Applications of AAA Rational Approximation

Abstract:

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