RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

This article is cited in 4 scientific papers (total in 4 papers)

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

M. A. Komarov

Vladimir State University, Vladimir, Russia

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.

Full text: PDF file (346 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.538
Received: 17.06.2013

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}


Linking options:
  • http://mi.mathnet.ru/eng/smj2569
  • http://mi.mathnet.ru/eng/smj/v55/i4/p750

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    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  mathnet  crossref  isi
    3. M. A. Komarov, “O priblizhenii spetsialnymi raznostyami naiprosteishikh drobei”, Algebra i analiz, 30:4 (2018), 47–60  mathnet
    4. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
  • Сибирский математический журнал Siberian Mathematical Journal
    Number of views:
    This page:214
    Full text:58
    References:33
    First page:18

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020