Univariate cubic \(L_1\) interpolating splines: spline functional, window size and analysis-based algorithm
Summary: We compare univariate \(L_1\) interpolating splines calculated on 5-point windows, on 7-point windows and on global data sets using four different spline functionals, namely, ones based on the second derivative, the first derivative, the function value and the antiderivative. Computational results indicate that second-derivative-based 5-point-window \(L_1\) splines preserve shape as well as or better than the other types of \(L_1\) splines. To calculate second-derivative-based 5-point-window \(L_1\) splines, we introduce an analysis-based, parallelizable algorithm. This algorithm is orders of magnitude faster than the previously widely used primal affine algorithm.
scientific article; zbMATH DE number 6920527
scientific article