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

^*المؤلف المقابل لهذا العمل

نتاج البحث: المساهمة في مجلة › Article › مراجعة النظراء

2 اقتباسات (Scopus)

ملخص

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).

اللغة الأصلية	English
رقم المقال	1992
دورية	SpringerPlus
مستوى الصوت	5
رقم الإصدار	1
المعرِّفات الرقمية للأشياء	https://doi.org/10.1186/s40064-016-3667-2
حالة النشر	Published - ديسمبر 1 2016
منشور خارجيًا	نعم

ASJC Scopus subject areas

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10.1186/s40064-016-3667-2

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title = "Convergence and norm estimates of Hermite interpolation at zeros of Chevyshev polynomials",

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).",

keywords = "Chevyshev polynomials, Hermite interpolation operator, Norm estimates",

author = "Kamel Al-Khaled and Marwan Alquran",

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year = "2016",

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doi = "10.1186/s40064-016-3667-2",

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T1 - Convergence and norm estimates of Hermite interpolation at zeros of Chevyshev polynomials

AU - Al-Khaled, Kamel

AU - Alquran, Marwan

PY - 2016/12/1

Y1 - 2016/12/1

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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UR - http://www.scopus.com/inward/citedby.url?scp=84996528890&partnerID=8YFLogxK

U2 - 10.1186/s40064-016-3667-2

DO - 10.1186/s40064-016-3667-2

M3 - Article

C2 - 27933248

AN - SCOPUS:84996528890

SN - 2193-1801

VL - 5

JO - SpringerPlus

JF - SpringerPlus

IS - 1

M1 - 1992

ER -

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

ملخص

ASJC Scopus subject areas

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