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Algorithm/algorithmus 42 an algorithm for cubic spline fitting with convexity constraints

Algorithmus 42. Ein Algorithmus für den Ausgleich mit Konvexitätsbedingungen durch kubische Spline-Funktionen

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Abstract

In this paper an algorithm is presented for fitting a cubic spline satisfying certain local concavity and convexity constraints, to a given set of data points. When using theL 2 norm, this problem results in a quadratic programming problem which is solved by means of the Theil-Van de Panne procedure. The algorithm makes use of the well-conditioned B-splines to represent the cubic splines. The knots are located automatically, as a function of a given upper limit for the sum of squared residuals. A Fortran IV implementation is given.

Zusammenfassung

Es wird ein Algorithmus vorgestellt für den Ausgleich durch kubische Spline-Funktionen, die gewissen Konvexitätsbedingungen genügen müssen. Wenn man dieL 2-Norm verwendet, führt dieses Problem auf ein quadratisches Programmierungsproblem, das man mit dem Verfahren von Theil und Van de Panne lösen kann. Für die Darstellung der kubischen Splines verwendet unser Algorithmus die gut konditionierten B-splines. Die Knoten werden automatisch in Abhängigkeit von einer Obergrenze für die Fehlerquadratsumme lokalisiert. Eine Fortran-IV-Version des Algorithmus ist beigefügt.

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  1. Applied Mathematics and Programming Division, Katholieke Universiteit Leuven, Celestijnenlaan 200 A, B-3030, Heverlee, Belgium

    P. Dierckx

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  1. P. Dierckx
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Dierckx, P. Algorithm/algorithmus 42 an algorithm for cubic spline fitting with convexity constraints. Computing 24, 349–371 (1980). https://doi.org/10.1007/BF02237820

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  • DOI: https://doi.org/10.1007/BF02237820

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