- 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 showing that in all o...
Expand abstract - Publication status:
- Published
- Peer review status:
- Peer reviewed
- Publisher:
- Springer Publisher's website
- Journal:
- Numerische Mathematik Journal website
- Publication date:
- 2021-01-02
- Acceptance date:
- 2020-11-19
- DOI:
- EISSN:
-
0945-3245
- ISSN:
-
0029-599X
- Pubs id:
-
1123281
- Local pid:
- pubs:1123281
- Language:
- English
- Keywords:
- Copyright date:
- 2020
Journal article
Exponential node clustering at singularities for rational approximation, quadrature, and PDEs
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