Skip to main content

Two case-studies in parametric semi-infinite programming

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 66))

Abstract

It is shown that the problem of approximating the eigenvalues and eigenfunctions of a homogeneous membrane as well as that of approximating (in the sense of Chebyshev) a function by generalized rational functions can be treated as semi-infinite programming problems depending on a real parameter.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barrodale, I.;Powell, M.J.D.; Roberts, F.D.K.: The differential correction algorithm for rational l-approximation, SIAM J. Numer. Anal., 9 (1972), 493–504

    Google Scholar 

  2. Cheney, E.W.; Loeb, H.L.: Two new algorithms for rational approximation, Numer. Math., 3 (1961), 72–75

    Google Scholar 

  3. Courant, R.; Hilbert, D.: Methoden der mathematischen Physik, Band I, Springer, Berlin-Heidelberg-New York, 1968

    Google Scholar 

  4. Donnelly, J.D.P.: Eigenvalues of membranes with rentrant corners, SIAM J. Numer. Anal., 6 (1969), 47–61

    Google Scholar 

  5. Fox, L.; Henrici, P.; Moler, C.: Approximations and bounds for eigen-values of elliptic operators, SIAM J. Numer. Anal., 4 (1967), 89–102

    Google Scholar 

  6. Hersch, J.: Erweiterte Symmetrieeigenschaften von Lösungen gewisser linearer Rand-und Eigenwertprobleme, J.Reine u. Angew. Math., 218 (1965), 143–158

    Google Scholar 

  7. Hettich, R.; Zencke, P.: Numerische Methoden der Approximationsund semi-infiniten Optimierung, Teubner, Stuttgart, 1981

    Google Scholar 

  8. Moler, C.; Payne, L.F.: Bounds for eigenvalues and eigenvectors of symmetric operators, SIAM J. Numer. Anal., 5 (1968), 64–70

    Google Scholar 

  9. Nickel, K.: Extension of a recent paper by Fox, Henrici and Moler on eigenvalues of elliptic operators, SIAM J. Numer. Anal. 4 (1967), 483–488

    Google Scholar 

  10. Piel, G.: Approximationsmethoden zur näherungsweisen Bestimmung von Eigenwerten und Eigenfunktionen elliptischer Differentialoperatoren, Diplomarbeit, Universität Bonn, 1981

    Google Scholar 

  11. Speich, G.: Ein Algorithmus zur Lösung allgemeiner rationaler Approximationsprobleme. Thesis, University of Bonn, 1981

    Google Scholar 

  12. Zencke, P.: A Newton-Differential-Correction-Algorithm for generalized rational Chebyshev approximation, in preparation

    Google Scholar 

  13. Zencke, P.; Hettich, R.: A theorem on directional derivatives of the value of parametric semi-infinite programming problems, in preparation

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Arunabha Bagchi Hubertus Theodorus Jongen

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Hettich, R., Zencke, P. (1985). Two case-studies in parametric semi-infinite programming. In: Bagchi, A., Jongen, H.T. (eds) Systems and Optimization. Lecture Notes in Control and Information Sciences, vol 66. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043396

Download citation

  • DOI: https://doi.org/10.1007/BFb0043396

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15004-6

  • Online ISBN: 978-3-540-39215-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics