Generalizations of classical quadrature formulas and related inequalities (CROSBI ID 561611)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
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