The weierstrass canonical form of a regular matrix pencil: Numerical issues and computational techniques

Grigorios Kalogeropoulos, Marilena Mitrouli, Athanasios Pantelous, Dimitrios Triantafyllou

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Title of host publicationNumerical Analysis and Its Applications - 4th International Conference, NAA 2008, Revised Selected Papers
Number of pages8
Volume5434 LNCS
Publication statusPublished - 2009
Externally publishedYes
Event4th International Conference on Numerical Analysis and Its Applications, NAA 2008 - Lozenetz, Bulgaria
Duration: 16 Jun 200820 Jun 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5434 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference4th International Conference on Numerical Analysis and Its Applications, NAA 2008

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