Journal article
Exponential node clustering at singularities for rational approximation, quadrature, and PDEs
- Abstract:
-
Rational approximations of functions with singularities can converge at a root-exponential rate if the poles are exponentially clustered. We begin by reviewing this effect in minimax, least-squares, and AAA approximations on intervals and complex domains, conformal mapping, and the numerical solution of Laplace, Helmholtz, and biharmonic equations by the “lightning” method. Extensive and wide-ranging numerical experiments are involved. We then present further experiments giving evidence that ...
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- Publication status:
- Published
- Peer review status:
- Peer reviewed
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Authors
Bibliographic Details
- Publisher:
- Springer Publisher's website
- Journal:
- Numerische Mathematik Journal website
- Volume:
- 147
- Issue:
- 1
- Pages:
- 227-254
- Publication date:
- 2021-01-02
- Acceptance date:
- 2020-11-17
- DOI:
- EISSN:
-
0945-3245
- ISSN:
-
0029-599X
Item Description
- Language:
- English
- Keywords:
- Pubs id:
-
1123281
- Local pid:
- pubs:1123281
- Deposit date:
- 2020-11-20
Terms of use
- Copyright holder:
- Trefethen et al.
- Copyright date:
- 2020
- Rights statement:
- © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021.
- Notes:
- This is the accepted manuscript version of the article. The final version is available from Springer at https://doi.org/10.1007/s00211-020-01168-2
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