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## Generalizations of classical quadrature formulas and related inequalities

Kovač, Sanja; Pečarić, Josip
Generalizations of classical quadrature formulas and related inequalities // AIHT 2009 booklet
Lulea, 2009. str. 16-16 (pozvano predavanje, međunarodna recenzija, sažetak, znanstveni)

Naslov
Generalizations of classical quadrature formulas and related inequalities

Autori
Kovač, Sanja ; Pečarić, Josip

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
AIHT 2009 booklet / - Lulea, 2009, 16-16

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

Mjesto i datum
Lulea, Švedska, 8-11.06.2009

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Quadrature formula; w-harmonic sequences of functions; harmonic polynomials; error estimates

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA

Projekt / tema
117-1170889-0888 - Generalne nejednakosti i primjene (Josip Pečarić, )

Ustanove
Tekstilno-tehnološki fakultet, Zagreb,
Geotehnički fakultet, Varaždin