Exponential node clustering at singularities for rational approximation, quadrature, and PDEs
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 ...Expand abstract
- Publication status:
- Peer review status:
- Peer reviewed
(Accepted manuscript, 1.4MB)
- Publisher copy:
- Copyright holder:
- Trefethen et al.
- Copyright date:
- Rights statement:
- © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021.
- 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
If you are the owner of this record, you can report an update to it here: Report update to this record