Nonhomogeneous recursions and Generalised Continued Fractions |
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Authors: | P van der Cruyssen |
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Institution: | (1) Department of Mathematics, University of Antwerp, Universiteitsplein 1, B-2610 Wilrijk, Belgium |
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Abstract: | Consider the (n+1)st order nonhomogeneous recursionX
k+n+1=b
k
X
k+n
+a
k
(n)
X
k+n-1+...+a
k
(1)
X
k
+X
k
.Leth be a particular solution, andf
(1),...,f
(n),g independent solutions of the associated homogeneous equation. It is supposed thatg dominatesf
(1),...,f
(n) andh. If we want to calculate a solutiony which is dominated byg, but dominatesf
(1),...,f
(n), then forward and backward recursion are numerically unstable. A stable algorithm is derived if we use results constituting a link between Generalised Continued Fractions and Recursion Relations. |
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Keywords: | |
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