A geometric approach to perturbation theory of matrices and matrix pencils. Part II: A stratification-enhanced staircase algorithm

Computing the Jordan form of a matrix or the Kronecker structure of a penci l is a well-known ill-posed problem. We propose that knowledge of the closu re relations, i.e., the stratification, of the orbits and bundles of the va rious forms may be applied in the staircase algorithm. Here we discuss and complete the mathematical theory of these relationships and show how they m ay be applied to the staircase algorithm. This paper is a continuation of o ur Part I paper on versal deformations, but it may also be read independent ly.