2021/09/02 by Shilin Li, Yuanyuan Liu, Li, Shi-Lin +5
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #General Mathematics (math.GM) #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.2109.03610
openalex publication_date 2021/09/02 · openalex created_date 2021/09/13 · openalex updated_date 2026/07/28
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.