Integral Error Representation of Hermite Interpolating Polynomial and Related Inequalities for Quadrature Formulae

We consider integral error representation related to the Hermite inter-polating polynomial and derive some new estimations of the remainder in quadrature formulae of Hermite type, using Hölder's inequality and some inequalities for the Čebyšev functional. As a special case, generalizations for...

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Published inMathematical modelling and analysis Vol. 21; no. 6; pp. 836 - 851
Main Authors Aras-Gazic, Gorana, Pečaric, Josip, Vukelic, Ana
Format Journal Article
LanguageEnglish
Published Taylor & Francis 01.11.2016
Vilnius Gediminas Technical University
Subjects
Errors
Formulas (Mathematics)
Green function
Hermite interpolating polynomial
Hermite polynomials
Holder’s inequality
Hölder's inequality
Inequalities
Inequalities (Mathematics)
Integrals
Mathematical models
Mathematical research
orthogonal polynomials
Polynomials
quadrature formulae
Quadratures
Representations
Čebyšev functional
Hermite interpolating polynomial
Čebyšev functional
Holder’s inequality
quadrature formulae
Green function
orthogonal polynomials
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Abstract We consider integral error representation related to the Hermite inter-polating polynomial and derive some new estimations of the remainder in quadrature formulae of Hermite type, using Hölder's inequality and some inequalities for the Čebyšev functional. As a special case, generalizations for the zeros of orthogonal polynomials are considered.
AbstractList We consider integral error representation related to the Hermite interpolating polynomial and derive some new estimations of the remainder in quadrature formulae of Hermite type, using Holder’s inequality and some inequalities for the Čebyšev functional. As a special case, generalizations for the zeros of orthogonal polynomials are considered.
We consider integral error representation related to the Hermite inter-polating polynomial and derive some new estimations of the remainder in quadrature formulae of Hermite type, using Hölder's inequality and some inequalities for the Čebyšev functional. As a special case, generalizations for the zeros of orthogonal polynomials are considered.
We consider integral error representation related to the Hermite inter-polating polynomial and derive some new estimations of the remainder in quadrature formulae of Hermite type, using Holder's inequality and some inequalities for the Cebysev functional. As a special case, generalizations for the zeros of orthogonal polynomials are considered.
We consider integral error representation related to the Hermite interpolating polynomial and derive some new estimations of the remainder in quadrature formulae of Hermite type, using Holder's inequality and some inequalities for the Cebysev functional. As a special case, generalizations for the zeros of orthogonal polynomials are considered.Keywords: Hermite interpolating polynomial, Green function, quadrature formulae, Holder's inequality, Cebysev functional, orthogonal polynomials.AMS Subject Classification: 26D15; 26D07; 26A51.
Audience Academic
Author Pečarić, Josip
Aras-Gazić, Gorana
Vukelić, Ana
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10.7153/jmi-03-39
10.1007/978-94-011-2026-5
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10.1016/j.mcm.2006.05.009
10.5486/PMD.2002.2706
10.1017/S144618110000835X
10.1016/j.aml.2006.02.013
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Issue 6
Keywords Hermite interpolating polynomial
Čebyšev functional
Holder’s inequality
quadrature formulae
Green function
orthogonal polynomials
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Snippet We consider integral error representation related to the Hermite inter-polating polynomial and derive some new estimations of the remainder in quadrature...
We consider integral error representation related to the Hermite interpolating polynomial and derive some new estimations of the remainder in quadrature...
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SubjectTerms Errors
Formulas (Mathematics)
Green function
Hermite interpolating polynomial
Hermite polynomials
Holder’s inequality
Hölder's inequality
Inequalities
Inequalities (Mathematics)
Integrals
Mathematical models
Mathematical research
orthogonal polynomials
Polynomials
quadrature formulae
Quadratures
Representations
Čebyšev functional
Title Integral Error Representation of Hermite Interpolating Polynomial and Related Inequalities for Quadrature Formulae
URI https://www.tandfonline.com/doi/abs/10.3846/13926292.2016.1247755
https://journals.vilniustech.lt/index.php/MMA/article/view/867
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