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Fast $L_1$-$C^k$ polynomial spline interpolation algorithm with shape-preserving properties

Abstract : In this article, we address the interpolation problem of data points per regular $L_1$-spline polynomial curve that is invariant under a rotation of the data. We iteratively apply a minimization method on ¯ve data, belonging to a sliding window, in order to obtain this interpolating curve. We even show in the $C^k$-continuous interpolation case that this local minimization method preserves well the linear parts of the data, while a global $L_p$ (p >=1) minimization method does not in general satisfy this property. In addition, the complexity of the calculations of the unknown derivatives is a linear function of the length of the data whatever the order of smoothness of the curve.
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Eric Nyiri, Olivier Gibaru, Philippe Auquiert. Fast $L_1$-$C^k$ polynomial spline interpolation algorithm with shape-preserving properties. Computer Aided Geometric Design, Elsevier, 2011, 28 (1), pp.65-74. ⟨10.1016/j.cagd.2010.10.002⟩. ⟨hal-00777464⟩

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