Skip to main content

Direct and inverse theorems for best approximation by Λ-Splines

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

Keywords

  • Besov Space
  • Smoothness Condition
  • Inverse Theorem
  • Good Approxi
  • Nest Partition

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. NILSON—J.L. WALSH: The Theory of Splines and their Applications, Academic Press, New York, 1967.

    MATH  Google Scholar 

  2. A. FRIEDMAN: Partial Differential Equations, Holt, Rinehart, and Winston, New York 1969.

    MATH  Google Scholar 

  3. G.W. HEDSTROM—R.S. VARGA: Application of Besov spaces to spline approximation, J. Approximation Theory 4 (1971), 295–327.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. J.W. JEROME: On uniform approximation by certain generalized spline functions. J. Approximation Theory 7 (1973), 143–154.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. H. JOHNEN: Inequalities connected with the moduli of smoothness, Mat. Vesnik, 9 (24) (1972), 289–303.

    MathSciNet  MATH  Google Scholar 

  6. F. RICHARDS—R. de VORE: Saturation and inverse theorems for spline approximation. Spline Functions Approx. Theory, Proc. Sympos. Univ. Alberta, Edmonton 1972, ISNM 21 (1973), 73–82.

    MathSciNet  Google Scholar 

  7. K. SCHERER: Characterization of generalized Lipschitz classes by best approximation with splines, SIAM J. Numer. Anal. 11 (1974), 283–304.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. K. SCHERER: Best approximation by Chebychevian Splines and generalized Lipschitz spaces, Proceedings of the Conference on “Constructive Theory of Functions”, Cluj (1973).

    Google Scholar 

  9. B.K. SWARTZ—R.S. VARGA: Error bounds for spline and L-spline interpolation, J. Approximation Theory 6 (1972), 6–49.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. A.F. TIMAN: Theory of Approximation of Functions of a Real Variable. Pergamon Press, New York 1963.

    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

Johnen, H., Scherer, K. (1976). Direct and inverse theorems for best approximation by Λ-Splines. In: Böhmer, K., Meinardus, G., Schempp, W. (eds) Spline Functions. Lecture Notes in Mathematics, vol 501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079744

Download citation

  • DOI: https://doi.org/10.1007/BFb0079744

  • 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