\(L_1C^1\) polynomial spline approximation algorithms for large data sets
type: Item
instance of: scholarly article
title: \(L_1C^1\) polynomial spline approximation algorithms for large data sets
zbMATH Open document ID: 1308.65024
author: Laurent Gajny
author: O. Gibaru
author: Eric Nyiri
published in: Numerical Algorithms
publication date: 2014-12-03T00:00:00Z
review text: The authors propose a new strategy of \( L_1 \) approximation. The main idea is to minimize a shape functional based on the second derivative in an a priori fixed neighborhood of the data set. This functional enables to control locally the deviation between the data set and the resulting curve contrary to \( L_1 \) smoothing splines or \( L_1 \) spline fits. They introduce a new approximating strategy to create an iterative local \( L_1C^1 \) spline approximation extending to the bicubic spline approximation over \( 3D \) data grids and using this result for the image cases. Rich literature and some conclusion and supporting examples are provided at the end of the paper.
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 6376434
zbMATH Keywords: \(L_1\) spline
zbMATH Keywords: smooth spline
zbMATH Keywords: noisy data
zbMATH Keywords: bicubic spline approximation
reviewed by: Haydar Akca
MaRDI profile type: Publication
full work available at URL: s11075-014-9828-x
OpenAlex ID: W2079481585
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DOI: 10.1007/S11075-014-9828-X
description: scientific article; zbMATH DE number 6376434