Skip to main content
SpringerLink
Log in

An algorithm for computing a companion block diagonal form for a system of linear differential equations

  • Published:
Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

In this paper we describe a new algorithm which reduces in a finite number of steps a linear system of differential equations to a companion block diagonal form. This form is particularly convenient if one wishes to compute invariants at singularities.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Adjamagbo, K.: Sur l'ectivité du lemme du vecteur cyclique. C.R. Acad. Sci. Paris, t306, Série, I, 543–546 (1988)

    Google Scholar 

  2. Bertrand, D.: Systèmes différentiels et équations différentielles. Séminaire d'arithmétique, Saint-Etienne, 1983, exposé V

  3. Bertrand, D.: Constructions effectives de vectures cycliques pour un D-module. Publ. d'étude d'analyse ultramétrique, 12e année

  4. Cope, F.: Formal solutions of irregular linear differential equations. Am. J. Math.58, 130–140 (1936)

    Google Scholar 

  5. Dabèche, A.: Formes canoniques rationnelles d'un système différentiel à point singulier irrégulier. In: Equations Différentielles et Systèmes de Pfaff dans le Champ Complexe. Lectures Notes in Mathematics Vol. 712, pp. 20–32. Berlin, Heidelberg, New York: Springer 1979

    Google Scholar 

  6. Deligne, P.: Equations différentielles à points singuliers réguliers. Lectures Notes in Mathematics, Vol. 163. Berlin, Heidelberg, New York: Springer 1970

    Google Scholar 

  7. Hilali, A.: Solutions formelles de systèmes différentiels linéaires au voisinage d'un point singulier. Thèse de l'université Joseph Fourier Grenoble France, Juin 1987, pp. 71–103

  8. Jacobson, N.: Pseudo-Linear transformations. Ann. Math.38, 484–507 (1937)

    Google Scholar 

  9. Katz, N.: A simple algorithm for cyclic vectors. Am. J. Math.109, 65–70 (1987)

    Google Scholar 

  10. Ozello, P.: Calcul exact des formes normales de matrices. Thèse Doctorale de l'université Joseph Fourier Grenoble France, Janvier 1987

  11. Ramis, J. P.: Théorèmes d'indices Gevrey pour les équations différentielles ordinaires. Pub. IRMA, Strasbourg France, pp. 57–60 (1981).

    Google Scholar 

  12. Tournier, E.: Solutions formelles d'équations différentielles. Thèse de l'université Joseph Fourier Grenoble France, Avril 1987

Download references

Author information

Authors and Affiliations

  1. Département de Mathématiques, Faculté des Sciences, 123 Av. A. Thomas, F-87060, Limoges, France

    M. A. Barkatou

Authors
  1. M. A. Barkatou
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barkatou, M.A. An algorithm for computing a companion block diagonal form for a system of linear differential equations. AAECC 4, 185–195 (1993). https://doi.org/10.1007/BF01202037

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01202037

Keywords

Search

Navigation