Seminar on Numerical Analysis

Applications of AAA Rational Approximation

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

Aula Volterra (Scuola Normale Superiore)

Aula Volterra

Scuola Normale Superiore

Piazza dei Cavalieri, 7 - 56126 Pisa
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.