Skip to main content
Log in

An Efficient Algorithm for Decomposing a Vector into Two Vectors with a Small Uniform Norm

  • Short Communications
  • Published:
Mathematical Notes Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.

References

  1. B. S. Kashin, Math. USSR-Izv. 11 (2), 317 (1977).

    Article  Google Scholar 

  2. Yu. Lyubarskii and R. Vershynin, IEEE Trans. Inform. Theory 56 (7), 3491 (2010).

    Article  MathSciNet  Google Scholar 

  3. W. Lim, N. Luong, and D. Hoang, IEEE Comm. Surv. Tut. 22 (3), 2031 (2020).

    Article  Google Scholar 

  4. W. Chen, P. Kairouz, and A. Ozgur, IEEE Trans. Inform. Theory 69 (2), 1261 (2023).

    Article  MathSciNet  Google Scholar 

  5. S. Vargaftik, R. B. Basat, A. Portnoy, G. Mendelson, Y. Ben-Itzhak, and M. Mitzenmacher, Adv. Neural Inform. Proc. Sys. 34 (2021).

    Google Scholar 

  6. V. N. Temlyakov, Greedy Approximation, in Cambridge Monogr. Appl. Comput. Math. (Cambridge Univ. Press, Cambridge, 2011), Vol. 20.

    Book  Google Scholar 

  7. F. Mezzadri, Notices Amer. Math. Soc. 54 (5), 592 (2007).

    MathSciNet  Google Scholar 

Download references

Funding

The research on Theorem 1 was carried out by B. S. Kashin and was supported by the Russian Science Foundation under grant no. 21-11-00131 (https://rscf.ru/en/project/21-11-00131/) at Lomonosov Moscow State University. The work on computer implementation and numerical experiments carried out by D. G. Romskii was supported by the Foundation for the Development of Theoretical Physics and Mathematics.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B. S. Kashin.

Ethics declarations

The authors of this work declare that they have no conflicts of interest.

Additional information

Translated from Matematicheskie Zametki, 2023, Vol. 114, pp. 945–948 https://doi.org/10.4213/mzm14132.

Publisher’s note. Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kashin, B.S., Romskii, D.G. An Efficient Algorithm for Decomposing a Vector into Two Vectors with a Small Uniform Norm. Math Notes 114, 1484–1487 (2023). https://doi.org/10.1134/S0001434623110755

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434623110755

Keywords

Navigation