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Positive, monotone, andS-convexC 1-interpolation on rectangular grids

Positive, monotone undS-konvexeC 1-Interpolation auf Rechteckgittern

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Abstract

This paper is concerned with shape preservingC 1-interpolation of data sets given on rectangular grids. Using special rational biquadratic splines, criteria are derived which are sufficient for the positivity, monotonicity, andS-convexity and which, in addition, are satisfied for sufficiently large rationality parameters.

Zusammenfassung

Diese Arbeit befaßt sich mit formerhaltenderC 1-Interpolation von Daten auf Rechteckgittern. Bei Verwendung von speziellen rational-biquadratischen Splines werden Bedingungen hergeleitet, welche hinreichend für die Positität, Monotonie undS-Konvexität sind und welche sich darüber hinaus erfüllen lassen, sofern die Rationalitätsparameter hinreichend groß sind.

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References

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Authors and Affiliations

  1. Insitute of Numerical Analysis, Technical University of Dresden, Mommsenstraße 13, D-O-8027, Dresden, Federal Republic of Germany

    J. W. Schmidt

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  1. J. W. Schmidt
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Schmidt, J.W. Positive, monotone, andS-convexC 1-interpolation on rectangular grids. Computing 48, 363–371 (1992). https://doi.org/10.1007/BF02238643

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  • DOI: https://doi.org/10.1007/BF02238643

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