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

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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/}
}
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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/