On the computation of the Jordan canonical form of regular matrix polynomials (Q1827503)

Generalizing results by \textit{N. Karcanias} and \textit{G. Kalogeropoulos} [Int. J. Control 44, 991--1015 (1986; Zbl 0631.15005)], the authors present a new method for the computation of the Jordan canonical form of a regular matrix polynomial \(P(\lambda )=A_{m}\lambda ^{m}+A_{m-1}\lambda ^{m-1}+\dots+A_{1}\lambda +A_{0},\) with \(A_{j}\in \mathbb{C}^{n\times n},\) \( j=0,1,\dots,m.\) The proposed method does not require the computation of the Jordan chains or the elementary divisors of \(P(\lambda )\) and can be expressed in terms of the notion of Weyr characteristic. A detailed algorithm is given. Two interesting examples enlighten the features of the method.