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 [122] 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).