Journal article
Chebfun in three dimensions
- Abstract:
- We present an algorithm for numerical computations involving trivariate functions in a 3D rectangular parallelepiped in the context of Chebfun. Our scheme is based on low-rank representation through multivariate adaptive cross approximation (MACA). The component 1D functions are represented by finite Chebyshev expansions, or trigonometric expansions in the periodic case. Numerical experiments show the power and convenience of Chebfun3 for problems such as function manipulation, differentiation, optimization, and integration, as well as for exploration of fundamental issues of multivariate approximation and low-rank compression.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 1.1MB, Terms of use)
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- Publisher copy:
- 10.1137/16M1083803
Authors
+ European Research Council
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- Grant:
- FP7/20072013/ERC grant agreement no. 291068
- Publisher:
- Society for Industrial and Applied Mathematics
- Journal:
- SIAM Journal on Scientific Computing More from this journal
- Volume:
- 39
- Issue:
- 5
- Pages:
- C341–C363
- Publication date:
- 2017-09-21
- Acceptance date:
- 2017-04-07
- DOI:
- EISSN:
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1095-7197
- ISSN:
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1064-8275
- Keywords:
- Pubs id:
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pubs:689005
- UUID:
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uuid:7a2ec901-8b4b-4fed-bed1-1980571e5bf9
- Local pid:
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pubs:689005
- Source identifiers:
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689005
- Deposit date:
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2017-04-11
Terms of use
- Copyright holder:
- Society for Industrial and Applied Mathematics
- Copyright date:
- 2017
- Notes:
- Copyright © 2017 Society for Industrial and Applied Mathematics. This is the accepted manuscript version of the article. The final version is available online from SIAM at: https://doi.org/10.1137/16M1083803
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