Gauss- Seidel Error tolerance

I am using this code below to implement gauss-seidel method equation solving. I did set a maximum error value i.e tol in my code. The code should run as long as current error is greater than maximum error. However for tol = 10^-5 , A = [8 -3 2; 4 11 -1; 6 3 12] and b = [20;33;35], the while loop breaks even when the condition is still not brached i.e current error is still greater than tol. Why is this happening so? It makes sense if I consider first 5 decimal points but I do not intend to limit it to five decimal points only.

function [X,err] = gauss_seidel(A,b)
tol = 10^-05;
[M,N] = size(A);
if(M~=N)
    error('Error');
end
for i=1:M
    row = abs(A(i,:));
    d = sum(row) - row(i);
    if d>=row(i)
        error("Given matrix is not diagonally dominant");   
    end 
end    
itr = 0;
X = zeros(M,1);

err = inf;
while err>tol
    Xold = X;
    for i = 1:M
        total = 0;
        for j = 1:i-1
            total = total + A(i,j)*X(j);
        end
        
        for j = i+1 : N
            total = total + A(i,j)*Xold(j);
        end    
        
        X(i) = (1/A(i,i)) * (b(i)-total);
    end
    
    itr = itr+1;
   
    err = abs(Xold-X);
    
end
fprintf("%.10f ",tol);

fprintf("%.10f",err);
fprintf("Method converges in %d iteration\n",itr);       
end    

Answer 1

[Abolfazl Chaman Motlagh]

you have an unclear statement in while.after first iteration the err is 3x1 vector and tol is a scalar.

change the statement to a norm of vector err. for example inf-norm:

while max(err)>tol
...
end