Geodesic
Matrix continued fractions related to first-order linear recurrence systems
Electronic transactions on numerical analysis, Tome 4 (1996), pp. 46-63
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},
     year = {1996},
     volume = {4},
     zbl = {0860.65128},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1996__4__a7/}
}
TY  - JOUR
AU  - Levrie,  P.
AU  - Bultheel,  A.
TI  - Matrix continued fractions related to first-order linear recurrence systems
JO  - Electronic transactions on numerical analysis
PY  - 1996
SP  - 46
EP  - 63
VL  - 4
UR  - http://geodesic.mathdoc.fr/item/ETNA_1996__4__a7/
LA  - en
ID  - ETNA_1996__4__a7
ER  - 
%0 Journal Article
%A Levrie,  P.
%A Bultheel,  A.
%T Matrix continued fractions related to first-order linear recurrence systems
%J Electronic transactions on numerical analysis
%D 1996
%P 46-63
%V 4
%U http://geodesic.mathdoc.fr/item/ETNA_1996__4__a7/
%G en
%F ETNA_1996__4__a7
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/