Skip to main content
SpringerLink
Log in
Book cover

Polynomial and Spline Approximation pp 1–15Cite as

Some Applications of Polynomial and Spline Approximation

  • Chapter

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 49))

Summary

The distinction is described between qualitative error estimations (order of magnitude of the error) and quantitative error bounds (numerically computable strong mathematical pointwise error bounds). Progress by using approximation methods is made in the last years in singular nonlinear boundary value problems, in the method of finite elements, in free boundary value problems (exact inclusion for the free boundary in simple cases) and other areas.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover 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. Bredendiek, E. [69] Simultant Approximation, Arch. Rat. Mech. Anal., 33 (1969), 307–330.

    Article  MATH  MathSciNet  Google Scholar 

  2. Bredendiek, E. and L, Collatz [76] Simultant Approximation bei Randwertaufgaben, to appear in Intern. Ser. Num. Math. 1976.

    Google Scholar 

  3. Cheney E.W. [66] Introduction to approximation theory N.W. McGraw-Hill, 1966.

    MATH  Google Scholar 

  4. Collatz, L. [56] Approximation von Funktionen bei einer und bei mehreren unabhängigen Veränderlichen, Z. Angew. Math. Mech. 36 (1956), 198–211.

    Article  MATH  MathSciNet  Google Scholar 

  5. Collatz, L. [69] Nichtlineare Approximation bei Randwertaufgaben V.JKM. Weimer 1969, 169–182.

    Google Scholar 

  6. Collatz, L. [75a] Methods for Solution of Partial Differential Equations, Symp. Numer. Solution Part. Diff. Equ. Kjeller, Norway 1975, 1–16.

    Google Scholar 

  7. Collatz, L. [74] Monotonicity with discontinuities in partial differential equations, Proc. Conf. Ord. Part. Diff. Equ. Dundee 1974, Lect. Notes Math. Bd. 415 (1974) 85–102.

    MathSciNet  Google Scholar 

  8. Collatz, L. [75] Bemerkungen Zur verketteten Approximation, Intern. Ser. Num. Math. 26 (1975), 41–45.

    Google Scholar 

  9. Collatz, L. [77] The numerical treatment of some singular boundary value problems, Conference on Numer. Analysis, Dundee 1977, to appear.

    Google Scholar 

  10. Collatz, L. [78] Application of approximation to some singular boundary value problems, Proc. Conference Num. Anal. Dundee, Springer Lect. Not. Math. Bd. 630 (1978) 41–50.

    MathSciNet  Google Scholar 

  11. Collatz, L. — W. Krabs [73] Approximationstheorie, Teubner, Stuttgart, 1973, 208 S.

    Book  MATH  Google Scholar 

  12. Hoffmann, K.H. [78] Monotonie bei nichtlinearen Stefan-Problemen, Internat. Ser. Num. Math. 39 (1978), 162–190.

    Google Scholar 

  13. Meinardus, G. [67] Approximation of Functions, Theory and Numerical Methods, Springer Verlag, 1967, 198 S.

    Google Scholar 

  14. Meinardus, G. [76] Periodische Splines Functionen, Lect. Notes Math. Bd. 501 (1976) 177–199.

    Article  MathSciNet  Google Scholar 

  15. Meyer, A.G. [60] Schranken für die Lösungen von Randwertaufgaben mit elliptischer Differentialgleichung. Arch. rat. Mech. Anal. 6 (1960), 277–298.

    Article  MATH  Google Scholar 

  16. Meyn, K.-H. -B. Werner [78] Randomaximum- und Monotonieprinzipien für elliptische Randwertaufgaben mit Gebietszerlegungen, erscheint demnächst, to appear.

    Google Scholar 

  17. Mitchell, A. R. — R. Wait [77] The finite Element Method in Partial Differential Equations, 1977, 192 p.

    MATH  Google Scholar 

  18. Natterer, F. [78] Berechnung oberer Schranken für die Norm der Ritz-Projektion auf finite Elemente Internat. Ser. Num. Math. 39 (1978) 236–245.

    MathSciNet  Google Scholar 

  19. Osborne, M.R. — G.A. Watson [78] Nonlinear Approximation Problems in Vektornorms, Lect. Notes Math, 630 Springer 1978, 117–132.

    Google Scholar 

  20. Prenter, P. [71] Polynomial operators and equations, in Proc. Symp. Nonlinear functional analysis and applications, ed. L.B. Rail, Academic Press 1971.

    Google Scholar 

  21. Redheffer, R.M. [63] Die Collatzshce Monotonie bei Anfangswertproblemen, Arch. Rat. Mech. Anal. 14 (1963), 196–212.

    Article  MATH  MathSciNet  Google Scholar 

  22. Schröder, J. [56] Das Iterationsverfahren bei allgemeinerem Abstandbegriff, Math. Z. 1956, 66, 111–116.

    Article  MATH  MathSciNet  Google Scholar 

  23. Schröder, J. [59] Vom Defekt ausgehende Fehlerabschätzungen bei Differentialgleichungen. Arch. Rat. Mech. Anal. 3 (1959) 219–228.

    Article  MATH  Google Scholar 

  24. Sprekels, J. [78] Iterationsverfahren zur Einschliebung positiver Lösungen superlinearer Integralgleichungen. Intern. Ser. Num. Math. 39, (1978) 261–279.

    MathSciNet  Google Scholar 

  25. Taylor, G.D. [72] On minimal H-sets, J. Approximation Theory 5 (1972), 113–117.

    Article  MATH  MathSciNet  Google Scholar 

  26. Voss, H. [77] Existenz und Einschliebung positiver Losungen superlinearer Integralgleichungen und Randowertaufgaben, Habil. Schrift, Hamburg, 1977.

    Google Scholar 

  27. Walter, W. [70] Differential and Integral Inequalities, Springer 1970, 352 S.

    Google Scholar 

  28. Weinitschke, H. [77] Verzweigungsprobleme bei kreisförmigen elastischen Platten, Intern. Ser. Num. Math. 38 (1977) 195–212.

    MathSciNet  Google Scholar 

  29. Werner, B. [75] Monotonie und finite Elemente bei elliptischen Differentialgleichungen, Intern. Ser. Num. Math. 27 (1975) 309–329.

    Google Scholar 

  30. Wetterling, W. [68] Lösungsschranken bei elliptischen Differen-tialgleichungen, Intern. Ser. Num. Math. 9 (1968) 393–401.

    MathSciNet  Google Scholar 

  31. Wetterling, W. [77] Quotienteneinschliebung bei Eignewertaufgaben mit partieller Differentialgleichung, Int. Ser. Num. Math. 38 (1977) 213–218.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Hamburg, Germany

    Lothar Collatz

Authors
  1. Lothar Collatz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Calgary, Canada

    Badri N. Sahney

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Collatz, L. (1979). Some Applications of Polynomial and Spline Approximation. In: Sahney, B.N. (eds) Polynomial and Spline Approximation. NATO Advanced Study Institutes Series, vol 49. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9443-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-9443-0_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-9445-4

  • Online ISBN: 978-94-009-9443-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation