# Math 444 Homework 4

1. (15 points) Edit the Wikipedia page that you have been
working on

to incorporate the changes you proposed (after adjusting for feedback

you received). Turn in a formal report of the weakness you had iden-

tified, your proposed improvement, feedback you received through the

discussion page, and the changes you ended up doing. This report will

become part of your final project, so it will also be graded on format-

ting, clarity, etc.

2. (15 points)

(a) Write a Matlab function to do Newton’s method.

(b) Section 2.4 problem 2. Use the code that you wrote, having it

print out xi.

3. (20 points)

(a) Write a Matlab function to do the modified Newton method

based on the iteration in equation (2.11) in Section 2.4.

(b) Section 2.4 problem 4. Use the code that you wrote, having it

print out x_{i}.

4. (15 points) Determine the order of convergence of the iteration from

Section 2.2 problem 20.

5. (20 points) Do this problem as a Good Problem.

Section 2.5 problem 9.

6. (15 points) Consider the polynomial

f(x) = x^{4} + 5x^{3}− 9x^{2}− 85x
− 136.

Starting with x_{0} = 2, do one iteration of
Newton’s method, using

synthetic division to evaluate f(x) and f′(x).