Journal article
Trigonometric interpolation and quadrature in perturbed points
- Abstract:
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The trigonometric interpolants to a periodic function f in equispaced points converge if f is Dini-continuous, and the associated quadrature formula, the trapezoidal rule, converges if f is continuous. What if the points are perturbed? With equispaced grid spacing h, let each point be perturbed by an arbitrary amount ≤ α h, where α ∈ [0,1/2) is a fixed constant. The Kadec 1/4 theorem of sampling theory suggests there may be be trouble for α ≥ 1/4. We show that convergence of both the interpol...
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- Publication status:
- Published
- Peer review status:
- Peer reviewed
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Authors
Funding
+ Seventh Framework Programme
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Grant:
291068
291068
Funding agency for:
Trefethen, L
Bibliographic Details
- Publisher:
- Society for Industrial and Applied Mathematics Publisher's website
- Journal:
- SIAM Journal on Numerical Analysis Journal website
- Volume:
- 55
- Issue:
- 5
- Pages:
- 2113–2122
- Publication date:
- 2017-09-01
- Acceptance date:
- 2017-06-27
- DOI:
Item Description
- Keywords:
- Pubs id:
-
pubs:666274
- UUID:
-
uuid:3d9d4624-3a01-463e-b785-d3e50bc5cc39
- Local pid:
- pubs:666274
- Source identifiers:
-
666274
- Deposit date:
- 2016-12-17
Terms of use
- Copyright holder:
- Society for Industrial and Applied Mathematics
- Copyright date:
- 2017
- Notes:
- © 2017 Society for Industrial and Applied Mathematics
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