Eliminating oscillation in partial sum approximation of periodic function
General Mathematics
2021-10-06 v2
Abstract
If we cannot obtain all terms of a series, or if we cannot sum up a series, we have to turn to the partial sum approximation which approximate a function by the first several terms of the series. However, the partial sum approximation often does not work well for periodic functions. In the partial sum approximation of a periodic function, there exists an incorrect oscillation which cannot be eliminated by keeping more terms, especially at the domain endpoints. A famous example is the Gibbs phenomenon in the Fourier expansion. In the paper, we suggest an approach for eliminating such oscillations in the partial sum approximation of periodic functions.
Cite
@article{arxiv.2109.03610,
title = {Eliminating oscillation in partial sum approximation of periodic function},
author = {Shi-Lin Li and Yuan-Yuan Liu and Wen-Du Li and Wu-Sheng Dai},
journal= {arXiv preprint arXiv:2109.03610},
year = {2021}
}