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Zeitschrift für Analysis und ihre Anwendungen

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Volume 10, Issue 2, 1991, pp. 255–262
DOI: 10.4171/ZAA/449

Published online: 1991-06-30

Parametric Quadratic Splines with Minimal Curvature

Gerhard Maess[1] and Kurt Frischmuth[2]

(1) Universität Rostock, Germany
(2) Universität Rostock, Germany

The concept of curvature-minimizing is extended to parametric polynomial splines of degree two. In contrast to the non-parametric case the resulting smooth curve is invariant under rotation of the co-ordinate system. Moreover, for a certain choice of the parameters (defining the functional to be minimized) it may be interpreted as a minimizer of the strain energy. For the case that the given data are points on a sufficiently smooth curve there is given an $O(h^2)$ error estimation ($h$ - steplength).

Keywords: Interpolating parametric polynomial splines of degree two, minimization of the curvature

Maess Gerhard, Frischmuth Kurt: Parametric Quadratic Splines with Minimal Curvature. Z. Anal. Anwend. 10 (1991), 255-262. doi: 10.4171/ZAA/449