Geodesic
Matrix continued fractions related to first-order linear recurrence systems
Electronic transactions on numerical analysis, Tome 4 (1996), pp. 46-63.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We introduce a matrix continued fraction associated with the first-order linear recurrence system $Yk = \theta $kYk - 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 $\theta k$ is constant for all k and the limiting case where limk$\rightarrow +\infty \theta k$ is constant. Finally the notion of adjoint fraction is introduced which generalizes the notion of the adjoint of a recurrence relation of order n.
Classification : 40A15, 65Q05
Keywords: recurrence systems, recurrence relations, matrix continued fractions, non-dominant solutions 
@article{ETNA_1996__4__a7,
     author = {Levrie, P. and Bultheel, A.},
     title = {Matrix continued fractions related to first-order linear recurrence systems},
     journal = {Electronic transactions on numerical analysis},
     pages = {46--63},
     publisher = {mathdoc},
     volume = {4},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1996__4__a7/}
}
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Levrie, P.; Bultheel, A. Matrix continued fractions related to first-order linear recurrence systems. Electronic transactions on numerical analysis, Tome 4 (1996), pp. 46-63. http://geodesic.mathdoc.fr/item/ETNA_1996__4__a7/