Naslov
The corrected two-point weighted quadrature formulae

Autori
Kovač, Sanja

Izvornik
Journal of Mathematical Inequalities (1846-579X) 4 (2010), 2; 237-257

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Weight function; corrected quadrature formula; two-point quadrature formula; $w-$harmonic sequences of functions; $L_p$ spaces; corrected Gauss formula; weighted corrected Maclaurin formula; weighted corrected trapezoid formula; weighted corrected midpoint formula; weighted corrected Newton-Cotes two-point formula

Sažetak
We derive a corrected version of the weighted two- point quadrature formula, which provides a better approximation accuracy than the ordinary two-point quadrature formulae. In the corrected two-point formula the integral is approximated both with the values of the integrand in nodes $-x$ and $x$, and the values of its first derivative at the endpoints of the interval $[-1, 1]$. The error estimates under various regularity conditions for such formulae are established. As special cases, the corrected two-point formulae of Gauss type are obtained. Also, corrected version of weighted trapezoid, midpoint, two-point Maclaurin and two- point Newton-Cotes formulae are considered.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA