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

• Published in: Mathematical modelling and analysis Vol. 21; no. 6; pp. 836 - 851
• Main Authors: Aras-Gazic, Gorana, Pečaric, Josip, Vukelic, Ana
• Format: Journal Article
• Language: English
• 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

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...