Застосування dt-модуля гладкості для оцінки рівномірного наближення функцій
Abstract
Application of DT-module of smoothness for uniform approximation of functions
O. Dyuzhenkova
To assess the function approximation by algebraic polynomials in approximation theory using modules of continuity (smoothness) functions or their derivatives.
The purpose of research - linking DT-module r-ies smoothness of the original features f and the usual smoothness module k-ies order r-s derivative of periodic function f.
The paper used methods uniform approximation of functions, including polynomial interpolation functions Lagrange.
We consider the DT - module of smoothness, introduced by Ditzian and Totik, for continuous on the [-1;1] functions. We investigate the connection between the DT- module of smoothness of the r-s derivative of the function f and classical module of smoothness of the r-s derivative of the periodic function=f(const). In particular, we get the lower estimate for the -module of smoothness for odd r.
References
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Dyuzhenkova, O. Yu. (1995). Zamechaniye o module gladkosty Z. Dytzyana y V. Totyka [Note on the smoothness module Z. Design and Totik]. Ukr. mat. Zhurnal, 47 (12), 1627–1638.
Fuksman, L. (1965). Strukturnaya kharakterystyka funktsyy, u kotorykh [Structural characteristic of functions for which ]. Uspekhy mat. Nauk, 20 (4), 187–190.
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Ditzian, Z., Totik, V. (1987). Moduli of smoothness. Springer-Verlag, New York/Berlin, 300.
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