Skip to main content

An extension of Sard's method

Part of the Lecture Notes in Mathematics book series (LNM,volume 501)

Keywords

  • Integral Relation
  • Optimal Interpolation
  • Abstract Setting
  • Green Kernel
  • Periodic Spline

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.95
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. H. AHLBERG, E. N. NILSON, and J. L. WALSH, “The theory of splines and their applications”, Academic Press, New York, 1967.

    MATH  Google Scholar 

  2. C. DE BOOR and R. E. LYNCH, On splines and their minimum properties, J. Math. Mech., 15 (1966), 953–989.

    MathSciNet  MATH  Google Scholar 

  3. F. J. DELVOS, and W. SCHEMPP, Sard's method and the theory of spline systems, J. Approximation Theory 14 (1975), 230–243.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. F. J. DELVOS and W. SCHEMPP, On optimal periodic spline interpolation, J. Math. Analysis Appl., to appear.

    Google Scholar 

  5. S. KARLIN, “Total positivity”, Stanford University Press, Stanford, California, 1968.

    MATH  Google Scholar 

  6. S. g. MIKHLIN, “The problem of the minimum of a quadratic functional”, Holden Day, San Francisco-London-Amsterdam, 1965.

    MATH  Google Scholar 

  7. F. RIESZ, and B. SZ. NAGY, “Vorlesungen über Funktionalanalysis”, Deutscher Verlag der Wissenschaften, Berlin, 1956.

    MATH  Google Scholar 

  8. A. SARD, Optimal approximation, J. Functional Analysis 1 (1967), 222–244; 2 (1968), 368–369.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. A. SARD, Approximation based on nonscalar observations, J. Approximation Theory 8 (1973), 315–334.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. A. SARD, Instances of generalized splines, in “Spline-Funktionen” (eds.: K. Böhmer, G. Meinardus, W. Schempp), BI-Wissenschaftsverlag, Mannheim-Wien-Zürich, 1974.

    Google Scholar 

  11. R. SCHABACK, Konstruktion and algebraische Eigenschaften von m-Spline-Interpolierenden, Numer. Math. 21 (1973), 166–180.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. R. SCHABACK, Konstruktion von Spline-Interpolierenden und Peano-Kerne, in “Spline-Funktionen” (ed.: K. Böhmer, G. Meinardus, W. Schempp), BI-Wissenschaftsverlag, Mannheim-Wien-Zürich, 1974.

    Google Scholar 

  13. W. SCHEMPP und U. TIPPENHAUER, Reprokerne zu Spline-Grundräumen, Math. Z., 136 (1974), 357–369.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. M. H. SCHULTZ, “Spline Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1973.

    MATH  Google Scholar 

  15. W. I. SMIRNOW, “Lehrgang der höheren Mathematik V”, Deutscher Verlag der Wissenschaften, Berlin, 1967.

    MATH  Google Scholar 

  16. H. TRIEBEL, “Höhere Analysis”, Deutscher Verlag der Wissenschaften, Berlin, 1972.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1976 Springer-Verlag

About this paper

Cite this paper

Delvos, FJ., Schempp, W. (1976). An extension of Sard's method. In: Böhmer, K., Meinardus, G., Schempp, W. (eds) Spline Functions. Lecture Notes in Mathematics, vol 501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079741

Download citation

  • DOI: https://doi.org/10.1007/BFb0079741

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07543-1

  • Online ISBN: 978-3-540-38073-3

  • eBook Packages: Springer Book Archive