Approximation of Irregular Geometric Data by Locally Calculated Univariate Cubic \(L^1\) Spline Fits
\(L^1\) 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 \(L^1\) 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 \(L^1\) spline fits with globally calculated \(L^1\) 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.
approximation univariate \(l^1\) spline spline fit shape preservation cubic spline