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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) = x⁴ + 5x³− 9x²− 85x − 136.

Starting with x₀ = 2, do one iteration of Newton’s method, using
synthetic division to evaluate f(x) and f′(x).