Finding optimal weight factor for SOR - matlab

Question

I am using the SOR method and need to find the optimal weight factor. I think a good way to go about this is to run my SOR code with a number of omegas from 0 to 2, then store the number of iterations for each of these. Then I can see which iteration is the lowest and which omega it corresponds to. Being a novice programer, however, I am unsure how to go about this.
Here is my SOR code:
function [x, l] = SORtest(A, b, x0, TOL,w)
[m n] = size(A); % assigning m and n to number of rows and columns of A
l = 0; % counter variable
x = [0;0;0]; % introducing solution matrix
max_iter = 200;
while (l < max_iter) % loop until max # of iters.
l = l + 1; % increasing counter variable
for i=1:m % looping through rows of A
sum1 = 0; sum2 = 0; % intoducing sum1 and sum2
for j=1:i-1 % looping through columns
sum1 = sum1 + A(i,j)*x(j); % computing sum using x
end
for j=i+1:n
sum2 = sum2 + A(i,j)*x0(j); % computing sum using more recent values in x0
end
x(i) =(1-w)*x0(i) + w*(-sum1-sum2+b(i))/A(i,i); % assigning elements to the solution matrix.
end
if abs(norm(x) - norm(x0)) < TOL % checking tolerance
break
end
x0 = x; % assigning x to x0 before relooping
end
end

Answer 1

That's pretty easy to do. Simply loop through values of w and determine what the total number of iterations is at each w. Once the function finishes, check to see if this is the current minimum number of iterations required to get a solution. If it is, then update what the final solution would be. Once we iterate over all w, the result would be the solution vector that produced the smallest number of iterations to converge. Bear in mind that SOR has the w such that it does not include w = 0 or w = 2, or 0 < w < 2, so we can't include 0 or 2 in the range. As such, do something like this:
omega_vec = 0.01:0.01:1.99;
final_x = x0;
min_iter = intmax;
for w = omega_vec
[x, iter] = SORtest(A, b, x0, TOL, w);
if iter < min_iter
min_iter = iter;
final_x = x;
end
end
The loop checks to see if the total number of iterations at each w is less than the current minimum. If it is, log this and also record what the solution vector was. The final solution vector that was the minimum over all w will be stored in final_x.