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Generalizations of classical quadrature formulas and related inequalities (CROSBI ID 561611)

Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija

Kovač, Sanja ; Pečarić, Josip Generalizations of classical quadrature formulas and related inequalities // AIHT 2009 booklet. Luleå, 2009. str. 16-16

Podaci o odgovornosti

Kovač, Sanja ; Pečarić, Josip

engleski

Generalizations of classical quadrature formulas and related inequalities

The main idea of this thak is to develop a general method for deriving generalizations of classical quadrature formulae using the concept of harmonic sequences of polynomials and w−harmonic sequences of functions. These generalizations involve the values of higher ordered derivatives in the ? inner? nodes, beside the values of the functions in nodes of integration. At first we introduce a general integral identity with harmonic sequences ofpolynomials, which represents the general m −point quadrature formula. In addition, the weighted version of this identity is obtained. For these identities the error estimates are given, and sharp and the best possible constants are established. Then we investigate the special cases of m−point quadrature formulae, for m = 1, 2, 3, 4, so the generalizations of the well-known Newton- Cotes and Gauss-type quadrature formulae are obtained. Also, related inequalities and some new error estimates for these formulae are obtained.

quadrature formula; w-harmonic sequences of functions; harmonic polynomials; error estimates

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Podaci o prilogu

16-16.

2009.

objavljeno

Podaci o matičnoj publikaciji

AIHT 2009 booklet

Luleå:

Podaci o skupu

Analysis, Inequalities and Homogenization Theory (AIHT)- Midnightsun conference in honour of Professor Lars-Erik Persson on the occasion of his 65th birthday

pozvano predavanje

08.06.2009-11.06.2009

Luleå, Švedska

Povezanost rada

Matematika