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On decoupling of linear recursions

Published online by Cambridge University Press:  17 April 2009

R.M.M. Mattheij
R.M.M. Mattheij
Affiliation:
Mathematisch Institut, Katholieke Universiteit, Toernooiveld, Nijmegen, The Netherlands.
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 27 , Issue 3 , June 1983 , pp. 347 - 360
Copyright
Copyright © Australian Mathematical Society 1983

References

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