Advertisement

Mehrdimensionale Spline-Interpolation mit Hilfe der Methode von Sard

  • Karl-Heinz Schloßer
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 501)

Keywords

Spline Approximation Bivariate Spline Spline System Dann Gilt 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literaturverzeichnis

  1. [1]
    Birkhoff, G.: Piecewise bicubic interpolation and approximation in polygons. In: Approximation with special emphasis on spline functions. (I.J. Schoenberg ed.) pp. 185–221. New York-London: Academic Press 1969.Google Scholar
  2. [2]
    De Boor, C.R., Lynch, R.E.: On splines and their minimum properties. J. Math. Mech. 15, 953–969(1966).MathSciNetzbMATHGoogle Scholar
  3. [3]
    Delvos, F.J.: Über die Konstruktion von Spline Systemen. Dissertation. Ruhr-Universität Bochum 1972.Google Scholar
  4. [4]
    Delvos, F.J., Schempp, W.: Sard's method and the theory of spline systems. Erscheint in J. Approximation Theory.Google Scholar
  5. [5]
    Delvos, F.J., Schempp, W.: On spline systems. Monatsh. Math. 34, 399–409(1970).MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Delvos, F.J., Schloßer, K.-H.: Das Tensorpro-duktschema von Spline Systemen. In: Spline-Funktionen. Vorträge und Aufsätze. (K. Böhmer, G. Meinardus, W. Schempp eds.) pp. 59–73. Mannheim-Wien-Zürich: Bibliographisches Institut 1974.Google Scholar
  7. [7]
    Kösters, H.W., Schloßer, K.-H.: On spaces related to bivariate Spline Interpolation. (Erscheint demnächst).Google Scholar
  8. [8]
    Mansfield, L.: On the variational characterization and convergence of bivariate splines. Numer. Math. 20, 99–114(1972).MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    Nielson, G.M.: Bivariate spline functions and the approximation of linear functionals. Numer. Math. 21, 138–160(1973).MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Sard, A.: Optimal approximation. J. Functional Anal. 1. 224–244 (1967) and 2, 368–369 (1968).MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    Sard, A.: Approximation based on nonscalar observations. J. Approximation Theory 8, 315–334 (1973).MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Sard, A.: Instances of generalized Splines. In: Spline-Funktionen. Vorträge und Aufsätze. (K. Böhmer, G. Meinardus, W. Schemppeds.) pp. 215–241. Mannheim-Wien-Zürich: Bibliographisches Institut 1974.Google Scholar
  13. [13]
    Sard, A.: Linear approximation. Providence, Rhode Island, American Mathematical Society, 1963.CrossRefzbMATHGoogle Scholar
  14. [14]
    Scheffold, E., Schloßer, K.-H.: Spline-Funktionen mehrerer Veränderlicher. (Erscheint demnächst).Google Scholar
  15. [15]
    Schempp, W.: Zur Theorie der Spline Systeme. In: Spline-Funktionen. Vorträge und Aufsätze. (K. Böhmer, G. Meinardus, W. Schempp eds.) pp. 275–289. Mannheim-Wien-Zürich: Bibliographisches Institut 1974.Google Scholar
  16. [16]
    Schempp, W., Tippenhauer, U.: Reprokerne zu Spline-Grundräumen. Math. Z. 136, 357–369(1974).MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    Schloßer, K.-H.: Mehrdimensionale Spline-Interpolation mittels Spline-Systemen. Zeitr. Angew. Math. Mech. 55, T260–T262 (1975).MathSciNetzbMATHGoogle Scholar
  18. [18]
    Schloßer, K.-H.: Zur mehrdimensionalen Spline-Interpolation. Dissertation. 79pp. Bochum 1974.Google Scholar
  19. [19]
    Schoenberg, I.J.: On best approximation of linear operators. Nederl. Akad. Wetensch. Indag. Math. 26, 155–163(1964).MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Tippenhauer, U.: Reproduzierende Kerne in Spline-Grundräumen. Dissertation 101pp. Bochum 1973.Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Karl-Heinz Schloßer
    • 1
  1. 1.Ruhr-Universität BochumBochumBundesrepublik Deutschland

Personalised recommendations