(c) John H. Mathews, 1998