On the reduction of linear systems of difference equations

ABSTRACT

This paper deals with linear systems of difference equations whose coefficients admit generalized factorial series representations at z = ∞. We shall give a criterion by which a given system is determined to have a regular singularity. In the same manner, we give an algorithm, implementable in a computer algebra system, which reduces in a finite number of steps the system of difference equations on an irreducible form.

REFERENCES

• B: M.A. Barkatou, Contribution ~ l'dtude des dquations diffdrentielles et des dquations aux diffdrences dans le champ complexe, Thbse de I'INPG (Grenoble) (h paraitre).
• M: j.K. Moser, The order of a singularity in Fuchs' theory, Math. Z. Vol. 72, 1960, 379-398.
• N: N.E. NOrlund, Lemons sur les sdries d'interpolation. chap.6, Gauthiers Villars et Cie, Paris, 1926.
• H1: W.A. Harris, Jr., Linear systems of difference equations, Contributions to Differential Equations, vol 1 (1963), 489-518.
• H2: W.A. Harris, Jr., Equivalent classes of difference equations, Contributions to Differential Equations, vol. 2 (1963), 253-264.
• HT: W.A. Harris, and H.L. Turritin, Reciprocals of inverse factorial series, Funkcial. Ekvac.6 (1964),37-46.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Linear systems (direct and iterative methods)

General Terms:
Algorithms, Theory