#MACM #Discrete Maths

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

Continued on page 2.

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