Univariate cubic \(L_1\) interpolating splines: spline functional, window size and analysis-based algorithm
type: Item
instance of: scholarly article
title: Univariate cubic \(L_1\) interpolating splines: spline functional, window size and analysis-based algorithm
zbMATH Open document ID: 1461.65016
author: Lu Yu
author: John E. Lavery
author: Shu-Cherng Fang
author: Qingwei Jin
published in: Algorithms
publication date: 2018-08-20T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 6920527
zbMATH Keywords: antiderivative
zbMATH Keywords: cubic \(L_1\) spline
zbMATH Keywords: first derivative
zbMATH Keywords: 5-point window
zbMATH Keywords: function value
zbMATH Keywords: global
zbMATH Keywords: interpolation
zbMATH Keywords: locally calculated
zbMATH Keywords: second derivative
zbMATH Keywords: univariate
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a3030311
OpenAlex ID: W2043189673
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DOI: 10.3390/A3030311
description: scientific article; zbMATH DE number 6920527