Geodesic
Extremal functional interpolation and splines
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 200-225

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The paper is a survey of the results obtained in the problems of extremal function interpolation over the past 50 years. Various statements of problems in this direction are analyzed both for the case of one variable and for the case of several variables. A special focus is put on the role of interpolation splines of different types (polynomial, interpolating in the mean, $\mathcal{L}$-splines, $m$-harmonic, etc.) in solving the problems of extremal function interpolation. Important applications of the results and methods of extremal interpolation to other problems in approximation theory and the theory of splines are specified.
Mots-clés : interpolation
Keywords: splines, approximation, differential operators, difference operators. 
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     author = {Yu. N. Subbotin and S. I. Novikov and V. T. Shevaldin},
     title = {Extremal functional interpolation and splines},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {200--225},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2018_24_3_a18/}
}
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Yu. N. Subbotin; S. I. Novikov; V. T. Shevaldin. Extremal functional interpolation and splines. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 200-225. http://geodesic.mathdoc.fr/item/TIMM_2018_24_3_a18/