Question

DO NOT GIVE ME A STEP BY STEP SOLUTION ON PAPER.

JUST GIVE ME THE MATLAB FUNCTION FILE (code) TO BE USED IN MATLAB. ONLY

(a) use the Gauss-Seidel method to solve the following system until the percent relative error falls below s a. 5%. 10x1 + 2x2-x,-27 3x1 -6x2 + 2x3 61.5 25x321.5 b. (b) write an M-file to implement the Gauss-Seidel method using the above system as a test case

Answer 1

MATLAB CODE

clear;clc
format compact
%% Read or Input any square Matrix
A = [10 2 -1;
-3 -6 2;
1 1 5];% coefficients matrix
C = [27;-61.5;-21.5];% constants vector
n = length(C);
X = zeros(n,1);
Error_eval = ones(n,1);
%% Check if the matrix A is diagonally dominant
for i = 1:n
j = 1:n;
j(i) = [];
B = abs(A(i,j));
Check(i) = abs(A(i,i)) - sum(B); % Is the diagonal value greater than the remaining row values combined?
if Check(i) < 0
fprintf('The matrix is not strictly diagonally dominant at row %2i\n\n',i)
end
end
%% Start the Iterative method
iteration = 0;
while max(Error_eval) > 0.05
iteration = iteration + 1;
Z = X; % save current values to calculate error later
for i = 1:n
j = 1:n; % define an array of the coefficients' elements
j(i) = []; % eliminate the unknow's coefficient from the remaining coefficients
Xtemp = X; % copy the unknows to a new variable
Xtemp(i) = []; % eliminate the unknown under question from the set of values
X(i) = (C(i) - sum(A(i,j) * Xtemp)) / A(i,i);
end
Xsolution(:,iteration) = X;
Error_eval = sqrt((X - Z).^2);
end
%% Display Results
GaussSeidelTable = [1:iteration;Xsolution]'
Coeff_Mat_Contant_Mat_X_value= [A C X]

OUTPUT

GaussSeidelTable =
1.0000 2.7000 8.9000 -6.6200
2.0000 0.2580 7.9143 -5.9345
3.0000 0.5237 8.0100 -6.0067
4.0000 0.4973 7.9991 -5.9993
Coeff_Mat_Contant_Mat_X

_value =
10.0000 2.0000 -1.0000 27.0000 0.4973
-3.0000 -6.0000 2.0000 -61.5000 7.9991
1.0000 1.0000 5.0000 -21.5000 -5.9993
>>

:n, 古 ae l ine an array the coelllClents' elements j (1)-[]; % eliminate the unknow's coefficient from the remaining coefficients Xtemp = x; copy the unknows to a new variable Xtemp(i) = []; % eliminate the unknown under question from the set of values x(i) (C(1) -sum (A (i,j) * Xtemp)) / A(1,1); endl Xsolution(:,iteration)X: Error_eval sqgrt ( (X Z).2). end Display Results GaussSeidelTable [l:iteration;Xsolution]' Coeff Mat Contant Mat X value: tA c xI

GaussSeide!Table = 1.0000 2.0000 3.0000 4.0000 2.7000 0.2580 0.5237 0.4973 8.9000 -6.6200 7.9143 5.9345 8.0100 6.0067 7.99915.9993 Coeff Mat Contant Mat X value = 10.0000 -3.0000 -6.0000 2.0000 1.0000 27.0000 2.0000 -61.5000 0.4973 7.9991 5.0000 -21.5000-5.9993 1.0000 1.0000 fx >>