On Lebesgue constants of local parabolic splines
type: Item
instance of: scholarly article
title: On Lebesgue constants of local parabolic splines
zbMATH Open document ID: 1332.65025
DOI: 10.1134/S008154381505017X
author: E. V. Strelkova
author: Valerii T. Shevaldin
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2015-08-20T00:00:00Z
review text: The paper deals with the stability of a linear approximation method based on polynomial splines of minimal defect of degree with arbitrary knots. The stability is expressed in terms of the behavior of a uniform norm of a linear operator, called Lebesgue constant which, for a good stability, is aimed to be as small as possible with respect to a change in approximation conditions. The authors approach the method of local spline approximation as a useful alternative for the interpolation method taking into account the simplicity of construction, shape preserving property and smoothing properties. One issue addressed in the paper is to compare these two different approaches with respect to their stability to a change in the initial data and with respect to the value of Lebesgue constants. Two types of local parabolic splines are considered and in both cases, the Lebesgue constant is smaller than the corresponding constant for the interpolating parabolic splines.
reviewed by: Nicoleta Breaz
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 6474036
zbMATH Keywords: Lebesgues constants
zbMATH Keywords: local parabolic splines
zbMATH Keywords: arbitrary knots
zbMATH Keywords: stability
zbMATH Keywords: polynomial splines
zbMATH Keywords: interpolation
zbMATH Keywords: shape preserving
zbMATH Keywords: smoothing
MaRDI profile type: Publication
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full work available at URL: s008154381505017x
OpenAlex ID: W2205869353
description: scientific article; zbMATH DE number 6474036