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 Yk=θkYk1. A Pincherle type convergence theorem is proved. We show that the n-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 θk is constant for all k and the limiting case where limk+θk is constant. Finally the notion of adjoint fraction is introduced which generalizes the notion of the adjoint of a recurrence relation of order n.

Full Text (PDF) [218 KB], BibTeX

Key words

recurrence systems, recurrence relations, matrix continued fractions, non-dominant solutions.

AMS subject classifications

40A15, 65Q05.