Moment-preserving spline approximation on finite intervals
type: Item
instance of: scholarly article
title: Moment-preserving spline approximation on finite intervals
zbMATH Open document ID: 0644.41005
DOI: 10.1007/BF01408572
author: M. Frontini
author: Walter Gautschi
author: Gradimir V. Milovanović
published in: Numerische Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133168
review text: The authors discuss the problem of approximating a function f on the interval [0,1] by a spline function of degree m, with n (variable) knots, matching as many of the initial moments of f as possible. Additional constraints on the derivates of the approximation at one endpoint of [0,1] may also be imposed. They show that, if the approximations exist, they can be represented in terms of generalized Gauss-Lobatto and Gauss- Radau quadrature rules relative to appropriate moment functionals or measures (depending on f). Pointwise convergence as \(n\to \infty\), for fixed \(m>0\), is shown for functions f that are completely monotonic on [0,1], among others. Numerical examples conclude the paper.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 4050195
zbMATH Keywords: constraints
zbMATH Keywords: Gauss-Lobatto
zbMATH Keywords: Gauss-Radau quadrature rules
zbMATH Keywords: Numerical examples
MaRDI profile type: Publication
Wikidata QID: Q115058821
cites work: Q3938409
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OpenAlex ID: W2053212745
description: scientific article; zbMATH DE number 4050195