Skip to main content
SpringerLink
Log in

Global approximation of a compact set by elements of a convex set in a normed space

  • Published:
Numerische Mathematik Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Bourbaki, N.: Eléments de Mathématiques. Espaces vectoriels topologiques. Ch. 1 et 2, fascicule XV. Paris: Hermann 1966.

    Google Scholar 

  2. Dunford, N., Schwartz, J. T.: Linear operators, part I. New York: Int. Pub. 1958.

    Google Scholar 

  3. Dunham, C. B.: Simultaneous Chebyshev approximation of functions on an interval. Proc. Am. Math. Soc.18, No. 3, 472–477 (1967).

    Google Scholar 

  4. Eggleston, L. G.: Convexity. Camb. Univ. Press 1963

  5. Golomb, M.: On the uniformly best approximation of functions given by incomplete data. M. R. C. Technical Summary Report 121, Dec. 1959, Madison, The University of Wisconsin.

    Google Scholar 

  6. Laurent, P. J.: Théorèmes de caractérisation d'une meilleure approximation dans un espace normé et généralisation de l'algorithme de Rémès. Num. Math.10, 190–208 (1967).

    Google Scholar 

  7. ——: Cônes de déplacements admissibles, sous-gradients et approximation convexe dans un espace vectoriel normé. Nato Summer School, Venice, June 1968.

    Google Scholar 

  8. - Théorèmes de caractérisation en approximation convexe. Colloque ≪Théorie de l'approximation des fonctions≫ Cluj (Roumanie), 15–20 Sept. 1967 Mathematica10 (33), 95–111 (1968).

  9. - Cours de théorie de l'approximation, fascicule 5, 1968–1969, Université de Grenoble.

  10. Moreau, J. J.: Fonctionnelles convexes. Séminaire du Collège de France, Paris, 1966-1967.

    Google Scholar 

  11. Pham-Dinh-Tuan: Approximation d'un ensemble compact de fonctions dans un espace vectoriel normé. Projet de fin d'étude, Institut Polytechnique de Grenoble, Mathématiques appliquées, 1967–1968.

  12. Rémès, E.: Sur la détermination des polynomes d'approximation de degré donné. Comm. de la Soc. Math. de Kharkof, sér. 4,10, 41–63 (1934).

    Google Scholar 

  13. Singer, I.: Caractérisation des éléments de meilleure approximation dans un espace de Banach quelconque. Act. Sci. Math. Szeged17, 181–189 (1956).

    Google Scholar 

  14. ——: Cea mai buna aproximare in spatii vectoriale normate prin elemente din subspatii vectoriale. Ed. Acad. Rep. Soc. Romania, Bucuresti (1967)

    Google Scholar 

  15. Valadier, M.: Quelques propriétés des sous-gradients. Rapport de l'IRIA, Sept. 1968.

Download references

Author information

Authors and Affiliations

  1. Math. Res. Center, The University of Wisconsin, 53706, Madison, Wis., USA

    P. J. Laurent

  2. Math. Appliquées, CEDEX 53, Université de Grenoble, 38-Grenoble-Gare, France

    Pram-Dinh-Tuan

Authors
  1. P. J. Laurent
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pram-Dinh-Tuan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Prof. Dr. Dr. h. c. L. Collatz for his 60th birthday

Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No.: DA-31-124-ARO-D-462.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Laurent, P.J., Pram-Dinh-Tuan Global approximation of a compact set by elements of a convex set in a normed space. Numer. Math. 15, 137–150 (1970). https://doi.org/10.1007/BF02165378

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02165378

Keywords

Search

Navigation