Advertisement

Abstract

A sufficient conditions for the nodes xi (where X0 < x1 < … < xn) and for the numbers yi (i = 0, 1..., n) and J’0 for which a polynomial spline function s of degree k+1 (k ≥ 1) interpolating the data yi in nodes xi and such that s’(x0) = y’0 sϵCk [x0,xn] are given. An explicit form for the spline function s are given.

Konvexe Interpolierende Spline-Funktionen Beliebigen Grades

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    de Boor, C.: Splines as Linear Combinations of B-Splines. A Survey. Approximation Theory II (G.G. Lorentz, C.K. Chui, L.L. Schumaker, Eds.). Hew York, Academie Press 1976, 1–47.Google Scholar
  2. [2]
    de Boor, C., Swartz, B.: Piecewise Monotone Interpolation. J. Approximation Theory 21 (1977), 411–416.CrossRefGoogle Scholar
  3. [3]
    Curry, H.B., Schoehberg, I.J.: On Pólya Frequency Functions IV. The Fundamental Spline Functions and Their Limits, J. d’Analyse Math. 17 (1966), 71–107.CrossRefGoogle Scholar
  4. [4]
    Dimsdale, B.: Convex Cubic Splines II. IBM Los Angeles Scientific Center, Report No. G320–2692, September 1977.Google Scholar
  5. [5]
    Dimsdale, B.: Convex Cubic Splines. IBM J. Res. Develop. 22 (1978), 168–178.Google Scholar
  6. [6]
    Hornung, U.: Interpolation by Smooth Functions under Restrictions for the Derivatives. Preprint No. 33, Rechenzentrum der Universtität Münster, 1978.Google Scholar
  7. [7]
    Hornung, U.: Numerische Berechnung monotoner und konvexer Spline--Interpolierender. Z. Angew. Math. Mech. 59 (1979), T64–T65.Google Scholar
  8. [8]
    McAllister, D.F., Passow, E., Roulier, J.A.: Algorithms for Computing Shape Preserving Spline Interpolations to Data. Math. Comput. 31 (1977), 717–725.CrossRefGoogle Scholar
  9. [9]
    McAllister, D.F., Boulier, J.A.: Interpolation by Convex Quadratic Splines. Math. Comput. 32 (1978), 1154–1162.CrossRefGoogle Scholar
  10. [10]
    Neuman, E.: Convex Interpolating Splines of Odd Degree. Utilitas Math. 14 (1978), 129–140.Google Scholar
  11. [11]
    Neuman, E.: Uniform Approximation by Some Hermite Interpolating Splines. J. Comput. and Appl. Math. 4 (1978), 7–9.CrossRefGoogle Scholar
  12. [12]
    Passow, E.: Piecewise Monotone Spline Interpolation. J. Approximation Theory 12 (1974), 240–241.CrossRefGoogle Scholar
  13. [13]
    Passow, E.: Monotone Quadratic Spline Interpolation. J. Approximation Theory 19 (1977), 143–147.CrossRefGoogle Scholar
  14. [14]
    Passow, E., Boulier, J.A.: Shape Preserving Spline Interpolation. Approximation Theory II (G.G. Lorentz, C.K. Chui, L.L. Schumaker, Eds.). New York, Academic Press, 1976, 503–507.Google Scholar
  15. [15]
    Passow, E., Boulier, J.A.: Monotone and Convex Spline Interpolation. SIAM J. Numer. Anal. 14 (1977), 904–909.CrossRefGoogle Scholar
  16. [16]
    Passkowski, S.t Problems in Numerical Analysis. Part I (in Polish). Lódz, PWN, 1969.Google Scholar

Copyright information

© Springer Basel AG 1980

Authors and Affiliations

  • Edward Neuman
    • 1
  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland

Personalised recommendations