Advertisement

Shape preserving rational spline interpolation

  • John A. Gregory
Numerical Methods
Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)

Abstract

A rational cubic function is presented which has shape preserving interpolation properties. It is shown that the rational cubic can be used to construct C2 rational spline interpolants to monotonic or convex sets of data which are defined on a partition x1 < x2 < … < xn of the real interval [x1, xn].

Keywords

Spectral Radius Convex Constraint Convexity Condition Consistency Equation SHAPE Preserve 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Delbourgo, R. and Gregory, J.A., C2 rational quadratic spline interpolation to monotonic data, IMA J. Num. Analysis 3 (1983), 141–152.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Delbourgo, R. and Gregory, J.A., Shape preserving piecewise rational interpolation, to appear in SIAM J. Sci. Stat. Comput.Google Scholar
  3. 3.
    Fritsch, F.N. and Carlson, R.E., Monotone piecewise cubic interpolation, SIAM J. Num. Analysis 17 (1980), 235–246.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Gregory, J.A. and Delbourgo, R., Piecewise rational quadratic interpolation to monotonic data, IMA J. Num. Analysis 2 (1982), 123–130.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Ortega J.M. and Rheinboldt, W.C., Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.zbMATHGoogle Scholar
  6. 6.
    Schaback, R., Spezielle rationale splinefunktionen, J. Approx. Theory 7 (1973), 281–292.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Schaback, R., Interpolation mit nichtlinearen klassen von spline-funktionen, J. Approx. Theory 8 (1973), 173–188.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Varga, R., Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, 1962.Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • John A. Gregory
    • 1
  1. 1.Department of Mathematics and StatisticsBrunel UniversityUxbridgeEngland

Personalised recommendations