MACM 316 - Computing Assignment 2
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From the textbook, Burden and Faires (10th edition):
Consider the matrix equation in Applied Exercise 14a of Section 7.3. We
shall refer to the corresponding matrix as , the vector
as . The iterate of a numerical approximation will be denoted .

(a) Write your own Jacobi code for solving the system with a general and
a stopping criterion

Approximate the solution with and . How
many iterations are needed for each ? Plot the approximation for


(b) Solve the system using Matlab’s “backslash operator” for
. We shall assume that the backslash operator gives the
exact solutions.
Once again, approximate the solution with using your code,
but now iterate until the relative error is less than . Find a
mathematical relationship between and the number of iterations.
(c) Do the number of iterations in part (a) and (b) agree? Explain why this
result occurs.
A [P1,P2,…,Pn−1]T
p kth p(k)
n
| |p(k) − p(k−1) | |∞
| |p(k) | |∞
< TOL
n = 20, 40, 80 TOL = 10−3
n
n = 80.
n = 20,40,80
n = 20,40,80
TOL = 10−3
n
MACM 316 - Computing Assignment 2
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