Abstract
L1 splines have been under development for interpolation and approximation of irregular geometric data. We investigate the advantages in terms of shape preservation and computational efficiency of calculating univariate cubic L1 spline fits using a steepest-descent algorithm to minimize a global data-fitting functional under a constraint implemented by a local analysis-based interpolating-spline algorithm on 5-node windows. Comparison of these locally calculated L1 spline fits with globally calculated L1 spline fits previously reported in the literature indicates that the locally calculated spline fits preserve shape on the average slightly better than the globally calculated spline fits and are computationally more efficient because the locally-calculated-spline-fit algorithm can be parallelized.
Keywords: Approximation; Cubic spline; L1 spline; Shape preservation; Spline fit; Univariate