Skip to main content
SpringerLink
Log in

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

  • Conference paper
Numerical Analysis and Its Applications (NAA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5434))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chen, C.T.: Linear System Theory and Design, pp. 546–550. CBS College Publishing (1984)

    Google Scholar 

  2. Datta, B.N.: Numerical Linear Algebra and Applications, 2nd edn. Brooks/Cole Publishing Company, United States of America (1995)

    Google Scholar 

  3. Gantmacher, R.F.: The theory of matrices, Chelsea, New York., U.S.A, vol. I, II (1959)

    Google Scholar 

  4. Kalogeropoulos, G.: Matrix Pencils and linear systems theory. PhD thesis. Control Engineering Centre, City University, London (1985)

    Google Scholar 

  5. Kalogeropoulos, G., Mitrouli, M.: On the computation of the Weierstrass Canonical form of a Regular Matrix Pencil. Control and Computers 20(3), 61–67 (1992)

    Google Scholar 

  6. Kalogeropoulos, G.I., Pantelous, A.A.: Can be linear difference descriptor systems appeared in insurance? In: Proceedings of the 7th International Conference APLIMAT 2008, Bratislava, Slovakia, pp. 467–478 (2008)

    Google Scholar 

  7. Karcanias, N., Kalogeropoulos, G.: On the Segre′, Weyl characteristics of right (left) regular pencils. International Journal of Control 44, 991–1015 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  8. Karcanias, N., Kalogeropoulos, G.: The prime and generalized nullspaces of right regular pencils. Circuits Systems Signal Processes 14(4), 495–524 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  9. Leontief, W.: Input-Output Economics, 2nd edn. Oxford Univ. Press, N. Y (1986)

    Google Scholar 

  10. Van Huffel, S., Vandewalle, J.: An efficient and reliable algorithm for computing the singular subspace of a matrix, associated with its smallest singular values. Journal of Computers and Applied Mathematics 19, 313–330 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  11. Van Huffel, S.: Partial singular value decomposition algorithm. Journal of Computers and Applied Mathematics 33, 105–112 (1990)

    Article  MATH  Google Scholar 

  12. Yalamov, P.Y., Mitrouli, M.: A fast Algorithm for Index Annihilation Computations. Journal of Computers and Applied Mathematics 108, 99–111 (1999)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Athens, Panepistimiopolis, 15784, Athens, Greece

    Grigorios Kalogeropoulos, Marilena Mitrouli, Athanasios Pantelous & Dimitrios Triantafyllou

Authors
  1. Grigorios Kalogeropoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marilena Mitrouli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Athanasios Pantelous
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dimitrios Triantafyllou
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  2. FNSE, Department of Numerical Methods and Statistics, University of Rousse, 8 Studentska str., 7017, Rousse, Bulgaria

    Lubin G. Vulkov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, 2800, Kongens, Lyngby, Denmark

    Jerzy Waśniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kalogeropoulos, G., Mitrouli, M., Pantelous, A., Triantafyllou, D. (2009). The Weierstrass Canonical Form of a Regular Matrix Pencil: Numerical Issues and Computational Techniques. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00464-3_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00463-6

  • Online ISBN: 978-3-642-00464-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation