Seminar on Numerical Analysis

Applications of AAA Rational Approximation

by Prof. Lloyd N. Trefethen (Mathematical Institute, University of Oxford)

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.