Computation of Kronecker-like forms of periodic matrix pairs

Abstract

We propose a computationally efficient and numerically reliable algorithm to compute Kronecker-like forms of periodic matrix pairs. The eigenvalues and Kronecker indices are defined via the Kronecker structure of an associated lifted matrix pencil. The proposed reduction method relies on structure preserving manipulations of this pencil to extract successively lower complexity subpencils which contains the finite and infinite eigenvalues as well as the left and right Kronecker structures. The new algorithm uses exclusively orthogonal transformations and for the overall reduction the backward numerical stability can be proved.