Journal article
Error localization of best $L_{1}$ polynomial approximants
- Abstract:
- An important observation in compressed sensing is that the $\ell_0$ minimizer of an underdetermined linear system is equal to the $\ell_1$ minimizer when there exists a sparse solution vector and a certain restricted isometry property holds. Here, we develop a continuous analogue of this observation and show that the best $L_0$ and $L_1$ polynomial approximants of a polynomial that is corrupted on a set of small measure are nearly equal. We demonstrate an error localization property of best $L_1$ polynomial approximants and use our observations to develop an improved algorithm for computing best $L_1$ polynomial approximants to continuous functions.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, 1014.5KB, Terms of use)
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- Publisher copy:
- 10.1137/19M1242860
Authors
- Publisher:
- Society for Industrial and Applied Mathematics
- Journal:
- SIAM Journal on Numerical Analysis More from this journal
- Volume:
- 59
- Issue:
- 1
- Pages:
- 314–333
- Publication date:
- 2021-02-01
- Acceptance date:
- 2020-11-05
- DOI:
- EISSN:
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1095-7170
- ISSN:
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0036-1429
- Language:
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English
- Keywords:
- Pubs id:
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1146198
- Local pid:
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pubs:1146198
- Deposit date:
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2020-11-20
Terms of use
- Copyright holder:
- Society for Industrial and Applied Mathematics
- Copyright date:
- 2021
- Rights statement:
- © 2021 Society for Industrial and Applied Mathematics.
- Notes:
- This is the publisher's version of the article. The final version is available online from the Society for Industrial and Applied Mathematics at: https://doi.org/10.1137/19M1242860
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