Fast Algorithms for Fourier extension based on boundary interval data Article Swipe
Zhiying Zhao
,
Yajing Wang
,
A. G. Yagola
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2409.04265
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2409.04265
This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary interval data, which is subsequently combined with original function samples to form an extended periodic representation. We develop a parameter optimization framework that preserves superalgebraic convergence while requiring only a few boundary node deployment, resulting in computational complexity marginally exceeding that of standard FFT implementations. Furthermore, we present an improved version of the algorithm tailored for functions exhibiting boundary oscillations. This variant employs grid refinement near the boundaries, which reduces the resolution constant to approximately one-fourth of that in conventional approaches. Comprehensive numerical experiments confirm the efficiency and accuracy of the proposed methods and establish practical guidelines for parameter selection.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2409.04265
- https://arxiv.org/pdf/2409.04265
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4403751257
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W4403751257Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2409.04265Digital Object Identifier
- Title
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Fast Algorithms for Fourier extension based on boundary interval dataWork title
- Type
-
preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
-
2024-09-06Full publication date if available
- Authors
-
Zhiying Zhao, Yajing Wang, A. G. YagolaList of authors in order
- Landing page
-
https://arxiv.org/abs/2409.04265Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2409.04265Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2409.04265Direct OA link when available
- Concepts
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Extension (predicate logic), Algorithm, Interval (graph theory), Boundary (topology), Computer science, Fourier transform, Interval data, Mathematics, Mathematical analysis, Data mining, Combinatorics, Measure (data warehouse), Programming languageTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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