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


Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 2, Pages 211–216 (Mi zvmmf10829)  

Tensor trains approximation estimates in the Chebyshev norm

A. I. Osinskii

Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, 119333 Russia

Abstract: A new elementwise bound on the cross approximation error used for approximating multi-index arrays (tensors) in the format of a tensor train is obtained. The new bound is the first known error bound that differs from the best bound by a factor that depends only on the rank of the approximation $r$ and on the dimensionality of the tensor $d$, and the dependence on the dimensionality at a fixed rank has only the order $d^{\operatorname{const}}$ rather than $\operatorname{const}^d$. Thus, this bound justifies the use of the cross method even for high dimensional tensors.

Key words: multidimensional arrays, nonlinear approximations, maximum volume principle.

Funding Agency Grant Number
Russian Science Foundation 14-11-00806
This work was supported by the Russian Science Foundation, project no. 14-11-00806.


DOI: https://doi.org/10.1134/S0044466919020121


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:2, 201–206

Bibliographic databases:

UDC: 517.977
Received: 23.05.2018

Citation: A. I. Osinskii, “Tensor trains approximation estimates in the Chebyshev norm”, Zh. Vychisl. Mat. Mat. Fiz., 59:2 (2019), 211–216; Comput. Math. Math. Phys., 59:2 (2019), 201–206

Citation in format AMSBIB
\Bibitem{Osi19}
\by A.~I.~Osinskii
\paper Tensor trains approximation estimates in the Chebyshev norm
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2019
\vol 59
\issue 2
\pages 211--216
\mathnet{http://mi.mathnet.ru/zvmmf10829}
\crossref{https://doi.org/10.1134/S0044466919020121}
\elib{https://elibrary.ru/item.asp?id=36962807}
\transl
\jour Comput. Math. Math. Phys.
\yr 2019
\vol 59
\issue 2
\pages 201--206
\crossref{https://doi.org/10.1134/S096554251902012X}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000468087400003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85066025561}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf10829
  • http://mi.mathnet.ru/eng/zvmmf/v59/i2/p211

    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
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:58

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021