A linear time-invariant dynamical system is controllable if its trajectory can be adjusted to pass through any pair of points by the proper selection of an input. Controllability can be equivalently characterized as a rank problem and therefore cannot be verified reliably numerically in finite precision. To measure the degree of controllability of a system the distance to uncontrollability is introduced as the spectral or Frobenius norm of the smallest perturbation yielding an uncontrollable system. For a first order system we present a polynomial time algorithm to find the nearest uncontrollable system that improves the computational costs of the previous techniques. The algorithm locates the global minimum of a singular value optimization problem equivalent to the distance to uncontrollability. In the second part for higher-order systems we derive a singular-value characterization and exploit this characterization for the computation of the higher-order distance to +uncontrollability to low precision. Keywords: dynamical system, controllability, distance to uncontrollability, Arnoldi, inverse iteration, eigenvalue optimization, polynomial eigenvalue problem