Abstract:
In this article we obtain characteristic properties of piecewise-polynomial functions (“spline” functions) that have least deviation from zero in the metric of C. This has allowed us to obtain quadrature formulas with least estimate of the remainder on a number of classes of differentiable functions.
Citation:
N. P. Korneichuk, N. E. Lushpai, “Best quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation”, Math. USSR-Izv., 3:6 (1969), 1335–1355
\Bibitem{KorLus69}
\by N.~P.~Korneichuk, N.~E.~Lushpai
\paper Best quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation
\jour Math. USSR-Izv.
\yr 1969
\vol 3
\issue 6
\pages 1335--1355
\mathnet{http://mi.mathnet.ru/eng/im2244}
\crossref{https://doi.org/10.1070/IM1969v003n06ABEH000875}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=278519}
\zmath{https://zbmath.org/?q=an:0198.08902|0209.09802}
Linking options:
https://www.mathnet.ru/eng/im2244
https://doi.org/10.1070/IM1969v003n06ABEH000875
https://www.mathnet.ru/eng/im/v33/i6/p1416
This publication is cited in the following 11 articles:
M. Sh. Shabozov, K. Tukhliev, “Best quadrature formulas for evaluating line integrals of the first kind for certain classes of functions and curves determined by moduli of continuity”, Vestnik St.Petersb. Univ.Math., 48:4 (2015), 241
S. V. Arkhipov, “The programmed MOCODISS package and its application to design of rod systems on the elastic base”, Autom. Remote Control, 72:7 (2011), 1380–1388
V.F. Babenko, S.V. Borodachov, “On the construction of optimal cubature formulae which use integrals over hyperspheres”, Journal of Complexity, 23:3 (2007), 346
N. P. Korneichuk, “S. M. Nikol'skii and the development of research on approximation theory in the USSR”, Russian Math. Surveys, 40:5 (1985), 83–156
S. M. Nikol'skii, “Aleksandrov and Kolmogorov in Dnepropetrovsk”, Russian Math. Surveys, 38:4 (1983), 41–55
M. A. Chahkiev, “Exponential polynomials of least deviation from zero and optimal quadrature formulas”, Math. USSR-Sb., 48:1 (1984), 273–285
A. A. Zhensykbaev, “Extremality of monosplines of minimal deficiency”, Math. USSR-Izv., 21:3 (1983), 461–482
A. A. Zhensykbaev, “Monosplines of minimal norm and the best quadrature formulae”, Russian Math. Surveys, 36:4 (1981), 121–180
A. A. Zhensykbaev, “Best quadrature formula for some classes of periodic differentiable functions”, Math. USSR-Izv., 11:5 (1977), 1055–1071
V. P. Motornyi, “On the best quadrature formula of the form ∑nk=1pkf(xk) for some classes of differentiable periodic functions”, Math. USSR-Izv., 8:3 (1974), 591–620
T. N. Busarova, “Best quadrature formulas for a class of differentiable periodic functions”, Ukr Math J, 25:3 (1974), 227
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