Convergence and norm estimates of Hermite interpolation at zeros of Chevyshev polynomials

In this paper, we investigate the simultaneous approximation of a function f(x) and its derivative [Formula: see text] by Hermite interpolation operator [Formula: see text] based on Chevyshev polynomials. We also establish general theorem on extreme points for Hermite interpolation operator. Some re...

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Detalles Bibliográficos
Autores principales: Al-Khaled, Kamel, Alquran, Marwan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5118382/
https://www.ncbi.nlm.nih.gov/pubmed/27933248
http://dx.doi.org/10.1186/s40064-016-3667-2
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author Al-Khaled, Kamel
Alquran, Marwan
author_facet Al-Khaled, Kamel
Alquran, Marwan
author_sort Al-Khaled, Kamel
collection PubMed
description In this paper, we investigate the simultaneous approximation of a function f(x) and its derivative [Formula: see text] by Hermite interpolation operator [Formula: see text] based on Chevyshev polynomials. We also establish general theorem on extreme points for Hermite interpolation operator. Some results are considered to be an improvement over those obtained in Al-Khaled and Khalil (Numer Funct Anal Optim 21(5–6): 579–588, 2000), while others agrees with Pottinger’s results (Pottinger in Z Agnew Math Mech 56: T310–T311, 1976).
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spelling pubmed-51183822016-12-08 Convergence and norm estimates of Hermite interpolation at zeros of Chevyshev polynomials Al-Khaled, Kamel Alquran, Marwan Springerplus Research In this paper, we investigate the simultaneous approximation of a function f(x) and its derivative [Formula: see text] by Hermite interpolation operator [Formula: see text] based on Chevyshev polynomials. We also establish general theorem on extreme points for Hermite interpolation operator. Some results are considered to be an improvement over those obtained in Al-Khaled and Khalil (Numer Funct Anal Optim 21(5–6): 579–588, 2000), while others agrees with Pottinger’s results (Pottinger in Z Agnew Math Mech 56: T310–T311, 1976). Springer International Publishing 2016-11-21 /pmc/articles/PMC5118382/ /pubmed/27933248 http://dx.doi.org/10.1186/s40064-016-3667-2 Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Al-Khaled, Kamel
Alquran, Marwan
Convergence and norm estimates of Hermite interpolation at zeros of Chevyshev polynomials
title Convergence and norm estimates of Hermite interpolation at zeros of Chevyshev polynomials
title_full Convergence and norm estimates of Hermite interpolation at zeros of Chevyshev polynomials
title_fullStr Convergence and norm estimates of Hermite interpolation at zeros of Chevyshev polynomials
title_full_unstemmed Convergence and norm estimates of Hermite interpolation at zeros of Chevyshev polynomials
title_short Convergence and norm estimates of Hermite interpolation at zeros of Chevyshev polynomials
title_sort convergence and norm estimates of hermite interpolation at zeros of chevyshev polynomials
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5118382/
https://www.ncbi.nlm.nih.gov/pubmed/27933248
http://dx.doi.org/10.1186/s40064-016-3667-2
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