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 Sibirsk. Mat. Zh., 2014, Volume 55, Number 4, Pages 750–763 (Mi smj2569)

A criterion for the solvability of the multiple interpolation problem by simple partial fractions

M. A. Komarov

Abstract: Using reduction to polynomial interpolation, we study the multiple interpolation problem by simple partial fractions. Algebraic conditions are obtained for the solvability and the unique solvability of the problem. We introduce the notion of generalized multiple interpolation by simple partial fractions of order $\le n$. The incomplete interpolation problems (i.e., the interpolation problems with the total multiplicity of nodes strictly less than $n$) are considered; the unimprovable value of the total multiplicity of nodes is found for which the incomplete problem is surely solvable. We obtain an order $n$ differential equation whose solution set coincides with the set of all simple partial fractions of order $\le n$.

Keywords: simple partial fraction, generalized multiple interpolation, uniqueness.

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English version:
Siberian Mathematical Journal, 2014, 55:4, 611–621

Bibliographic databases:

UDC: 517.538

Citation: M. A. Komarov, “A criterion for the solvability of the multiple interpolation problem by simple partial fractions”, Sibirsk. Mat. Zh., 55:4 (2014), 750–763; Siberian Math. J., 55:4 (2014), 611–621

Citation in format AMSBIB
\Bibitem{Kom14} \by M.~A.~Komarov \paper A criterion for the solvability of the multiple interpolation problem by simple partial fractions \jour Sibirsk. Mat. Zh. \yr 2014 \vol 55 \issue 4 \pages 750--763 \mathnet{http://mi.mathnet.ru/smj2569} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3242593} \transl \jour Siberian Math. J. \yr 2014 \vol 55 \issue 4 \pages 611--621 \crossref{https://doi.org/10.1134/S0037446614040041} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000340941400004} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84906512200} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. A. Komarov, “A criterion for the best uniform approximation by simple partial fractions in terms of alternance”, Izv. Math., 79:3 (2015), 431–448
2. M. A. Komarov, “Approximation by linear fractional transformations of simple partial fractions and their differences”, Russian Math. (Iz. VUZ), 62:3 (2018), 23–33
3. M. A. Komarov, “O priblizhenii spetsialnymi raznostyami naiprosteishikh drobei”, Algebra i analiz, 30:4 (2018), 47–60
4. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49
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