A Computation Algorithm of Quasi-diagonal Form of Pencil Matrices

Abstract

Recently a pencil model has attracted attention again in view of behavioral approach. It is well known that a pencil can be transformed into a canonical form, but the traditional numerical computation method is implemented in terms of pivoting operation. In this paper, we make it clear what kind of mode the invariant subspace corresponds to, and propose a new algorithm to transform the pencil into the quasi-diagonal form. Since the method is based on geometric approach, it has an advantage of numerical stability.