The Weierstrass Canonical Form of a Regular Matrix Pencil: Numerical Issues and Computational Techniques

Authors:
Grigorios Kalogeropoulos;Marilena Mitrouli;Athanasios Pantelous;Dimitrios Triantafyllou
Affiliations:
Department of Mathematics, University of Athens, Athens, Greece 15784;Department of Mathematics, University of Athens, Athens, Greece 15784;Department of Mathematics, University of Athens, Athens, Greece 15784;Department of Mathematics, University of Athens, Athens, Greece 15784
Venue:
Numerical Analysis and Its Applications
Year:
2009

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Abstract

In the present paper, we study the derivation of the Weierstrass Canonical Form (WCF) of a regular matrix pencil. In order to compute the WCF, we use two important computational tools: a) the QZ algorithm to specify the required root range of the pencil and b) the updating technique to compute the index of annihilation. The proposed updating technique takes advantages of the already computed rank of the sequences of matrices that appears during our procedure reducing significantly the required floating-point operations. The algorithm is implemented in a numerical stable manner, giving efficient results. Error analysis and the required complexity of the algorithm are included.