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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.