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, Volume 47, Issue 1, pp 87–96 | Cite as

Ratioanl biquadraicC1-splines inS-convex interpolation

  • J. W. Schmidt
Article

Abstract

The purpose of this paper is to give a necessary and sufficient condition for theS-convexity of rational biquadraticC1-spline interpolants on rectangular grids. The criterion is described in form of linear equalities and convex inequalities, and forS-convex data sets the criterion can be satisfied whenever the rationality parameters are sufficiently large.

AMS(MOS) Subject Classifications

65D07 41A15 41A63 

Key words

S-convex spline interpolation existence conditions search procedure for constructingS-convex splines 

Rational-biquadratischeC1-Splines bei derS-konvexen Interpolation

Zusammenfassung

In dieser Arbiet wird eine notwendige und hinreichende Bedingung für dieS-Konvexität von rational-biquadratischen Spline interpolierenden auf Rechteckgittern hergeleitet. Da Kriterium kann in Form von linearen Gleichungen und konvexen Ungleichungen formuliert werden, und es wird gezeigt, daß diese im Fall von hinreichend großen Rationalitätsparametern erfüllbar sind, sofer sind die zu interpolierende Datenmenge inS-konvexer Lage befindet.

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • J. W. Schmidt
    • 1
  1. 1.Institute of Numerical AnalysisTechinical University of DresdenDresdenFederal Republic of Germany

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