Eliminating oscillation in partial sum approximation of periodic function

Shi-Lin Li; Yuan-Yuan Liu; Wen-Du Li; Wu-Sheng Dai

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arXiv · 2109.03610

Eliminating oscillation in partial sum approximation of periodic function

Shi-Lin Li·Yuan-Yuan Liu·Wen-Du Li·Wu-Sheng Dai

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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.

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BibTeX RIS

Shi-Lin Li, Yuan-Yuan Liu, Wen-Du Li, Wu-Sheng Dai. 2021-09-02. Eliminating oscillation in partial sum approximation of periodic function. https://arxiv.org/abs/2109.03610

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