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MSIN0180 Computing
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.