First-order linear recurrence systems and matrix continued fractions

We introduce a matrix continued fraction associated with the first-order linear recurrence system Y_k = θ_k Y_{k-1}. A Pincherle type convergence theorem is proved. We show that the r-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 lim_{k → ∞} θ_k is constant. Finally the notion of adjoint fraction is introduced which generalizes the notion of the adjoint of a recurrence relation of order r.nrpages: 16status: publishe