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

Kamel Al-Khaled; Marwan Alquran

doi:10.1186/s40064-016-3667-2

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

Kamel Al-Khaled^*, Marwan Alquran

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper, we investigate the simultaneous approximation of a function f(x) and its derivative f^′(x) by Hermite interpolation operator H₂ _n ₊ ₁(f; x) 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).

Original language	English
Article number	1992
Journal	SpringerPlus
Volume	5
Issue number	1
DOIs	https://doi.org/10.1186/s40064-016-3667-2
Publication status	Published - Dec 1 2016

Keywords

Chevyshev polynomials
Hermite interpolation operator
Norm estimates

ASJC Scopus subject areas

General

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10.1186/s40064-016-3667-2

Cite this

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abstract = "In this paper, we investigate the simultaneous approximation of a function f(x) and its derivative f′(x) by Hermite interpolation operator H2 n + 1(f; x) 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{\textquoteright}s results (Pottinger in Z Agnew Math Mech 56: T310–T311, 1976).",

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AU - Alquran, Marwan

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N2 - In this paper, we investigate the simultaneous approximation of a function f(x) and its derivative f′(x) by Hermite interpolation operator H2 n + 1(f; x) 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).

AB - In this paper, we investigate the simultaneous approximation of a function f(x) and its derivative f′(x) by Hermite interpolation operator H2 n + 1(f; x) 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).

KW - Chevyshev polynomials

KW - Hermite interpolation operator

KW - Norm estimates

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JO - SpringerPlus

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

Abstract

Keywords

ASJC Scopus subject areas

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