Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find




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

Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 4, Pages 558–573
DOI: https://doi.org/10.7868/S0044466915040146 (Mi zvmmf10183) 		 
Algorithm for summation of divergent continued fractions and some applications

G. A. Kirichenkoa, V. I. Shmoylovb

a Southern Federal University, per. Nekrasovskii 44, Taganrog, 347928, Russia
b Southern Scientific Center, Russian Academy of Sciences, pr. Chekhova 41, Rostov-on-Don, 344006, Russia
Full-text PDF (403 kB)
References:
PDF
HTML
DOI: https://doi.org/10.7868/S0044466915040146
Abstract: The convergence of continued fractions is defined in a manner other than the conventional definition. A new summation method is used to determine the values of continued fractions and series that diverge in the classical sense. The method is applicable not only to ordinary continued fractions, but also to ones of other classes, for example, to Hessenberg continued fractions. As a result, an original algorithm for finding zeros of $n$th-degree polynomials is constructed. The $r/\varphi$-algorithm proposed is also used to solve infinite systems of linear algebraic equations.
Key words: high-degree algebraic equations, divergent continued fractions, infinite systems of linear algebraic equations, summation algorithm for divergent continued fractions.
Received: 23.04.2013
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 4, Pages 549–563
DOI: https://doi.org/10.1134/S0965542515040132
Bibliographic databases:
Document Type: Article
UDC: 519.651
MSC: Primary 30B70; Secondary 11A55, 40A15, 65B99
Language: Russian
Citation: G. A. Kirichenko, V. I. Shmoylov, “Algorithm for summation of divergent continued fractions and some applications”, Zh. Vychisl. Mat. Mat. Fiz., 55:4 (2015), 558–573; Comput. Math. Math. Phys., 55:4 (2015), 549–563
Citation in format AMSBIB
\Bibitem{KirShm15}
\by G.~A.~Kirichenko, V.~I.~Shmoylov
\paper Algorithm for summation of divergent continued fractions and some applications
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2015
\vol 55
\issue 4
\pages 558--573
\mathnet{http://mi.mathnet.ru/zvmmf10183}
\crossref{https://doi.org/10.7868/S0044466915040146}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3343118}
\zmath{https://zbmath.org/?q=an:06458231}
\elib{https://elibrary.ru/item.asp?id=23299884}
\transl
\jour Comput. Math. Math. Phys.
\yr 2015
\vol 55
\issue 4
\pages 549--563
\crossref{https://doi.org/10.1134/S0965542515040132}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000354067600003}
\elib{https://elibrary.ru/item.asp?id=24027874}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928892727}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf10183
  • https://www.mathnet.ru/eng/zvmmf/v55/i4/p558
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025