Necessary conditions of optimality of quadrature formulas with weight on some classes of differentiable functions

Ye.Ye. Dunaichuk (Dnipropetrovsk State University)

Abstract


For the quadrature formula (with positive, continuous weight function) that is defined by the values of the function and its derivatives of up to and including $$$(r-1)$$$-th order, we find necessary conditions of optimality on the classes $$$W^r_p$$$, $$$r = 1, 2, \ldots$$$, $$$p = 2$$$, $$$p = \infty$$$.

References


Lebed' G.K. "On quadrature formulas with the smallest estimate of remainder on some classes of functions", Izv. AN SSSR. Ser. Matem., 1970; 3(4): pp. 645-669. (in Russian) doi:10.1070/IM1970v004n03ABEH000925




DOI: https://doi.org/10.15421/248708

  

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Copyright (c) 1987 Ye.Ye. Dunaichuk

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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