A united approach to accelerating trigonometric expansions
The problem of the approximation of smooth functions on a compact interval by algebraic polynomials in the maximum norm is studied. The Fourier series of such functions has slow convergence due to the fact that the periodic extension has jumps at the interval endpoints. The acceleration of convergence attains with the help of some well-known methods under various symmetry conditions on the functions. The authors present a unified derivation of these accelerating methods by using only the Euler representation of a smooth function. There are given explicit integral remainder representations in terms of the Bernoulli functions for all types of acceleration methods. Simultaneous error estimates for these methods are obtained.
scientific article; zbMATH DE number 826954
scientific article