  The widely used nuclear norm heuristic for rank minimization problems
introduces a regularization parameter which is difficult to tune. We have
recently proposed a method to approximate the regularization path, i.e., the
optimal solution as a function of the parameter, which requires solving the
problem only for a sparse set of points. In this paper, we extend the algorithm
to provide error bounds for the singular values of the approximation. We
exemplify the algorithms on large scale benchmark examples in model order
reduction. Here, the order of a dynamical system is reduced by means of
constrained minimization of the nuclear norm of a Hankel matrix.
