References
Nikol'skii SM (1950) Concerning estimation of approximate quadrature formulas. (in Russian) Usp Mat Nauk 5:165–177
Busarova TN (1972) Quadratures with smallest residual estimate for a class of periodic functions. (in Russian) In: Studies in contemporary problems of summability and approximation of functions and their applications, Dnepropetrovsk, pp 16–19
Lušpai NE (1969) Best quadrature formulas on classes of differentiable periodic functions. (in Russian) Mat Zametki 6:475–481. English translation (1969) in Math Notes 6:740–744
Motornyi VP (1973) On the best quadrature formula of the formΣ m k =1 p k f(x k ) for some classes of periodic differentiable functions. (in Russian) Dokl Akad Nauk SSSR 211:1060–1062
Žensykbaev AA (1976) On the best quadrature formula on the classW r Lp. (in Russian) Dokl Akad Nauk SSSR 227:277–279. English translation (1976) in Sov Math Dokl 17:377–380
Nikol'skii SM (1974) Quadrature formulae, 2nd aug. ed. Nauka, Moscow
Oskolkov KI (1979) On optimality of quadrature formulae with equidistant nodes on classes of periodic functions. Sov Math Dokl 20/6
Akhiezer N (1967) Vorlesungen über Approximations Theorie, 2 verb. Aufl. (German translation) Akademie Verlag, Berlin. (in Russian) Lectures on approximation theory
Zygmund A (1959) Trigonometric series, vol. 1, 2nd ed. Cambridge University Press
Author information
Authors and Affiliations
Additional information
Communicated by L. S. Pontryagin
Rights and permissions
About this article
Cite this article
Oskolkov, K.I. On optimal quadrature formulae on certain classes of periodic functions. Appl Math Optim 8, 245–263 (1982). https://doi.org/10.1007/BF01447761
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01447761