Title: First-order linear recurrence systems and matrix continued fractions
Authors: Levrie, Paul ×
Bultheel, Adhemar
Issue Date: Nov-1995
Publisher: Department of Computer Science, K.U.Leuven
Series Title: TW Reports vol:TW235
Abstract: 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.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
× corresponding author

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