# Applications of AAA Rational Approximation – Lloyd N. Trefethen (Mathematical Institute, University of Oxford)

#### Venue

Scuola Normale Superiore, Aula Volterra.

#### 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.

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