Eliminating oscillation in partial sum approximation of periodic function Article Swipe
Shilin Li
,
Yuanyuan Liu
,
Wen-Du Li
,
Wu-Sheng Dai
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2109.03610
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2109.03610
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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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2109.03610
- https://arxiv.org/pdf/2109.03610
- OA Status
- green
- References
- 4
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3198859132
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https://openalex.org/W3198859132Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2109.03610Digital Object Identifier
- Title
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Eliminating oscillation in partial sum approximation of periodic functionWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2021Year of publication
- Publication date
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2021-09-02Full publication date if available
- Authors
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Shilin Li, Yuanyuan Liu, Wen-Du Li, Wu-Sheng DaiList of authors in order
- Landing page
-
https://arxiv.org/abs/2109.03610Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2109.03610Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2109.03610Direct OA link when available
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Gibbs phenomenon, Series (stratigraphy), Fourier series, Mathematics, Periodic function, Oscillation (cell signaling), Function (biology), Mathematical analysis, Applied mathematics, Genetics, Evolutionary biology, Paleontology, BiologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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4Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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