Regularizing algorithm for mixed matrix pencils

TL;DR

This paper extends Van Dooren's numerically stable algorithm for computing Kronecker's canonical form to complex matrices under consimilarity and to pairs of matrices, enhancing its applicability.

Contribution

It introduces a generalized algorithm for complex matrices and matrix pairs, improving stability and scope over the original method.

Findings

Algorithm successfully computes canonical forms for complex matrices.

Enhanced numerical stability through unitary transformations.

Applicable to pairs of matrices, broadening the original scope.

Abstract

P. Van Dooren (1979) constructed an algorithm for computing all singular summands of Kronecker's canonical form of a matrix pencil. His algorithm uses only unitary transformations, which improves its numerical stability. We extend Van Dooren's algorithm to square complex matrices with respect to consimilarity transformations and to pairs of m-by-n complex matrices.