Seminar on Numerical Analysis
# Applications of AAA Rational Approximation

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Europe/Rome

Aula Volterra (Scuola Normale Superiore)
### Aula Volterra

#### Scuola Normale Superiore

Piazza dei Cavalieri, 7 - 56126 Pisa

Description

For the first time, a method has recently become available for fast computation of near-best rational approximations on arbitrary sets in the real line or complex plane: the AAA algorithm (Nakatsukasa-Sete-T. 2018). We will present the algorithm and then demonstrate a number of applications, including

- detection of singularities,
- model order reduction,
- analytic continuation,
- functions of matrices,
- nonlinear eigenvalue problems,
- interpolation of equispaced data,
- smooth extension of multivariate real functions,
- extrapolation of ODE and PDE solutions into the complex plane,
- solution of Laplace problems,
- conformal mapping,
- Wiener-Hopf factorization.