MATRIX CONTINUED FRACTIONS RELATED TO FIRST-ORDER LINEAR RECURRENCE SYSTEMS
Paul Levrie, Adhemar Bultheel · 1996
. We introduce a matrix continued fraction associated with the first-order linear recurrence system Y k = # k Y k-1 . 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 # k is constant for all k and the limiting case where lim k#+# # k is constant. Finally the notion of adjoint fraction is introduced which generalizes the notion of the adjoint of a recurrence relation of order n. Key words. recurrence systems, recurrence relations, matrix continued fractions, non-dominant solutions. AMS subject classifications. 40A15, 65Q05. 1. Introduction. Continued fractions are closely related to linear recurrence relations (see [11], [14]) and can be defined using the composition of linear fractional transformations. In this paper we look at linear first-o...