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Ratioanl biquadraicC 1-splines inS-convex interpolation

Rational-biquadratischeC 1-Splines bei derS-konvexen Interpolation

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Abstract

The purpose of this paper is to give a necessary and sufficient condition for theS-convexity of rational biquadraticC 1-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.

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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  1. Institute of Numerical Analysis, Techinical University of Dresden, Mommsenstraße. 13, D-0-8027, Dresden, Federal Republic of Germany

    J. W. Schmidt

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Schmidt, J.W. Ratioanl biquadraicC 1-splines inS-convex interpolation. Computing 47, 87–96 (1991). https://doi.org/10.1007/BF02242024

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  • DOI: https://doi.org/10.1007/BF02242024

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