A Unified Approach to Recurrence Algorithms

  • J. R. Cash
  • R. V. M. Zahar
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 119)


We show that the known methods for the computation of subdominant solutions of linear difference equations, either scalar recurrences or difference systems, are based on the replacement of an initial value problem by a system of linear equations expressed in boundary value form. This fact allows the development of a single uniform analysis for the convergence of the methods, and for the condition of the problem. Moreover, it is demonstrated that each of the resulting recurrence algorithms is mathematically equivalent to a type of triangular decomposition of the linear algebraic system, all algorithms being a form of either LU or UL factorization.


Minimal Solution Fundamental Matrix Linear Difference Equation Linear Algebraic System Complementary Solution 


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Copyright information

© Birkhäuser 1994

Authors and Affiliations

  • J. R. Cash
    • 1
  • R. V. M. Zahar
    • 2
  1. 1.Department of MathematicsImperial College of Science, Technology and MedicineLondonEngland
  2. 2.Département d’informatique et de recherche opérationnelleUniversité de MontréalMontréalCanada

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