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Convexity preserving interpolation with exponential splines

Konvexe Interpolation mit Exponentialsplines

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Abstract

Sufficient and necessary conditions are derived under which interpolating splines are convex if the data set is in convex position. In order to select one of the interpolants, by means of a well-known objective function a quadratic optimization problem is stated which can be solved effectively by passing to a dual program.

Zusammenfassung

Während die Aufgabe der konvexen Interpolation im Falle kubischer Splines im allgemeineen nicht lösbar ist, kann jetzt gezeigt werden, daß sie bei Verwendung von Exponentialsplines Lösungen besitzt sofern die vorkommenden Parameter hinreichend roß sind, und es werden konkrete hinreichende und notwendige Lösbarkeitsbedingungen hergeleitet. Da eindeutige Lösbarkeit in der Regel nicht vorliegt, wird eine Auswahlfunktion eingeführt und das entstehende quadratische Optimierungsproblem nach Dualisierung numerisch behandelt.

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Authors and Affiliations

  1. Sektion Mathematik, Technische Universität Dresden, Mommsenstrasse 13, DDR-8027, Dresden, German Democratic Republic

    W. Heß & J. W. Schmidt

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  1. W. Heß
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  2. J. W. Schmidt
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Dedicated to Professor W. Knödel on the occasion of his 60th birthday

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Heß, W., Schmidt, J.W. Convexity preserving interpolation with exponential splines. Computing 36, 335–342 (1986). https://doi.org/10.1007/BF02240208

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  • DOI: https://doi.org/10.1007/BF02240208

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