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Positive interpolation with rational quadratic splines

Positive Interpolation mit rational-quadratishen Splines

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Abstract

A necessary and sufficient criterion is presented under which the property of positivity carry over from the data set to rational quadratic spline interpolants. The criterion can always be satisfied if the occuring parameters are properly chosen.

Zusammenfassung

Unter positiver Interpolation wird die Aufgabenstellung verstanden, zur einer nichtnegativen Datenmenge nichtnegative Interpolierende zu konstruieren. Im Fallen rational-quadratischer Splines wird eine notwendige und hinreichende Bedingung für die Durchführbarkeit positiver Interpolation hergeleitet, und es wird gezeigt, daß diese sich bei passender Wahl der vorkommenden Parameter stets erfüllen läßt.

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Authors and Affiliations

  1. Department of Mathematics, Technical University of Dresden, Mommsenstrasse 13, DDR-8027, Dresden, German Democratic Republic

    J. W. Schmidt & W. Heß

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  1. J. W. Schmidt
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  2. W. Heß
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Schmidt, J.W., Heß, W. Positive interpolation with rational quadratic splines. Computing 38, 261–267 (1987). https://doi.org/10.1007/BF02240100

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  • DOI: https://doi.org/10.1007/BF02240100

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