RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2012, Volume 92, Issue 1, Pages 27–43 (Mi mz7099)  

Complexity of Approximate Realizations of Lipschitz Functions by Schemes in Continuous Bases

Ya. V. Vegner, S. B. Gashkov

M. V. Lomonosov Moscow State University

Abstract: We show that any function satisfying the Lipschitz condition on a given closed interval can be approximately computed by a scheme (nonbranching program) in the basis composed of functions
$$ x-y,\quad |x|,\quad x*y=\min(\max(x,0),1)\min(\max(y,0),1), $$
and all constants from the closed interval $[0,1]$; here the complexity of the scheme is $O(1/\sqrt{\varepsilon})$, where $\varepsilon$ is the accuracy of the approximation. This estimate of complexity, is in general, order-sharp.

Keywords: Lipschitz function, (Lipshitz) continuous basis, Lipschitz condition, complexity of the approximate realization of functions, polynomial basis

DOI: https://doi.org/10.4213/mzm7099

Full text: PDF file (594 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2012, 92:1, 23–38

Bibliographic databases:

UDC: 519.712.4
Received: 26.01.2009
Revised: 23.08.2011

Citation: Ya. V. Vegner, S. B. Gashkov, “Complexity of Approximate Realizations of Lipschitz Functions by Schemes in Continuous Bases”, Mat. Zametki, 92:1 (2012), 27–43; Math. Notes, 92:1 (2012), 23–38

Citation in format AMSBIB
\Bibitem{VegGas12}
\by Ya.~V.~Vegner, S.~B.~Gashkov
\paper Complexity of Approximate Realizations of Lipschitz Functions by Schemes in Continuous Bases
\jour Mat. Zametki
\yr 2012
\vol 92
\issue 1
\pages 27--43
\mathnet{http://mi.mathnet.ru/mz7099}
\crossref{https://doi.org/10.4213/mzm7099}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3201538}
\zmath{https://zbmath.org/?q=an:1272.68464}
\elib{http://elibrary.ru/item.asp?id=20731565}
\transl
\jour Math. Notes
\yr 2012
\vol 92
\issue 1
\pages 23--38
\crossref{https://doi.org/10.1134/S0001434612070036}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000308042500003}
\elib{http://elibrary.ru/item.asp?id=20476649}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865772252}


Linking options:
  • http://mi.mathnet.ru/eng/mz7099
  • https://doi.org/10.4213/mzm7099
  • http://mi.mathnet.ru/eng/mz/v92/i1/p27

    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
  • Математические заметки Mathematical Notes
    Number of views:
    This page:251
    Full text:69
    References:40
    First page:15

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