Univariate Cubic L₁ Interpolating Splines: Spline Functional, Window Size and Analysis-based Algorithm

摘要

We compare univariate L₁ 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 L₁ splines preserve shape as well as or better than the other types of L₁ splines. To calculate second-derivative-based 5-point-window L₁ splines, we introduce an analysis-based, parallelizable algorithm. This algorithm is orders of magnitude faster than the previously widely used primal affine algorithm.