MSIN0180 Computing Task 2022
Instructions: This is a computing task to solve a linear system of equations Ax = b; using the Gauss-
Seidel iterative scheme starting with an initial guess of x(0) = (0; 0; 0) :
The coe¢ cient matrix A and vector b are
A =
0@ 10 1 01 10 2
0 2 10
1A and b =
0@ 97
6
1A :
Compute the solution to the system of linear equations, so that your solution vector x is consistent to four
decimal places. The exact solution is x =

473
475
;
91
95
;
376
475
T
:
The Gauss-Seidel method can be expressed as
x
(k+1)
i =
1
aii
24i1X
j=1

aijx
(k+1)
j


nX
j=i+1

aijx
(k)
j

+ bi
35 ; (i = 1; :::::::; n)
Your program should …rst test that A is strictly diagonally dominant.
Your submitted work should be a report consisting of
Brief description of method [15%]
Documented working java program included as an appendix [20%]
Table of the iterations from k = 1 up to when the required convergence has been reached [20%]
Error graph to show how this decreases as iterations increase [20%]
Any interesting observations or problems encountered [10%]
Bonus points for initiative and willingness to experiment [15%]
Submission: The work should be submitted no later than 11am on Thursday 24th March 2022. Please
allow yourself enough time to complete this task and upload to moodle.
All queries to r.ahmad@ucl.ac.uk
1