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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