Skip to main content
Log in

Construction of suboptimal coverings of the multidimensional unit sphere

  • Computer Science
  • Published:
Doklady Mathematics 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.

References

  1. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1968; Gordon and Breach, New York, 1986).

    Google Scholar 

  2. A. V. Lotov, V. A. Bushenkov, G. K. Kamenev, and O. L. Chernykh, Computer and Search for Balanced Tradeoff: The Feasible Goals Method (Nauka, Moscow, 1997) [in Russian].

    Google Scholar 

  3. A. V. Lotov, V. A. Bushenkov, and G. K. Kamenev, Interactive Decision Maps: Approximation and Visualization of Pareto Frontier (Kluwer Academic, Boston, 2004).

    MATH  Google Scholar 

  4. G. K. Kamenev, Yu. G. Evtushenko, V. A. Garanzha, and M. K. Kerimov, in Proceedings of International Conference on Numerical Geometry, Grid Generation, and Scientific Computing, October, 2010 (Vychisl. Tsentr Ross. Akad. Nauk, Moscow, 2010), pp, 47–52.

    Google Scholar 

  5. P. M. Gruber, in Convexity and Its Applications (Birkhäuser, Basel, 1983).

    MATH  Google Scholar 

  6. G. K. Kamenev, Optimal Adaptive Methods for Polyhedral Approximation of Convex Bodies (Vychisl. Tsentr Ross. Akad. Nauk, Moscow, 2007) [in Russian].

    MATH  Google Scholar 

  7. R. V. Efremov and G. K. Kamenev, Comput. Math. Math. Phys. 51, 952–964 (2011).

    Article  MathSciNet  Google Scholar 

  8. C. A. Rogers, Packing and Covering (Cambridge Univ. Press, Cambridge, 1964; Mir, Moscow, 1968).

    MATH  Google Scholar 

  9. J. H. Conway and N. Sloane, Sphere Packings, Lattices, and Groups (Springer-Verlag, New York, 1988; Mir, Moscow, 1990), Vol. 1.

    MATH  Google Scholar 

  10. R. Schneider, Math. Ann. 256, 289–301 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  11. T. S. Maiskaya, in Collected Papers of Young Scientists from the Faculty of Computational Mathematics and Cybernetics of Moscow State University (Vychisl. Mat. Kibern. Mosk. Gos. Univ., Moscow, 2011), No. 8, pp. 83–98 [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. K. Kamenev.

Additional information

Original Russian Text © G.K. Kamenev, A.V. Lotov, T.S. Mayskaya, 2012, published in Doklady Akademii Nauk, 2012, Vol. 444, No. 2, pp. 153–155.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kamenev, G.K., Lotov, A.V. & Mayskaya, T.S. Construction of suboptimal coverings of the multidimensional unit sphere. Dokl. Math. 85, 425–427 (2012). https://doi.org/10.1134/S1064562412030106

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562412030106

Keywords

Navigation