Reduction of the Gibbs phenomenon for smooth functions with jumps by the \(\varepsilon \)-algorithm
For smoothing the Gibbs phenomenon, \textit{C. Brezinski} [Numer. Algorithms 36, 309--324 (2004; Zbl 1071.42003)] proposed a procedure based on Padé approximation of the analytic function \(G_n(f)(z)\), \(z=e^{it}\), \(-\pi \leq t \leq \pi\), the real part of which is the truncated Fourier series of the unknown function \(f\). The aim of the paper is to provide error estimates for some model functions \(f\), possibly peturbed by a sufficiently smooth function.
scientific article; zbMATH DE number 5309299