Integral refinable operators exact on polynomials
type: Item
instance of: scholarly article
title: Integral refinable operators exact on polynomials
zbMATH Open document ID: 1154.41009
author: B. E. Eshmatov
published in: Journal of Computational and Applied Mathematics
publication date: 2008-10-22T00:00:00Z
review text: \textit{L. Gori, F. Pitolli, E. Santi} [Numer. Algorithms 28, No. 1-4, 199--213 (2001; Zbl 0993.65157)] studied refinable integral operators of Bernstein-Durrmeyer type. Those operators reproduce only the constant functions. Here the authors construct generalized refinable integral operators that reproduced polynomials of degree \(2m\) with \(0\leq 2m\leq n-2,\) having assumed that the basis functions, utilized for constructing the operators, have order of polynomial reproducibility \(n-2.\) The \(L^p\) norm of these operators is estimated, error bounds for approximation of functions and their derivatives in suitable classes are given. Numerical results and comparisons with other quasi-interpolatory operators having the same order of polynomial reproducibility are presented.
Mathematics Subject Classification ID: 41A35
zbMATH DE Number: 5355704
zbMATH Keywords: refinable functions
zbMATH Keywords: B-bases
zbMATH Keywords: integral operators
reviewed by: Alexei Lukashov
MaRDI profile type: Publication
full work available at URL: j.cam.2007.10.046
OpenAlex ID: W1983337840
cites work: Q4369106
cites work: Positive refinable operators
cites work: Q4406455
cites work: Refinable functions and positive operators
cites work: Q4416693
cites work: Convergence properties of certain refinable quasi-interpolatory operators
cites work: Q5479528
cites work: Q4022922
cites work: Q4316947
cites work: Q3432524
cites work: Error bounds for spline and L-spline interpolation
DOI: 10.1016/J.CAM.2007.10.046
Recommended article: Q3371341
Recommended article: Integro-differential polynomials and operators
Recommended article: On polynomially Riesz operators
Recommended article: Q4291320
Recommended article: Integral-type generalizations of operators obtained from certain multivariate polynomials
Recommended article: Q3651812
Recommended article: Q4015191
Recommended article: Q3196869
Recommended article: On polynomial approximation of operators
Recommended article: Q5149096
description: scientific article; zbMATH DE number 5355704