Geodesic
Criterion for the appearance of singular nodes under interpolation by simple partial fractions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 278 (2012), pp. 49-58.

Voir la notice de l'article provenant de la source Math-Net.Ru

Under simple interpolation by simple partial fractions, the poles of the interpolation fraction may arise at some nodes irrespective of the values of the interpolated function at these nodes. Such nodes are said to be singular. In the presence of singular nodes, the interpolation problem is unsolvable. We establish two criteria for the appearance of singular nodes under an extension of interpolation tables and obtain an algebraic equation for calculating such nodes. 
@article{TM_2012_278_a4,
     author = {V. I. Danchenko and E. N. Kondakova},
     title = {Criterion for the appearance of singular nodes under interpolation by simple partial fractions},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {49--58},
     publisher = {mathdoc},
     volume = {278},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_278_a4/}
}
TY  - JOUR
AU  - V. I. Danchenko
AU  - E. N. Kondakova
TI  - Criterion for the appearance of singular nodes under interpolation by simple partial fractions
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2012
SP  - 49
EP  - 58
VL  - 278
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2012_278_a4/
LA  - ru
ID  - TM_2012_278_a4
ER  - 
%0 Journal Article
%A V. I. Danchenko
%A E. N. Kondakova
%T Criterion for the appearance of singular nodes under interpolation by simple partial fractions
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2012
%P 49-58
%V 278
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2012_278_a4/
%G ru
%F TM_2012_278_a4
V. I. Danchenko; E. N. Kondakova. Criterion for the appearance of singular nodes under interpolation by simple partial fractions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 278 (2012), pp. 49-58. http://geodesic.mathdoc.fr/item/TM_2012_278_a4/

[1] Kondakova E.N., “Osobye sluchai interpolyatsii posredstvom naiprosteishikh drobei”, Mezhdunar. konf. po differentsialnym uravneniyam i dinamicheskim sistemam (Suzdal, 2010), Tez. dokl., MIAN, M., 2010, 105–106

[2] Kondakova E.N, “Osobye uzly pri interpolyatsii naiprosteishimi drobyami”, Teoriya funktsii, ee prilozheniya i smezhnye voprosy, Mater. 10-i Mezhdunar. kazanskoi letnei nauch. shk.-konf. (Kazan, 1–7 iyulya 2011 g.), Kazan. mat. o-vo, Kazan, 2011, 202–203

[3] Kondakova E.N., “Interpolyatsiya naiprosteishimi drobyami”, Izv. Saratov. un-ta. Matematika, mekhanika, informatika, 9:2 (2009), 30–37 | MR

[4] Danchenko V.I., Kondakova E.N., “Chebyshevskii alternans pri approksimatsii konstant naiprosteishimi drobyami”, Tr. MIAN, 270, 2010, 86–96 | MR | Zbl