Skip to main content

Nullstellen von Splines

  • Conference paper
  • First Online:
Approximation Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 556))

Abstract

This paper is concerned with Budan-Fourier theorems for rather general classes of spline functions. We extend the results known up to now, and at the same time simplify the underlying analysis. Some special cases are added.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. BIRKHOFF, G.D., General mean value and remainder theorems with applications to mechanical differentiation and quadrature. Trans. Amer.Math.Soc. 7 (1906), 107–136.

    Article  MathSciNet  Google Scholar 

  2. deBOOR, C. and I.J. SCHOENBERG, Cardinal interpolation and spline functions VIII. The Budan-Fourier theorem for splines and applications. In "Spline Functions", K. Böhmer, G. Meinardus and W. Schempp, Eds. Berlin-Heidelberg-New York: Springer-Verlag 1976, 1–79.

    Chapter  Google Scholar 

  3. FERGUSON, D.R., Sign changes and minimal support properties of Hermite-Birkhoff splines with compact support. SIAM J. Numer. Anal. 11 (1974), 769–779.

    Article  MathSciNet  MATH  Google Scholar 

  4. GANTMACHER, F.R. und M.G. KREIN, "Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Systeme", Berlin: Akademie-Verlag 1960.

    Google Scholar 

  5. HOUSEHOLDER, M., "The numerical treatment of a single non-linear equation". New York: McGraw Hill, 1970.

    MATH  Google Scholar 

  6. JETTER,K., Duale Hermite-Birkhoff-Probleme. Erscheint in J. Approximation Theory.

    Google Scholar 

  7. JETTER,K., Birkhoff interpolation by splines. Erscheint im Tagungsband des Symposiums über Approximationstheorie, Austin 1976.

    Google Scholar 

  8. JOHNSON, R.C., On monosplines of least deviation. Trans.Amer.Math.Soc. 96 (1960), 458–477.

    Article  MathSciNet  MATH  Google Scholar 

  9. KARLIN, S. and L.L. SCHUMAKER, The fundamental theorem of algebra for Tchebycheffian monosplines. J. d'Anal.Math. 20 (1967), 233–270.

    Article  MathSciNet  MATH  Google Scholar 

  10. LORENTZ, G.G., Zeros of splines and Birkhoff's kernel. Math.Z. 142 (1975), 173–180.

    Article  MathSciNet  MATH  Google Scholar 

  11. LORENTZ, G.G. and K.L. ZELLER, Birkhoff interpolation. SIAM J.Numer.Anal. 8 (1971), 43–48.

    Article  MathSciNet  MATH  Google Scholar 

  12. MELKMAN, A.A., The Budan-Fourier theorem for splines. Israel J. Math. 19 (1974), 256–263.

    Article  MathSciNet  MATH  Google Scholar 

  13. MICCHELLI, C., The fundamental theorem of algebra for monosplines with multiplicities. Proc.Conf.Oberwolfach 1971, ISNM 20 (1972), 419–430.

    MathSciNet  MATH  Google Scholar 

  14. SCHUMAKER,L.L., Zeros of spline functions and applications. Erscheint im J.Approximation Theory.

    Google Scholar 

  15. SCHUMAKER, L.L., Toward a constructive theory of generalized spline functions. In "Spline Functions", K. Böhmer, G. Meinardus and W. Schempp, Eds., Berlin-Heidelberg-New York: Springer-Verlag 1976, 265–331.

    Chapter  Google Scholar 

Download references

Authors

Editor information

Robert Schaback Karl Scherer

Rights and permissions

Reprints and permissions

Copyright information

© 1976 Springer-Verlag

About this paper

Cite this paper

Jetter, K. (1976). Nullstellen von Splines. In: Schaback, R., Scherer, K. (eds) Approximation Theory. Lecture Notes in Mathematics, vol 556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087413

Download citation

  • DOI: https://doi.org/10.1007/BFb0087413

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08001-5

  • Online ISBN: 978-3-540-37552-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics