How to avoid numerical errors when computing the Jordan form

Hello.

I've managed to get a script working that will calculate the jordan form for a specified matrix consisting of integer elements.I know it is working in theory, but the problem is that when the rankings are calculated it sometimes gives the wrong answer for certain matrices like compan(poly([1:10])).

Our code is the following:

function J = jordan2(A, tol)
  if nargin < 2, tol = 0.01; end
  [ev, mult] = heltalsev(A, tol);
  J = [];
  for i= 1:length(ev)
      status = false;
      j = 1;
      %Clear variables
      clear p;
      clear n;
      clear b;
      % Iterate until p_i is stationary

        while status == false 
            T = A-ev(i)*eye(size(A))
            for k = 1:j-1
                T = round(T*(A-ev(i)*eye(size(A))))
            end

            p(j) = length(A) - rank(T);
            if j>1 && (p(j) == p(j-1))
                status = true;
            end
            j = j+1;
        end
        p
        b = [p(1) diff(p)] % Assign b(1) = p(1), and b(i) = p(i)-p(i-1)

        n = -diff(b); % Minus sign because n is calculated as b(n)-b(n+1) while diff calculates in the reverse order.

        for j = 1:length(n) % j iterates through all the different types of blocks. 
            for k = 1:n(j) % k iterates through the amount of blocks of a certain type.
                Jk = [ev(i)*eye(j) + [zeros(j-1,1) eye(j-1) ; 0 zeros(1,j-1)]]; % Construct a Jordan block of size j.
                J = blkdiag(J, Jk); % Attach the Jordan block to the Jordan form.
            end
        end
    end
end

Here the function heltalsev returns a vector of eigenvalues, ev for the input matrix A. I assume that the errors appears because of some form of numerical round off errors, but I have no idea how to handle this. How can I rewrite my program to prevent this from happening?

Thanks!