Volume 4, pp. 46-63, 1996.
Matrix continued fractions related to first-order linear recurrence systems
P. Levrie and A. Bultheel
Abstract
We introduce a matrix continued fraction associated with the first-order linear
recurrence system . A Pincherle type convergence
theorem is proved. We show that the -th order linear recurrence relation
and previous generalizations of ordinary continued fractions form a special
case. We give an application for the numerical computation of a non-dominant
solution and discuss special cases where is constant for all
and the limiting case where
is constant. Finally the notion of adjoint fraction is introduced which
generalizes the notion of the adjoint of a recurrence relation of order
.
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Key words
recurrence systems, recurrence relations, matrix continued fractions, non-dominant solutions.
AMS subject classifications
40A15, 65Q05.