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 
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/
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     author = {V. I. Danchenko and E. N. Kondakova},
     title = {Criterion for the appearance of singular nodes under interpolation by simple partial fractions},
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     url = {http://geodesic.mathdoc.fr/item/TM_2012_278_a4/}
}
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Voir la notice du chapitre de livre 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.

[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

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