The GUPTRI algorithm and software is numerically stable in the sense that it computes the exact Kronecker structure (generalized Schur-staircase form) of a nearby pencil . is an upper bound on the distance to the closest with the KCF of . An accurate estimate of is the square root of the sum of the squares of all singular values interpreted as zeros during the reduction to GUPTRI form.
We refer to sections 5 and 6 in  for a more detailed discussion of the computed GUPTRI form and the associated error bounds for reducing subspaces and generalized eigenvalues. For example, section 6 presents a sample usage of all four routines for an application in control theory (computing the controllable subspace and uncontrollable modes).