On decoupling of linear recursions

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    Abstract

    We show how a well known algorithm to compute solutions of a second order recursion which are unstable both in forward and in backward direction, can be related to a number of other methods. They are: order reduction, invariant imbedding and decoupling based on triangularization. It is shown that these methods in this order form an increasingly general approach to solve the problem. In particular this means that the stability of the first three algorithms can be understood from the theory that has been established for the decoupling algorithm. In this way one does not need to investigate the stability of the large sparse system which is often related to the first method.
    Original languageEnglish
    Pages (from-to)347-360
    JournalBulletin of the Australian Mathematical Society
    Volume27
    Issue number3
    DOIs
    Publication statusPublished - 1983

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