On the best interval quadrature formulae for classes of differentiable periodic functions

In this paper we solve the problem about optimal interval quadrature formula for the class W r F of differentiable periodic functions with rearrangement invariant set F of their derivatives of order r. We prove that the formula with equal coefficients and n node intervals having equidistant midpoint...

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Bibliographic Details
Published inJournal of Complexity Vol. 23; no. 4; pp. 890 - 917
Main Authors Babenko, V.F., Skorokhodov, D.S.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.08.2007
Subjects
Monosplines
Quadrature formulae
Rearrangements
Quadrature formulae
Monosplines
Rearrangements
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Summary:In this paper we solve the problem about optimal interval quadrature formula for the class W r F of differentiable periodic functions with rearrangement invariant set F of their derivatives of order r. We prove that the formula with equal coefficients and n node intervals having equidistant midpoints is optimal for considering classes. To this end a sharp inequality for antiderivatives of rearrangements of averaged monosplines is proved.
ISSN:0885-064X
1090-2708
DOI:10.1016/j.jco.2007.03.005