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

Abstract

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.

Keywords

• antiderivative
• cubic L1 spline
• first derivative
• 5-point window
• function value
• global
• interpolation
• locally calculated
• second derivative
• univariate