On the best quadrature formula of the form $$$\sum\limits_{k=1}^n p_k f(x_k)$$$ on the class $$$W^2 H^{\omega}$$$

V.P. Motornyi; A.O. Kushch

doi:10.15421/248710

On the best quadrature formula of the form $\sum\limits_{k=1}^n p_k f(x_k)$ on the class $W^2 H^{\omega}$

V.P. Motornyi (Dnipropetrovsk State University)
A.O. Kushch (Dnipropetrovsk State University)

Abstract

We show that the formula of rectangles is the best on the class

$W^2 H^{\omega}$ among all quadrature formulas of the form

$\sum\limits_{k=1}^n p_k f(x_k)$ .

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References

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Malozemov V.N. "On accuracy of quadrature formula of rectangles for periodic functions", Matem. zametki, 1967; 2(4): pp. 357-360. (in Russian) doi:10.1007/BF01093645

Malozemov V.N. "Estimate of accuracy of one quadrature formula for periodic functions", Vestn. Leningrad. un-ta, 1967; 1. (in Russian)

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