Geodesic
Interpolation of analytic functions with finite number of special points by rational functions
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 863-881

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We consider an interpolation process for a class of functions having a finite number of singular points, using rational functions the poles of which coincide with the singular points of the interpolated function. Interpolation points form a triangular matrix where there is at least about one special point of the interpolated function having the limit of the ratio of the difference between the number of nodes of the $n$-th row associated with a singular point, and the corresponding n fraction multiplicity pole at this point to when $n$ is different from zero. The necessary and sufficient conditions of uniform convergence on any compact, which does not contain the singular points of the function; the sequence of interpolation fractions to the interpolated function were found, as well as other convergence conditions. Results on the interpolation of functions with a finite number of singular points by rational fractions and entire functions by polynomials are generalized.
Keywords: analytic function, singular point of a function, rational function
Mots-clés : interpolation process, uniform convergence, convergence conditions. 
@article{SEMR_2018_15_a131,
     author = {A. G. Lipchinskij and V. N. Stolbov},
     title = {Interpolation of analytic functions with finite number of special points by rational functions},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {863--881},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a131/}
}
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A. G. Lipchinskij; V. N. Stolbov. Interpolation of analytic functions with finite number of special points by rational functions. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 863-881. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a131/