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MATLAB Programs:

% SOR (Successive Over-Relaxation)

n = input('Enter number of equations, n:  ');
A = zeros(n,n+1);
x1 = zeros(1,n);

A=[4 2 3 8; 3 -5 2 -14; -2 3 8 27];
x1 = [0 0 0];

tol = input('Enter tolerance, tol:  ');
m = input('Enter maximum number of iterations, m:  ');
w = input('Enter the parameter w (omega):  ');

k = 1;
while  k <= m
err = 0;

for i = 1 : n
s = 0;
for j = 1 : n
s = s-A(i,j)*x1(j);
end
s = w*(s+A(i,n+1))/A(i,i);
if abs(s) > err
err = abs(s);
end
x1(i) = x1(i)+s;
end

if err <= tol
break;
else

k = k+1;
end
end

fprintf('The solution vector after %d iterations is :\n', k);
for i = 1 : n
fprintf('   %11.8f \n', x1(i));
end

OUTPUTs:
>> successive_over_relaxation
Enter number of equations, n:  3
Enter tolerance, tol:  0.001
Enter maximum number of iterations, m:  50
Enter the parameter w (omega):  1.25
The solution vector after 29 iterations is :
-1.00019013
2.99962341
2.00017040
>>