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

Overview & Synopsis

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.